Time scale computation system including complete and weighted ensemble definition

Claim 3

A system according to claim 1, wherein: said ensemble of oscillators comprises N oscillators and said one of said oscillators is designated reference oscillator j, and each of said other N-1 oscillators provides an estimate of time and frequency states of the reference oscillator j with respect to said ensemble of oscillators.

Claim 4

The system according to claim 2, wherein: said first average that provides said time state of said reference oscillator j with respect to said ensemble of oscillators is defined by: ##EQU29## where u je (t+δ) is the time state of the reference oscillator j with respect to the ensemble of oscillators, a i (t) are the weights given to each oscillator of said ensemble of oscillators for time u ie (t+δ|t) are the forecasts of the time of each oscillator of said ensemble of oscillators with respect to the ensemble of oscillators at time (t+δ) based on the true state through time t, and u ji (t+δ) are times of said reference oscillator j with respect to each of said remaining oscillators of said ensemble of oscillators, and said second average for said frequency related state of said reference oscillator j with respect to said ensemble of oscillators is defined by: ##EQU30## where y je (t+δ) is the frequency related state of the reference clock j with respect to the ensemble of oscillators, b i (t) are the weights given to each oscillator of said ensemble of oscillators for frequency, y ie (t+δ|t) are forecasts of the frequency of each oscillator of said ensemble of oscillators with respect to the ensemble of oscillators at time (t+δ) based on the true states through time t, and y ji (t+δ) are frequencies of said reference oscillator j with respect to each of said remaining oscillators of said ensemble of oscillators.

Claim 5

A system according to claim 3, wherein: said second means comprises processing means and memory means, the ensemble time definition being embodied by Kalman filters stored in the memory means, the processing means receiving the at least one of a time and frequency difference from said first means and accessing the Kalman filters from the memory means and processing the frequency differences with the Kalman filters to provide the ensemble time.

Claim 6

A system according to claim 3, wherein: the weights a i (1) and b i (t) are chosen such that: ##EQU31##

Claim 9

A system according to claim 6, wherein: said ensemble of oscillators comprises N oscillators and said one of said oscillators is designated as a reference oscillator j, and each of said other N-1 oscillators provides an estimate of time, frequency and frequency aging states of the reference oscillator j with respect to said ensemble of oscillators.

Claim 10

A system according to claim 7, wherein: said first average, said second average, and said third average for said reference oscillator j with respect to the ensemble of oscillators are respectively defined by: ##EQU32## where u je (t+δ) is the time state of the reference oscillator j with respect to the ensemble of oscillators, a i (t) are the weights given to each oscillator of said ensemble of oscillators for time u ie (t+δ|t) are the forecasts of the time of each oscillator of said ensemble of oscillators with respect to the ensemble of oscillators at time (t+δ) based on observations through time t, and u ji (t+δ) are the times of said reference oscillator j with respect to each of said remaining oscillators of said ensemble of oscillators, ##EQU33## where y je (t+δ) is the frequency state of the reference oscillator j with respect to the ensemble of oscillators, b i (t) are the weights given to each oscillator of said ensemble of oscillators for frequency, y ie (t+δ|t) are the forecasts of the frequency of each oscillator of said ensemble of oscillators with respect to the ensemble of oscillators at time (t+δ) based on observations through time t, and y ji (t+δ) are the frequencies of said reference oscillator j with respect to each of said remaining oscillators of said ensemble of oscillators, and ##EQU34## where w je (t+δ) is the frequency aging state of the reference oscillator j with respect to the ensemble of oscillators, c i (t) are the weights given to each oscillator of said ensemble of oscillators for frequency aging, w ie (t+δ|t) are the forecasts of the frequency aging of each oscillator of said ensemble of oscillators with respect to the ensemble of oscillators at time (t+δ) based on observations through time t, and w ji (t+δ) are the frequency agings of said reference oscillator j with respect to each of said remaining oscillators of said ensemble of oscillators, where: ##EQU35##

Claim 11

A system according to claim 8, wherein: said second means comprises processing means and memory means, the ensemble time definition being embodied by Kalman filters stored in the memory means, said processing means receiving the frequency differences from said first means and accessing the Kalman filters from the memory means and processing the frequency differences with the Kalman filters to provide the ensemble time.

Claim 12

A system according to claim 9, further comprising: input means for inputting control data to said processing means for changing parameters of the Kalman filters, including the weights for each oscillator of said ensemble of oscillators relating to the time, frequency and the frequency aging of the ensemble time definition.

Claim 13

A system as claim in claim 1, wherein: said frequency related state term includes at least one of the following: a frequency state term and a frequency aging state term.

Claim 16

A system, as claimed in claim 12, wherein: said average includes a first average for a time dimension of said clock state term, wherein said first average for said time dimension is defined by the following: ##EQU36## where u je (t+δ) is the time state of the reference clock of said ensemble of clocks with respect to said ensemble of clocks, a i (t) are the weights given to each clock of said ensemble of clocks for time, u ie (t+δ|t) are the forecasts of the time of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and u ji (t+δ) are times of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term includes u ie (t+δ|t) and u ji (t+δ).

Claim 17

A system, as claimed in claim 13, wherein: said weights a i (t) are chosen such that: ##EQU37##

Claim 18

A system, as claimed in claim 12, wherein: said average includes a first average for a frequency dimension of said clock state term, wherein said first average for said frequency dimension is defined by the following: ##EQU38## where y je (t+δ) is the frequency state of said reference clock of said ensemble of clocks with respect to said ensemble of clocks, b i (t) are the weights given to each clock of said ensemble of clocks for frequency, y ie (t+δ|t) are the forecasts of the frequency of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and y ji (t+δ) are the frequencies of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term includes y ie (t+δ|t) and y ji (t+δ).

Claim 19

A system, as claimed in claim 15, wherein: said weights b i (t) are chose such that: ##EQU39##

Claim 20

A system, as claimed in claim 12, wherein: said average includes a first average for a frequency aging dimension of said clock term, wherein said first average for said frequency aging dimension is defined by the following: ##EQU40## where w je (t+δ) is the frequency aging state of said reference clock of said ensemble of clocks with respect to said ensemble of clocks, c i (t) are the weights given to each clock of said ensemble of clocks for frequency aging, w ie (t+δ|t) are the forecasts of the frequency aging of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and w ji (t+δ) are the frequency agings of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term includes w ie (t+δ|t) and w ji (t+δ).

Claim 21

A system, as claimed in claim 12, wherein: said weights and c i (t) are chosen such that: ##EQU41##

Claim 22

A system, as claimed in claim 12, wherein: said average includes at least two of the following averages: a first average for a time dimension, a second average for a frequency dimension, and a third average for a frequency aging dimension for said clock state term.

Claim 23

A system, as claimed in claim 12, wherein: said average includes at least two of the following averages: a first average for a time dimension, a second average for a frequency dimension, and a third average for a frequency aging dimension for said clock state term, wherein said first average for said time dimension is defined by the following: ##EQU42## where u je (t+δ) is the time state of the reference clock of said ensemble of clocks with respect to said ensemble of clocks, a i (t) are the weights given to each clock of said ensemble of clocks for time, u ie (t+δ|t) are the forecasts of the time of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and u ji (t+δ) are times of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term includes u ie (t+δ|t) and u ji (t+δ), wherein said second average for said frequency dimension is defined by the following: ##EQU43## where y je (t+δ) is the frequency state of said reference clock of said ensemble of clocks with respect to said ensemble of clocks, b i (t) are the weights given to each clock of said ensemble of clocks for frequency, y ie (t+δ|t) are the forecasts of the frequency of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and y ji (t+δ) are the frequencies of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term for said frequency dimension includes y ie (t+δ|t) and y ji (t+δ), wherein said third average for said frequency aging dimension is defined by the following: ##EQU44## where w je (t+δ) is the frequency aging state of said reference clock of said ensemble of clocks with respect to said ensemble of clocks, c i (t) are the weights given to each clock of said ensemble of clocks for frequency aging, w ie (t+δ|t) are the forecasts of the frequency aging of each clock of said ensemble of clocks with respect to said ensemble of clocks at time (t+δ) based on the true states through time t, and w ji (t+δ) are the frequency agings of said reference clock of said ensemble of clocks with respect to each clock of said ensemble of clocks, wherein said clock state term for said frequency aging dimension includes w ie (t+δ|t) and w ji (t+δ).

Claim 24

A system, as claimed in claim 20, wherein: the weights a i (t) and b i (t) and c i (t) of said at least two averages are chosen such that: ##EQU45##

Claim 25

A system, as claimed in claim 12, wherein: said parameter is at least one of a time and a frequency of a clock of said ensemble of clocks.

Claim 26

A system, as claimed in claim 12, wherein: said first means includes means for selecting a clock of said ensemble of clocks as said reference clock.

Claim 27

A system, as claimed in claim 12, wherein: said average is a weighted average.

Claim 28

A system, as claimed in claim 12, wherein: said average is a weighted average and said second means includes means for selecting a weight to be associated with at least one clock of said ensemble of clocks.