US5694342A — Method for detecting signals in non-Gaussian back…

Claim 1

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Gaussian input data from non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 2

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Gaussian input data from non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 3

Dependent Claim 42 words

The method of claim 1 wherein step (3) further includes estimating first parameters of an exponential mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

Claim 4

Dependent Claim 43 words

The method of claim 2 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

Claim 5

Dependent Claim 42 words

The method of claim 1 wherein step (3) further includes estimating first parameters of an Gaussian mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

Claim 6

Dependent Claim 43 words

The method of claim 4 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

Claim 7

Dependent Claim 59 words

The method of claim 1 step (5) further includes: adjusting estimates of a selected set of the first parameters that are a predetermined level below the estimated background noise level of the input data; creating uncertainty sets for the first parameters; and selecting a set of the first parameters from the uncertainty intervals to define a probability density function.

Claim 8

Dependent Claim 28 words

The method of claim 6 wherein step (5) further includes selecting second parameters from said uncertainty set to mimimize the maximum value of a false alarm probability function.

Claim 9

Dependent Claim 15 words

The method of claim 7 wherein step (5) includes scaling values of said second parameters.

Claim 10

Dependent Claim 21 words

The method of claim 6 wherein step (5) further includes selecting third parameters from said uncertainty set using an order statistic.

Claim 11

Dependent Claim 15 words

The method of claim 9 wherein step (5) includes scaling values of said third parameters.

Claim 12

Dependent Claim 39 words

The method of claim 2 further includes fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said exponential mixture function, where n is a positive integer.

Claim 13

Dependent Claim 34 words

The method of claim 2 further including fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said Gaussian mixture density function.

Claim 14

Dependent Claim 22 words

The method of claim 12 further including the step of combining the noise parameters from step (5) with the high intensity term.

Claim 15

Dependent Claim 65 words

The method of claim 2 wherein step (6) further includes the steps of: determining the average intensity of said input data; and determining an estimated signal strength value of the input data as the maximum of zero and the difference between the average intensity of said input data and the expected noise intensity calculated from the noise parameters of the input data from step (5).

Claim 16

Dependent Claim 26 words

The method of claim 2 wherein step (6) further includes using a maximum likelihood estimator to determine an estimated signal strength value of the input data.

Claim 17

Dependent Claim 16 words

The method of claim 1 wherein step (7) further includes determining a modified optimal detection statistic.

Claim 18

Dependent Claim 216 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to identify Gaussian input data and non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining a standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic Si, where S i =M i /N i , 10) determining a maximum value, S imax of S i , 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≦τ.sub.α.

Claim 19

Dependent Claim 216 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to identify Gaussian input data and non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining a standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic Si, where S i =M i /N i , 10) determining a maximum value, S imax of S i , 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≦τ.sub.α.

Claim 20

Dependent Claim 44 words

The program storage device of claim 17 wherein step (3) further includes estimating first parameters of an exponential mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

Claim 21

Dependent Claim 45 words

The program storage device of claim 17 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

Claim 22

Dependent Claim 44 words

The program storage device of claim 17 wherein step (3) further includes estimating first parameters of an Gaussian mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

Claim 23

Dependent Claim 45 words

The program storage device of claim 20 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

Claim 24

Dependent Claim 61 words

The program storage device of claim 17 step (5) further includes: adjusting estimates of a selected set of the first parameters that are a predetermined level below the estimated background noise level of the input data; creating uncertainty sets for the first parameters; and selecting a set of the first parameters from the uncertainty intervals to define a probability density function.

Claim 25

Dependent Claim 30 words

The program storage device of claim 22 wherein step (5) further includes selecting second parameters from said uncertainty set to mimimize the maximum value of a false alarm probability function.

Claim 26

Dependent Claim 17 words

The program storage device of claim 23 wherein step (5) includes scaling values of said second parameters.

Claim 27

Dependent Claim 23 words

The program storage device of claim 22 wherein step (5) further includes selecting third parameters from said uncertainty set using an order statistic.

Claim 28

Dependent Claim 17 words

The program storage device of claim 25 wherein step (5) includes scaling values of said third parameters.

Claim 29

Dependent Claim 41 words

The program storage device of claim 18 further includes fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said exponential mixture function, where n is a positive integer.

Claim 30

Dependent Claim 36 words

The program storage device of claim 18 further including fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said Gaussian mixture density function.

Claim 31

Dependent Claim 24 words

The program storage device of claim 28 further including the step of combining the noise parameters from step (5) with the high intensity term.

Claim 32

Dependent Claim 67 words

The program storage device of claim 18 wherein step (6) further includes the steps of: determining the average intensity of said input data; and determining an estimated signal strength value of the input data as the maximum of zero and the difference between the average intensity of said input data and the expected noise intensity calculated from the noise parameters of the input data from step (5).

Claim 33

Dependent Claim 28 words

The program storage device of claim 18 wherein step (6) further includes using a maximum likelihood estimator to determine an estimated signal strength value of the input data.

Claim 34

Dependent Claim 18 words

The program storage device of claim 17 wherein step (7) further includes determining a modified optimal detection statistic.

Claim 35

Dependent Claim 22 words

The program storage device of claim 32 wherein step (8) further includes determining the mean and standard deviation of said detection statistic.

Claim 36

Dependent Claim 30 words

The program storage device of claim 32 wherein step (8) further includes determining a threshold from the mean and standard deviation of said detection statistic and a predetermined false alarm.

Claim 37

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Rayleigh input data from non-Rayleigh input data; 2) estimating the intensity level of the Rayleigh input data; 3) determining the probability distributions of the non-Rayleigh input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 38

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Rayleigh input data from non-Rayleigh input data; 2) estimating the intensity level of the Rayleigh input data; 3) determining the probability distributions of the non-Rayleigh input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 39

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition exponential input data from non-exponential input data; 2) estimating the intensity level of the exponential input data; 3) determining the probability distributions of the non-exponential input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 40

Independent Claim 206 words

A method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition exponential input data from non-exponential input data; 2) estimating the intensity level of the exponential input data; 3) determining the probability distributions of the non-exponential input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 41

Dependent Claim 219 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to partition Rayleigh input data from non-Rayleigh input data; 2) estimating the intensity level of the Rayleigh input data; 3) determining the probability distributions of the non-Rayleigh input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 42

Dependent Claim 219 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to partition Rayleigh input data from non-Rayleigh input data; 2) estimating the intensity level of the Rayleigh input data; 3) determining the probability distributions of the non-Rayleigh input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 43

Dependent Claim 219 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to partition exponential input data from non-exponential input data; 2) estimating the intensity level of the exponential input data; 3) determining the probability distributions of the non-exponential input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Claim 44

Dependent Claim 219 words

A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising: 1) filtering input data to partition exponential input data from non-exponential input data; 2) estimating the intensity level of the exponential input data; 3) determining the probability distributions of the non-exponential input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N i of the detection statistic, M i ; 9) determining a normalized detection statistic S i , where S i =M i /N i , 10) determining a maximum value, S imax of S i ; 11) determining a mean value S Mean and a standard deviation S Std dev of all S i excluding S imax ; 12) determining a threshold τ.sub.α of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where α is a predetermined false alarm probability; and 13) generating an output signal if S i -S Mean !/S Std dev ≧τ.sub.α.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	2000-12-01	2001-06-02	2001-12-02	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	2004-12-01	2005-06-02	2005-12-02	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	2008-12-01	2009-06-02	2009-12-02	$7700.00	Window Closed / Lapsed

Method for detecting signals in non-Gaussian background clutter

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