Abstract: 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 xi, x2, x3 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 x3 by an affine transformation ?=?0+£x3, where k is a slope of a frequency error estimate and coo is a best estimate input signal frequency.

Abstract: 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, x2, x3 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 co of the model oscillator to x3 by an affine transformation ?=?0+£x3, where k is a slope of a frequency error estimate and coo is a best estimate input signal frequency.