TRACKING OF UNKNOWN NONSTATIONARY CHIRP SIGNALS USING UNSUPERVISED CLUSTERING IN THE WIGNER DISTRIBUTION SPACE

This paper is concerned with the problems of 1) detecting the presence of one or more FM chirp signals embedded in noise, and 2) tracking or estimating the unknown, time-varying instantaneous frequency of each chirp component. No prior knowledge is assumed about the number of chi rp signals present, the parameters of each chirp, or how the parameter s change with time. A detection/estimation algorithm is proposed that uses the Wigner distribution transform to find the best piecewise cubi c approximation to each chirp's phase function. The first step of the WD based algorithm consists of properly thresholding the WD of the rec eived signal to produce contours in the time-frequency plane that appr oximate the instantaneous frequency of each chirp component. These con tours can then be approximated as generalized lines in the (omega, t, t2) space. The number of chirp signals (or equivalently, generalized l ines) present is determined using maximum likelihood segmentation. Min imum mean square estimation techniques are used to estimate the unknow n phase parameters of each chirp component. We demonstrate that for th e cases of i) nonoverlapping linear or nonlinear FM chirp signals embe dded in noise or ii) over-lapping linear FM chirp signals embedded in noise, the approach is very robust, highly reliable, and can operate e fficiently in low signal-to-noise environments where it is hard for ev en trained operators to detect the presence of chirps while looking at the WD plots of the overall signal. For multicomponent signals, the p roposed technique is able to suppress noise as well as the troublesome cross WD components that arise due to the bilinear nature of the WD.