Analog least mean phase adaptive filter in stochastic differential equation formalism

In this paper, an analog least mean phase adaptive filter is proposed in stochastic differential equation formalism for estimating a complex sinusoidal signal and its parameters (frequency, amplitude and phase) from measurements corrupted by white noise. This adaptive filter is derived by introducing a cost function that is based on the phase error. This filter is useful for applications where the performance depends primarily on the phase of the estimated (recovered) signal. Simulations demonstrate that the proposed analog adaptive filter is effective as a method for estimating a single complex sinusoid and its frequency under a low signal-to-noise ratio (SNR), frequency jump and dynamic frequency variation.