Frequency tracking of nonsinusoidal periodic signals in noise

Abstract

For a periodic signal measured in noise, this paper applies extended Kalman filtering to the problem of estimating the signal's frequency and the amplitudes and phases of the signal's first m harmonic components. The resultant estimator will also track the signal's frequency and its amplitudes and phases should these change over time. In this respect, it is unique among approaches to this problem. A partial theoretical analysis of the estimator appears in the paper. This analysis shows that there is some measure of decoupling in the estimator: the amplitudes are estimated as if the phase and frequency estimates are correct; the phases and frequency are estimated as if the amplitude estimates are correct. For the special case that the signal is a sinusoid and has known amplitude, the estimator becomes the well-known phase-locked loop. The paper also contains extensive simulations demonstrating both the tracking and the asymptotic behaviour of the estimator. The asymptotic behaviour is compared with the results for another known estimator, and the relative strengths of each method are examined.