US5649065A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Optimal filtering by neural networks with range extenders and/or reducers
Assignee: Maryland Tech Corp
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Filing: 1993-08-09
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Granted: 1997-07-15
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Expires: 2013-08-09
Abstract
Abstract A method and apparatus is provided for processing a measurement process to estimate a signal process, even if the signal and/or measurement processes have large and/or expanding ranges. The method synthesizes training data comprising realizations of the signal and measurement processes into a primary filter for estimating the signal process and, if required, an ancillary filter for providing the primary filter's estimation error statistics. The primary and ancillary filters each comprise an artificial recurrent neural network (RNN) and at least one range extender or reducer. Their implementation results in the filtering apparatus. Many types of range extender and reducer are disclosed, which have different degrees of effectiveness and computational cost. For a neural filter under design, range extenders and/or reducers are selected from those types jointly with the architecture of the RNN in consideration of the filtering accuracy, the RNN size and the computational cost of each selected range extender and reducer so as to maximize the cost effectiveness of the neural filter. The aforementioned synthesis is performed through training RNNs together with range extenders and/or reducers.
Inventors
- 👤 James Ting-Ho Lo
- 👤 Lei Yu
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-02 16:30
CPC Classifications
H; H03; H03H; H03H17/00; H03H17/02; H03H17/0248; H03H17/0255; G; G06; G06N; G06N3/00; G06N3/02; G06N3/04; G06N3/044; G06N3/08; G06N3/084; G06N3/09; H03H21/00; H03H21/0012; H03H17/0223; H03H2222/00; H03H2222/04
Claims Analysis
Total Claims: 114
Claim 1
Independent Claim
151 words
A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating training data comprising realizations of said signal process and corresponding realizations of said measurement process; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said training data into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter; and (8) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.
Claim 2
Independent Claim
151 words
A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating training data comprising realizations of said signal process and corresponding realizations of said measurement process; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said training data into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter; and (8) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.
Claim 3
Dependent Claim
74 words
The method of claim 1 wherein said steps of selecting a recurrent neural network paradigm, selecting an estimation error criterion, and selecting at least one range transformer are accomplished such that a candidate primary filter with said at least one range transformer, whose recurrent neural network is of said recurrent neural network paradigm, exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 4
Dependent Claim
43 words
The method of claim 2 wherein said step of selecting at least one range transformer is accomplished by selecting at least one range transformer from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, and range reducers by differencing.
Claim 5
Dependent Claim
132 words
The method of claim 3 wherein said step of implementing said primary filter is accomplished by implementing said recurrent neural network by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, copying the weights and initial dynamic state into a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus, and by implementing said at least one range transformer by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus.
Claim 6
Dependent Claim
52 words
The method of claim 3 wherein said step of synthesizing said training data into a primary filter is performed, at least in part, directly on a piece of hardware used to implement at least part of said primary filter, thereby completing said step of implementing said primary filter at the same time.
Claim 7
Dependent Claim
65 words
The method of claim 3 wherein said step of implementing said primary filter includes implementing at least part of said primary filter on a piece of hardware, and wherein said step of synthesizing said training data into a primary filter is accomplished through including said piece of hardware in the synthesizing process so as to overcome the anomalies and imperfections of said piece of hardware.
Claim 8
Dependent Claim
40 words
The method of claim 1 wherein said step of selecting at least one range transformer is accomplished by selecting at least one range transformer from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 9
Dependent Claim
131 words
The method of claim 1 wherein said step of implementing said primary filter is accomplished by implementing said recurrent neural network by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, copying the weights and initial dynamic state into a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus, and by implementing said at least one range transformer by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural networkchip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus.
Claim 10
Dependent Claim
48 words
The method of claim 1 wherein said step of synthesizing said training data is, at least in part, performed directly on a piece of hardware used to implement at least part of said primary filter, thereby completing said step of implementing said primary filter at the same time.
Claim 11
Dependent Claim
65 words
The method of claim 1 wherein said step of implementing said primary filter includes implementing at least part of said primary filter on a piece of hardware, and wherein said step of synthesizing said training data into a primary filter is accomplished through including said piece of hardware in the synthesizing process so as to overcome the anomalies and imperfections of said piece of hardware.
Claim 12
Independent Claim
203 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating ancillary training data comprising realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said ancillary training data into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 13
Independent Claim
203 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating ancillary training data comprising realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said ancillary training data into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 14
Independent Claim
219 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating ancillary training data comprising realizations of said measurement process, corresponding realizations of said primary filter's output process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said ancillary training data into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 15
Independent Claim
219 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating ancillary training data comprising realizations of said measurement process, corresponding realizations of said primary filter's output process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said ancillary training data into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 16
Dependent Claim
53 words
A primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.
Claim 17
Dependent Claim
53 words
A primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.
Claim 18
Dependent Claim
55 words
The primary filter of claim 13 wherein said neural system has at least one adjustable weight that is determined by synthesizing, with respect to a training criterion constructed on the basis of said estimation error criterion, training data, comprising realizations of said signal process and corresponding realizations of said measurement process, into said neural system.
Claim 19
Dependent Claim
134 words
The primary filter of claim 14 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range extender transforming outputs from at least one output node of said recurrent neural network, which output node is included in said plurality of neurons.
Claim 20
Dependent Claim
151 words
The primary filter of claim 14 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range reducer transforming at least one component of said primary filter's input vector at a time and having the resultant sent to at least one input node of said recurrent neural network, said input node being included in said plurality of neurons.
Claim 21
Dependent Claim
51 words
The primary filter of claim 14 wherein said recurrent neural network paradigm includes such a candidate recurrent neural network that a candidate neural system employing said candidate recurrent neural network exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 22
Dependent Claim
52 words
The primary filter of claim 14 wherein said one range transformer is of such a type that a candidate neural system employing at least one candidate range transformer of said type exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 23
Dependent Claim
29 words
The primary filter of claim 18 wherein said one range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 24
Dependent Claim
53 words
The primary filter of claim 19 wherein said one range transformer is selected from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, range extenders by linear prediction, range extenders by feedforward linear estimation, range reducers by model-aided prediction, range reducers by differencing and range reducers by linear prediction.
Claim 25
Dependent Claim
33 words
The primary filter of claim 20 wherein the said one range transformer is selected from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, and range reducers by differencing.
Claim 26
Dependent Claim
139 words
The primary filter of claim 21 wherein the implementation of said recurrent neural network is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a specially designed electronic circuit, a programmed neural network chip, a neural network chip into which the weights and initial dynamic state have been copied after completion of said synthesis, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus, and wherein the implementation of said at least one range transformer is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a programmed neural network chip, a specially designed electronic circuit, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus.
Claim 27
Dependent Claim
139 words
The primary filter of claim 14 wherein the implementation of said recurrent neural network is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a specially designed electronic circuit, a programmed neural network chip, a neural network chip into which the weights and initial dynamic state have been copied after completion of said synthesis, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus, and wherein the implementation of said at least one range transformer is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a programmed neural network chip, a specially designed electronic circuit, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus.
Claim 28
Dependent Claim
73 words
An ancillary filter for evaluating, with respect to an ancillary estimation error criterion, a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said ancillary filter being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 29
Dependent Claim
73 words
An ancillary filter for evaluating, with respect to an ancillary estimation error criterion, a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said ancillary filter being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 30
Dependent Claim
54 words
The ancillary filter of claim 24 wherein said ancillary neural system has at least one adjustable weight that is determined by synthesizing ancillary training data, comprising realizations of an ancillary signal process, selected on the basis of said estimation error statistic process, and corresponding realizations of said measurement process, into said ancillary neural system.
Claim 31
Dependent Claim
56 words
The ancillary filter of claim 25 wherein said ancillary recurrent neural network paradigm includes such a candidate ancillary recurrent neural network that a candidate ancillary neural system employing said candidate ancillary recurrent neural network exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 32
Dependent Claim
56 words
The ancillary filter of claim 25 wherein said one ancillary range transformer is of such a type that a candidate ancillary neural system employing at least one candidate range ancillary transformer of said type exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 33
Dependent Claim
30 words
The ancillary filter of claim 27 wherein said one ancillary range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 34
Independent Claim
210 words
A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said augmented training data into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter with augmented input terminals; and (8) receiving one measurement vector of said measurement process and one vector of said p-dimensional vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.
Claim 35
Independent Claim
210 words
A method for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said augmented training data into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter with augmented input terminals; and (8) receiving one measurement vector of said measurement process and one vector of said p-dimensional vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.
Claim 36
Dependent Claim
80 words
The method of claim 29 wherein said steps of selecting a recurrent neural network paradigm, selecting an estimation error criterion, and selecting at least one range transformer arc accomplished such that a candidate primary filter with augmented input terminals, that contains said at least one range transformer and whose recurrent neural network is of said recurrent neural network paradigm, exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 37
Dependent Claim
40 words
The method of claim 29 wherein said step of selecting at least one range transformer is accomplished by selecting at least one range transformer from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 38
Dependent Claim
131 words
The method of claim 27 wherein said step of implementing said primary filter with augmented input terminals is accomplished by implementing said recurrent neural network by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, copying the weights and initial dynamic state into a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus, and implementing said at least one range transformer by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus.
Claim 39
Dependent Claim
53 words
The method of claim 29 wherein said step of synthesizing said augmented training data is, at least in part, performed directly on a piece of hardware used to implement at least part of said primary filter, thereby completing said step of implementing said primary filter with augmented input terminals at the same time.
Claim 40
Dependent Claim
78 words
The method of claim 29 wherein said step of implementing said primary filter with augmented input terminals includes implementing at least part of said primary filter with augmented input terminals on a piece of hardware, and wherein said step of synthesizing said augmented training data into a primary filter with augmented input terminals is accomplished through including said piece of hardware in the synthesizing process so as to overcome the anomalies and imperfections of said piece of hardware.
Claim 41
Independent Claim
262 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one measurement vector of said measurement process and one vector of said p-dimensional vector-valued time function at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 42
Independent Claim
262 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one measurement vector of said measurement process and one vector of said p-dimensional vector-valued time function at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 43
Independent Claim
283 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one vector of said p-dimensional vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 44
Independent Claim
283 words
A method for evaluating a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one vector of said p-dimensional vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 45
Dependent Claim
82 words
A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.
Claim 46
Dependent Claim
82 words
A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.
Claim 47
Dependent Claim
74 words
The primary filter with augmented input terminals of claim 37 wherein said neural system has at least one adjustable weight that is determined by synthesizing, with respect to a training criterion constructed on the basis of said estimation error criterion, augmented training data, comprising a set of exemplary time functions, and realizations of said signal process and realizations of said measurement process, that correspond to each said exemplary time function, into said neural system.
Claim 48
Dependent Claim
138 words
The primary filter with augmented input terminals of claim 38 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range extender transforming outputs from at least one output node of said recurrent neural network, said output node being included in said plurality of neurons.
Claim 49
Dependent Claim
161 words
The primary filter with augmented input terminals of claim 38 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range reducer transforming at least one component of the input vector of said primary filter with augmented input terminals at a time and having the resultant sent to at least one input node of said recurrent neural network, said input node being included in said plurality of neurons.
Claim 50
Dependent Claim
55 words
The primary filter with augmented input terminals of claim 38 wherein said recurrent neural network paradigm includes such a candidate recurrent neural network that a candidate neural system employing said candidate recurrent neural network exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 51
Dependent Claim
56 words
The primary filter with augmented input terminals of claim 38 wherein said one range transformer is of such a type that a candidate neural system employing at least one candidate range transformer of said type exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 52
Dependent Claim
33 words
The primary filter with augmented input terminals of claim 42 wherein said one range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 53
Dependent Claim
57 words
The primary filter with augmented input terminals of claim 43 wherein said one range transformer is selected from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, range extenders by linear prediction, range extenders by feedforward linear estimation, range reducers by model-aided prediction, range reducers by differencing and range reducers by linear prediction.
Claim 54
Dependent Claim
143 words
The primary filter with augmented input terminals of claim 38 wherein the implementation of said recurrent neural network is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a specially designed electronic circuit, a programmed neural network chip, a neural network chip into which the weights and initial dynamic state have been copied after completion of said synthesis, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus, and wherein the implementation of said at least one range transformer is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a programmed neural network chip, a specially designed electronic circuit, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus.
Claim 55
Dependent Claim
107 words
An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 56
Dependent Claim
107 words
An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a q-dimensional vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 57
Dependent Claim
65 words
The ancillary filter with augmented input terminals of claim 46 wherein said ancillary neural system has at least one adjustable weight that is determined by synthesizing ancillary training data, comprising a set of exemplary time functions, corresponding realizations of au ancillary signal process, selected on the basis of said estimation error statistic process, and corresponding realizations of said measurement process, into said ancillary neural system.
Claim 58
Dependent Claim
60 words
The ancillary filter with augmented input terminals of claim 47 wherein said ancillary recurrent neural network paradigm includes such a candidate ancillary recurrent neural network that a candidate ancillary neural system employing said candidate ancillary recurrent neural network exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 59
Dependent Claim
60 words
The ancillary filter with augmented input terminals of claim 47 wherein said one ancillary range transformer is of such a type that a candidate ancillary neural system employing at least one candidate ancillary range transformer of said type exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 60
Dependent Claim
34 words
The ancillary filter with augmented input terminals of claim 49 wherein said one ancillary range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 61
Independent Claim
169 words
A method for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating training data comprising realizations of said signal process and said measurement process; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said training data, while taking into account said interactive environment, into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter; and (8) receiving one measurement vector of said measurement process and at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.
Claim 62
Independent Claim
169 words
A method for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating training data comprising realizations of said signal process and said measurement process; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said training data, while taking into account said interactive environment, into a primary filter, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter; and (8) receiving one measurement vector of said measurement process and at a time at at least one input terminal of the implementation of said primary filter and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter.
Claim 63
Dependent Claim
74 words
The method of claim 51 wherein said steps of selecting a recurrent neural network paradigm, selecting an estimation error criterion, and selecting at least one range transformer are accomplished such that a candidate primary filter with said at least one range transformer, whose recurrent neural network is of said recurrent neural network paradigm, exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 64
Dependent Claim
40 words
The method of claim 51 wherein said step of selecting at least one range transformer is accomplished by selecting at least one range transformer from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 65
Dependent Claim
132 words
The method of claim 51 wherein said step of implementing said primary filter is accomplished by implementing said recurrent neural network by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, copying the weights and initial dynamic state into a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus, and by implementing said at least one range transformer by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus.
Claim 66
Dependent Claim
52 words
The method of claim 51 wherein said step of synthesizing said training data into a primary filter is, at least in part, performed directly on a piece of hardware used to implement at least part of said primary filter, thereby completing said step of implementing said primary filter at the same time.
Claim 67
Dependent Claim
65 words
The method of claim 51 wherein said step of implementing said primary filter includes implementing at least part of said primary filter on a piece of hardware, and wherein said step of synthesizing said training data into a primary filter is accomplished through including said piece of hardware in the synthesizing process so as to overcome the anomalies and imperfections of said piece of hardware.
Claim 68
Independent Claim
217 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating training data comprising realizations of said measurement process and said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said training data, while taking into account said interactive environment, into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 69
Independent Claim
217 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating training data comprising realizations of said measurement process and said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said training data, while taking into account said interactive environment, into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 70
Independent Claim
230 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating training data comprising realizations of said measurement process, said primary filter's output process, and said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said training data, while taking into account said interactive environment, into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 71
Independent Claim
230 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating training data comprising realizations of said measurement process, said primary filter's output process, and said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said training data, while taking into account said interactive environment, into an ancillary filter, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter; and (9) receiving one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter, and producing an estimate of one ancillary signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter.
Claim 72
Dependent Claim
66 words
A primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process with respect to a selected estimation error criterion in an interactive environment composed of an environment transition system and an environment observation system, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.
Claim 73
Dependent Claim
66 words
A primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process with respect to a selected estimation error criterion in an interactive environment composed of an environment transition system and an environment observation system, said primary filter being an implementation of a neural system comprising a recurrent neural network, of a selected recurrent neural network paradigm, and at least one range transformer.
Claim 74
Dependent Claim
63 words
The primary filter of claim 59 wherein said neural system has at least one adjustable weight that is determined by synthesizing, with respect to a training criterion constructed on the basis of said estimation error criterion, training data, comprising realizations of said signal process and corresponding realizations of said measurement process, into said recurrent neural system, while taking into account said interactive environment.
Claim 75
Dependent Claim
134 words
The primary filter of claim 60 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range extender transforming outputs from at least one output node of said recurrent neural network, said output node being included in said plurality of neurons.
Claim 76
Dependent Claim
151 words
The primary filter of claim 60 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range reducer transforming at least one component of said primary filter's input vector at a time and having the resultant sent to at least one input node of said recurrent neural network, said input node being included in said plurality of neurons.
Claim 77
Dependent Claim
51 words
The primary filter of claim 60 wherein said recurrent neural network paradigm includes such a candidate recurrent neural network that a candidate neural system employing said candidate recurrent neural network exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 78
Dependent Claim
52 words
The primary filter of claim 60 wherein said one range transformer is of such a type that a candidate neural system employing at least one candidate range transformer of said type exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 79
Dependent Claim
29 words
The primary filter of claim 64 wherein said one range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 80
Dependent Claim
53 words
The primary filter of claim 65 wherein said one range transformer is selected from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, range extenders by linear prediction, range extenders by feedforward linear estimation, range reducers by model-aided prediction, range reducers by differencing and range reducers by linear prediction.
Claim 81
Dependent Claim
139 words
The primary filter of claim 60 wherein the implementation of said recurrent neural network is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a specially designed electronic circuit, a programmed neural network chip, a neural network chip into which the weights and initial dynamic state have been copied after completion of said synthesis, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus, and wherein the implementation of said at least one range transformer is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a programmed neural network chip, a specially designed electronic circuit, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus.
Claim 82
Dependent Claim
85 words
An ancillary filter for evaluating, with respect to an ancillary estimation error criterion, a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said ancillary filter being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 83
Dependent Claim
85 words
An ancillary filter for evaluating, with respect to an ancillary estimation error criterion, a vector-valued estimation error statistic process, that is required for a primary filter for processing a vector-valued measurement process to estimate a vector-valued signal process in an interactive environment composed of an environment transition system and an environment observation system, said ancillary filter being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 84
Dependent Claim
61 words
The ancillary filter of claim 68 wherein said ancillary neural system has at least one adjustable weight that is determined by synthesizing ancillary training data, comprising realizations of an ancillary signal process, selected on the basis of said estimation error statistic process, and corresponding realizations of said measurement process, into said ancillary neural system, while taking into account said interactive environment.
Claim 85
Dependent Claim
56 words
The ancillary filter of claim 69 wherein said ancillary recurrent neural network paradigm includes such a candidate ancillary recurrent neural network that a candidate ancillary neural system employing said candidate ancillary recurrent neural network exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 86
Dependent Claim
56 words
The ancillary filter of claim 69 wherein said one ancillary range transformer is of such a type that a candidate ancillary neural system employing at least one candidate ancillary range transformer of said type exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 87
Dependent Claim
30 words
The ancillary filter of claim 71 wherein said one ancillary range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 88
Independent Claim
228 words
A method for processing a vector-valued measurement process to estimate a vector-valued signal process, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said augmented training data, while taking into account said interactive environment, into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter with augmented input terminals; and (8) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.
Claim 89
Independent Claim
228 words
A method for processing a vector-valued measurement process to estimate a vector-valued signal process, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting a recurrent neural network paradigm; (2) selecting an estimation error criterion; (3) generating augmented training data comprising a set of exemplary time functions and realizations of said signal and measurement processes that correspond to each said exemplary time function; (4) constructing a training criterion; (5) selecting at least one range transformer; (6) synthesizing said augmented training data, while taking into account said interactive environment, into a primary filter with augmented input terminals, which comprises a recurrent neural network of said recurrent neural network paradigm and said at least one range transformer; (7) implementing said primary filter with augmented input terminals; and (8) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said primary filter with augmented input terminals, and producing an estimate of one signal vector of said signal process at a time at at least one output terminal of the implementation of said primary filter with augmented input terminals.
Claim 90
Dependent Claim
80 words
The method of claim 73 wherein said steps of selecting a recurrent neural network paradigm, selecting an estimation error criterion, and selecting at least one range transformer are accomplished such that a candidate primary filter with augmented input terminals, that contains said at least one range transformer and whose recurrent neural network is of said recurrent neural network paradigm, exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 91
Dependent Claim
78 words
The method of claim 74 wherein said step of implementing said primary filter with augmented input terminals includes implementing at least part of said primary filter with augmented input terminals on a piece of hardware, and wherein said step of synthesizing said augmented training data into a primary filter with augmented input terminals is accomplished through including said piece of hardware in the synthesizing process so as to overcome the anomalies and imperfections of said piece of hardware.
Claim 92
Dependent Claim
40 words
The method of claim 73 wherein said step of selecting at least one range transformer is accomplished by selecting at least one range transformer from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 93
Dependent Claim
131 words
The method of claim 73 wherein said step of implementing said primary filter with augmented input terminals is accomplished by implementing said recurrent neural network by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, copying the weights and initial dynamic state into a neural network chip, making an electronic circuit, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus, and implementing said at least one range transformer by a method selected from the group consisting of programming a computer, programming a microprocessor, programming an analog device, programming a digital device, programming a neural network chip, making a mechanical device, constructing an optical apparatus, and constructing an electro-optical apparatus.
Claim 94
Dependent Claim
53 words
The method of claim 73 wherein said step of synthesizing said augmented training data is, at least in part, performed directly on a piece of hardware used to implement at least part of said primary filter, thereby completing said step of implementing said primary filter with augmented input terminals at the same time.
Claim 95
Independent Claim
279 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 96
Independent Claim
279 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one measurement vector of said measurement process and one vector of said vector-valued time function at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 97
Independent Claim
300 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one vector of said vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 98
Independent Claim
300 words
A method for evaluating a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said method comprising the steps of: (1) selecting an ancillary signal process on the basis of said estimation error statistic process; (2) selecting an ancillary estimation error criterion on the basis of said estimation error statistic process; (3) selecting an ancillary recurrent neural network paradigm; (4) generating augmented ancillary training data comprising a set of exemplary time functions, corresponding realizations of said measurement process, corresponding realizations of the output process of said primary filter with augmented input terminals, and corresponding realizations of said ancillary signal process; (5) constructing an ancillary training criterion; (6) selecting at least one ancillary range transformer; (7) synthesizing said augmented ancillary training data, while taking into account said interactive environment, into an ancillary filter with augmented input terminals, which comprises an ancillary recurrent neural network of said ancillary recurrent neural network paradigm and said at least one ancillary range transformer; (8) implementing said ancillary filter with augmented input terminals; and (9) receiving one vector of said vector-valued time function, one measurement vector of said measurement process and one output vector of said primary filter at a time at at least one input terminal of the implementation of said ancillary filter with augmented input terminals and producing an estimate of one signal vector of said ancillary signal process at a time at at least one output terminal of said implementation of said ancillary filter with augmented input terminals.
Claim 99
Dependent Claim
82 words
A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.
Claim 100
Dependent Claim
82 words
A primary filter with augmented input terminals for processing an m-dimensional vector-valued measurement process to estimate an n-dimensional vector-valued signal process with respect to a selected estimation error criterion, which signal and measurement processes are time-variant with said signal and measurement processes' time-variant property described by a p-dimensional vector-valued time function, said primary filter with augmented input terminals being an implementation of a neural system comprising a recurrent neural network, of a selected neural network paradigm, and at least one range transformer.
Claim 101
Dependent Claim
81 words
The primary filter with augmented input terminals of claim 81 wherein said neural system has at least one adjustable weight that is determined by synthesizing, with respect to a training criterion constructed on the basis of said estimation error criterion, augmented training data, comprising a set of exemplary time functions, and realizations of said signal process and realizations of said measurement process, that correspond to each said exemplary time function, into said neural system, while taking into account said interactive environment.
Claim 102
Dependent Claim
138 words
The primary filter with augmented input terminals of claim 82 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range extender transforming outputs from at least one output node of said recurrent neural network, said output node being included in said plurality of neurons.
Claim 103
Dependent Claim
161 words
The primary filter with augmented input terminals of claim 82 wherein said recurrent neural network comprises (1) a plurality of neurons, each neuron being means for receiving said neuron's input values, processing said input values and producing an output value, that is called the activation level of said neuron; and (2) a plurality of delay connections, each delay connection being means for multiplying a first neuron's activation level by said delay connection's weight, holding the resulting product for at least one unit of time, and then sending said product to a second neuron as one of said second neuron's input values; and wherein said at least one range transformer is at least one range reducer transforming at least one component of the input vector of said primary filter with augmented input terminals at a time and having the resultant sent to at least one input node of said recurrent neural network, said input node being included in said plurality of neurons.
Claim 104
Dependent Claim
55 words
The primary filter with augmented input terminals of claim 82 wherein said recurrent neural network paradigm includes such a candidate recurrent neural network that a candidate neural system employing said candidate recurrent neural network exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 105
Dependent Claim
56 words
The primary filter with augmented input terminals of claim 82 wherein said one range transformer is of such a type that a candidate neural system employing at least one candidate range transformer of said type exists that approximates an optimal filter in performance with respect to said estimation error criterion to any predetermined level of accuracy.
Claim 106
Dependent Claim
33 words
The primary filter with augmented input terminals of claim 86 wherein said one range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
Claim 107
Dependent Claim
57 words
The primary filter with augmented input terminals of claim 87 wherein said one range transformer is selected from the group consisting of range extenders by Kalman filtering, range extenders by accumulation, range extenders by linear prediction, range extenders by feedforward linear estimation, range reducers by model-aided prediction, range reducers by differencing and range reducers by linear prediction.
Claim 108
Dependent Claim
143 words
The primary filter with augmented input terminals of claim 82 wherein the implementation of said recurrent neural network is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a specially designed electronic circuit, a programmed neural network chip, a neural network chip into which the weights and initial dynamic state have been copied after completion of said synthesis, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus, and wherein the implementation of said at least one range transformer is selected from the group consisting of a programmed computer, a programmed microprocessor, a programmed analog device, a programmed digital device, a programmed neural network chip, a specially designed electronic circuit, a specially made mechanical device, a specially constructed optical apparatus, and a specially constructed electro-optical apparatus.
Claim 109
Dependent Claim
118 words
An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 110
Dependent Claim
118 words
An ancillary filter with augmented input terminals for evaluating, with respect to an ancillary estimation error criterion, a vector-valued estimation error statistic process, that is required for a primary filter with augmented input terminals for processing a vector-valued measurement process to estimate a vector-valued signal process, said signal and measurement processes being time-variant with said signal and measurement processes' time-variant property described by a vector-valued time function, in an interactive environment composed of an environment transition system and an environment observation system, said ancillary filter with augmented input terminals being an implementation of an ancillary neural system comprising an ancillary recurrent neural network, of a selected ancillary recurrent neural network paradigm, and at least one ancillary range transformer.
Claim 111
Dependent Claim
72 words
The ancillary filter with augmented input terminals of claim 90 wherein said ancillary neural system has at least one adjusahle weight that is determined by synthesizing ancillary training data, comprising a set of exemplary time functions, corresponding realizations of an ancillary signal process, selected on the basis of said estimation error statistic process, and corresponding realizations of said measurement process, into said ancillary neural system, while taking into account said interactive environment.
Claim 112
Dependent Claim
60 words
The ancillary filter with augmented input terminals of claim 91 wherein said ancillary recurrent neural network paradigm includes such a candidate ancillary recurrent neural network that a candidate ancillary neural system employing said candidate ancillary recurrent neural network exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 113
Dependent Claim
60 words
The ancillary filter with augmented input terminals of claim 91 wherein said one ancillary range transformer is of such a type that a candidate ancillary neural system employing at least one candidate ancillary range transformer of said type exists that approximates an optimal filter in performance with respect to said ancillary estimation error criterion to any predetermined level of accuracy.
Claim 114
Dependent Claim
34 words
The ancillary filter with augmented input terminals of claim 93 wherein said one ancillary range transformer is selected from the group consisting of range extenders by estimate addition and range reducers by estimate subtraction.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2000-07-14 | 2001-01-13 | 2001-07-15 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2004-07-14 | 2005-01-13 | 2005-07-15 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2008-07-14 | 2009-01-13 | 2009-07-15 | $7700.00 | Window Closed / Lapsed |