Tracking of unknown non-stationary chirp signals using unsupervised clustering in the Wigner distribution space

The authors are concerned with the problems of detecting the presence and tracking the unknown, time-varying instantaneous frequencies of nonoverlapping linear or nonlinear FM chirp signals embedded in noise and overlapping linear FM chirp signals embedded in noise. No prior knowledge is assumed about the signal parameters, or when the signal changes its parameters in time, or the number of signals present. For both the overlapping and nonoverlapping cases, the authors analyze the Wigner distribution (WD) of the received signals s(t). The WD of many FM chirp signals is highly concentrated above a 2-D curve in the time-frequency plane that corresponds with the signal´s instantaneous frequency. The contours that are produced by properly thresholding the WD are generalized lines in the (ω, t, t²) space. Hence, the tracking problem for both cases reduces to the simpler problem of tracking generalized lines, and is done using unsupervised weighted maximum-likelihood clustering, and minimum-mean-square estimation