Bias correction and forward-backward averaging in frequency/DOA tracking problems

In this paper, we discuss some issues relevant to frequency and direction of arrival (DOA) tracking problems. First, we develop a linear Frequency Modulated (FM) signal model for accurately describing windowed, slowly time varying narrowband signals that typically occur in tracking problems. We then derive first order bias expressions for the peak locations of a Discrete Time Fourier Transform (DTFT) spectrum of a windowed, slowly time varying linear FM signal. We also show that Forward-Backward (FB) averaging is generally inappropriate for nonstationary data, but that it is appropriate when applied to tracking the frequencies of windowed, slowly time varying narrowband signals. A major motivation for using FB averaging is to increase the efficiency of subspace based frequency/DOA estimation in tracking problems. Finally, simulations confirm our first order bias expressions, and show that FB averaging does not significantly alter (or degrade) the time varying MUSIC based frequency estimation performance over that of Forward only averaging.This research was supported in part by the National Science Foundation Grant MIP-9203296 and Texas Advanced Research Program Grant 009741-022 and 009741-065.