Fast frequency estimator
In one aspect, the invention provides a method implemented by an analog hardware circuit for fast frequency estimation. The analog circuit may be implemented a main oscillator circuit block [ 100] , a P matrix circuit block [ 102] , a K matrix circuit block[ 104] , and a sigma integrator circuit block [ 106] . From input signals [ 108] having unknown frequency, amplitude and phase, the analog hardware circuit generates estimates of state variables x i , x 2 , x 3 of a model oscillator, and outputs a sinusoidal estimate [ 110] of the model oscillator signal. The analog hardware circuit generates the estimates by implementing in continuous time an extended Kalman filter that relates a generating frequency 107 of the model oscillator to x 3 by an affine transformation ω=ω 0 +£x 3 , where k is a slope of a frequency error estimate and coo is a best estimate input signal frequency.
1. A method implemented by an analog hardware circuit for fast frequency estimation, the method comprising:
receiving by the analog hardware circuit input signals having unknown frequency, amplitude and phase;
generating by the analog hardware circuit from the input signals estimates of state variables x 1 , x 2 , x 3 of a model oscillator;
outputting by the analog hardware circuit a sinusoidal estimate of the model oscillator signal;
wherein the analog hardware circuit generates the estimates by implementing in continuous time an extended Kalman filter;
wherein the extended Kalman filter relates a generating frequency ω of the model oscillator to x 3 by an affine transformation ω=ω 0 +kx 3 , where k is a slope of a frequency error estimate and ω0 is a best estimate input signal frequency.
2. The method of claim 1 wherein the extended Kalman filter uses a balanced state space representation in continuous time.
3. The method of claim 1 wherein an error variance matrix P of the extended Kalman filter is limited to a cone of positivity.
4. The method of claim 1 wherein the analog hardware circuit comprises a main oscillator circuit block, a P matrix circuit block that produces an error covariance of the state variable estimates, a K matrix circuit block that produces an optimal Kalman gain, and a sigma integrator circuit block that produces a variance of x 3 .
5. The method of claim 1 wherein the analog hardware circuit comprises transconductance amplifiers and transconductance multipliers.
6. The method of claim 1 wherein the analog hardware circuit is a complementary metal-oxide-semiconductor (CMOS) integrated circuit (IC).
7. The method of claim 1 wherein the method further comprises receiving by the analog hardware circuit a forgetting factor (bandwidth) control signal.
8. The method of claim 1 wherein the method further comprises outputting by the analog hardware circuit a voltage proportional to a frequency estimate.
9. The method of claim 1 wherein the extended Kalman filter includes a forgetting factor matrix in a Riccati equation.
10. The method of claim 1 wherein the extended Kalman filter includes an additional ε term in an A matrix of a Riccati equation.
11. The method of claim 1 wherein the extended Kalman filter includes a frequency update equation including a damping factor ρ.
12. The method of claim 1 wherein the analog hardware circuit comprises multiple subcircuits connected to each other in series, in parallel, or in a combination of series and parallel; wherein each subcircuit performs the steps of claim 1 .
13. The method of claim 1 wherein the input signals have multiple unknown frequencies; and further comprising outputting multiple sinusoidal estimates of model oscillator signals corresponding to the input signals.
14. The method of claim 1 further comprising receiving multiple input signals having respective unknown frequencies, amplitudes, and phases; and outputting multiple sinusoidal estimates of model oscillator signals corresponding to the multiple input signals.
15. The method of claim 1 wherein the analog hardware circuit comprises an input mixer that frequency down-converts the input signals, and an output mixer that frequency up-converts the sinusoidal estimate.
16. The method of claim 1 wherein the extended Kalman filter uses alternate state variables and nonlinear transformations of frequency, amplitude and phase.