Two algorithms for adaptive retrieval of slowly time-varying multiple cisoids in noise

Two algorithms for tracking parameters of slowly varying multiple complex sine waves (cisoids) in noise (the multiple frequency tracker and the adaptive notch filter) are described. For high signal-to-noise ratio (SNR), the properties of the algorithms (i.e., stability, noise rejection, and tracking speed) are studied analytically using a linear filter approximation technique. The tradeoff between noise rejection and tracking error for both algorithms is shown to be similar. Different choices of the design variables are discussed, namely (i) minimal mean-square estimation error for random walk modeled frequency variations and (ii) minimal stationary estimation variance subject to a given tracking delay