Time-frequency Analysis. Multicomponent Polynomial Phase Signal Parameter Estimation

Time-frequency analysis and parameter estimation of noisy polynomial phase signal (PPS) are the general problems in such fields as radar, sonar, communication, biomedical application, seismic signal analysis and so on.The analysis of monocomponent PPS with high signal-to-noise ratio (SNR) has been extensively developed for several decades. These methods, however, can not efficiently process the multicomponent PPS corrupted by heavy or non-Gaussian noise which are most encountered in the practical applications. Hence, the analysis of the PPS under more complicated environments is received much attention. Aiming to solve this problem, the work of the thesis is shown below:1. The product ambiguity function (PAF)-based adaptive time-frequency distribution is proposed. In specific, two adaptive methods for kernel design, the Radon-PAF based method and the PAF-lag-varying filter based method, are presented. For multicomponent chirp signals with unbalanced amplitudes, an iterative algorithm combined with the PAF is proposed to suppress the error propagation effect and residual signal in the peeling-off procedure. The corresponding time-frequency distribution for unbalanced signals is derived.2. The specific noise distribution in the time-frequency rate distribution (TFRD) is analyzed. For the PPS signal corrupted by Gaussian noise or impulse noise, the M- and L-estimation-based robust TFRDs are proposed. The analysis of breakdown point is conducted.3. A fast algorithm, based on the jointly fractional operators, is proposed for the multicomponent linear-FM signals under low SNR environment. Moreover, the performance of the detection statistics is derived by performing the output SNR analysis.4. The spurious peaks of the cubic phase function (CPF) for multicomponent is first identified by theory and by simulations and hence the identifiability problem arises. By exploiting the different dependence of auto-terms and cross-terms on time, the product cubic phase function is proposed to resolve the identifiability problem.