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 chirp signals present, the parameters of each chirp, or how the parameters change with time. A detection/estimation algorithm is proposed that uses the Wigner distribution transform to find the best piecewise cubic approximation to each chirp´s phase function. The first step of the WD based algorithm consists of properly thresholding the WD of the received signal to produce contours in the time-frequency plane that approximate the instantaneous frequency of each chirp component. These contours can then be approximated as generalized lines in the (ω, t, t²) space. The number of chirp signals (or equivalently, generalized lines) present is determined using maximum likelihood segmentation. Minimum mean square estimation techniques are used to estimate the unknown phase parameters of each chirp component. The authors demonstrate that for the cases of (i) nonoverlapping linear or nonlinear FM chirp signals embedded in noise or (ii) overlapping linear FM chirp signals embedded in noise, the approach is very robust, highly reliable, and can operate efficiently in low signal-to-noise environments where it is hard for even trained operators to detect the presence of chirps while looking at the WD plots of the overall signal. For multicomponent signals, the proposed technique is able to suppress noise as well as the troublesome cross WD components that arise due to the bilinear nature of the WD