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US 6,958,951 B2Granted
Adaptive Kalman Filter process for controlling an ensemble clock
AssigneeThe Johns Hopkins University
InventorDennis J. Duven
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Abstract
In an ensemble oscillator system including multiple free-running oscillators, a voltage controlled oscillator having a frequency responsive to a control signal, and a differencer unit that measures time differences between the oscillators, an adaptive Kalman Filter Processor (AKFP) generates the control signal responsive to the time differences. The AKFP uses oscillator noise models to model noise/errors of the ensemble system oscillators, including random noise parameters, and adaptively estimates the errors and the random noise parameters to derive the control signal.
Claims10
In a system configured to generate:
- a reference time signal;
- m free-running frequencies having corresponding fractional frequency errors y1 . . . m and fractional frequency rate errors d1 . . . m, from which are derived m corresponding free-running times having corresponding time errors x1 . . . m;
- a controlled frequency responsive to a responsive to a control signal Uk, the controlled frequency having a fractional frequency error y0, from which is derived a controlled time having time error x0;
- and
- a difference measurement vector representing time differences between the controlled time and
- each of the free-running times, and
- the reference time;
- wherein:
- the fractional frequency errors are represented as functions of weighting parameters alpha1 . . . m and beta0, 1 . . . m;
- and
- the time errors are represented as functions of the fractional frequency errors, a method of adaptively estimating the alpha1 . . . m and beta0, 1 . . . m parameters, comprising:
- (a) initializing
- a system state vector including a priori estimates of the time, fractional frequency, and fractional frequency rate errors,
- a corresponding covariance matrix of estimation errors,
- the alpha1 . . . m and beta0, 1 . . . m parameters, and
- a corresponding set of partial derivative matrices;
- (b) performing a Kalman Measurement Update based on the time difference measurement vector, to produce
- current time a posteriori state vector estimates of the time errors x0, 1 . . . m, the fractional frequency errors y0, 1 . . . m, and the fractional frequency rate errors d1 . . . m, and
- a current time a posteriori covariance matrix;
- (c) updating the partial derivative matrices relative to the current time difference measurement vector;
- and
- (d) updating, based on the updated partial derivative matrices, the alpha1 . . . m and beta0, 1 . . . m parameters.
19 more elements
In a system configured to generate:
- a reference frequency;
- multiple free-running frequencies;
- a controlled frequency having a frequency responsive to a control signal;
- and
- difference measurements indicative of time and frequency-based errors associated with each free-running frequency and the controlled frequency relative to the reference frequency,
- a method of generating the control signal responsive to the difference measurements, comprising:
- (a) using dynamic relationships associated with each free-running frequency and the controlled frequency to represent time and frequency-based errors corresponding to variances and covariances having magnitudes and rates of growth determined by random process weighting (RPW) parameters, whereby the RPW parameters are indicative of relative noise levels associated with the corresponding frequencies;
- (b) the following adaptive Kalman filtering steps that, when executed in a steady-state condition, use the dynamic relationships and the difference measurements to produce their respective results:
- (i) adaptively estimating the RPW parameters associated with each free-running frequency;
- (ii) deriving, based on the RPW parameters from step (i), weighted time and frequency-based error estimates associated with each free-running frequency, wherein the weighted errors estimates are weighted to favor less noisy free-running frequencies over more noisy free-running frequencies;
- and
- (iii) estimating, based on the weighted error estimates from step (ii), time and frequency-based errors associated with the controlled frequency;
- and
- (c) generating the control signal based on the error estimates from step (b)(iii) such that the control signal causes the time and frequency-based errors associated with the controlled frequency to be driven toward, and maintained over time near, zero with respect to the reference frequency.
11 more elements
In a system configured to generate
- a reference frequency,
- multiple free-running frequencies,
- a controlled frequency having a frequency responsive to a control signal, and
- difference measurements indicative of time and frequency-based errors associated with each free-running frequency and the controlled frequency relative to the reference frequency,
- an Adaptive Kalman Filter Processor for generating the control signal responsive to the difference measurements, comprising:
- (a) dynamic relationships associated with each of the free-running frequencies and the controlled frequency to represent the time and frequency-based errors corresponding to variances and covariances having magnitudes and rates of growth determined by random process weighting (RPW) parameters, whereby the RPW parameters are indicative of relative noise levels associated with the corresponding frequencies;
- and
- (b) an adaptive Kalman Filter including the following modules that, when operated in a steady-state condition, use the dynamic relationships and the difference measurements to produce their respective results:
- (i) a first module configured to adaptively estimate the RPW parameters associated with each free-running frequency;
- (ii) a second module configured to derive, based on the RPW parameters from the first module, weighted time and frequency-based error estimates associated with each free-running frequency, wherein the weighted errors estimates are weighted to favor less noisy free-running frequencies over more noisy free-running frequencies;
- and
- (iii) a third module configured to estimate, based on the weighted error estimates from the second module, time and frequency-based errors associated with the controlled frequency;
- and
- (c) a state space controller configured to generate the control signal based on the error estimates from the third module such that the control signal causes the time and frequency-based errors associated with the controlled frequency to be driven toward, and maintained over time near, zero with respect to the reference frequency.
11 more elements
Dependencies are inferred from the claim text.