P. Tichavsky et P. Handel, 2 ALGORITHMS FOR ADAPTIVE RETRIEVAL OF SLOWLY TIME-VARYING MULTIPLE CISOIDS IN NOISE, IEEE transactions on signal processing, 43(5), 1995, pp. 1116-1127
Two algorithms for tracking parameters of slowly varying multiple comp
lex sine waves (cisoids) in noise (the multiple frequency tracker and
the adaptive notch filter) are described, For high signal-to-noise rat
io (SNR), the properties of the algorithms (i.e., stability, noise rej
ection, and tracking speed) are studied analytically using a linear fi
lter 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 a
nd ii) minimal stationary estimation variance subject to a given track
ing delay.