Least-Squares and Maximum-Likelihood Tfar Parameter Estimation for Nonstationary Processes

Time-frequency-autoregressive (TFAR) models allow the parsimonious modeling of underspread nonstationary random processes and are physically meaningful due to their formulation in terms of delays and Doppler frequency shifts. Here, we derive least-squares (LS) and maximum-likelihood (ML) methods for TFAR parameter estimation as well as approximative LS and ML methods specifically suited for the underspread case. We show that the LS, under-spread LS, and underspread ML estimators are equivalent to estimators based on linear time-frequency Yule-Walker (TFYW) equations. The exact ML estimator, on the other hand, requires numerical maximization but yields better estimation accuracy than TFYW techniques. We also discuss the application of block-based TFAR estimation to the spectral analysis of signals with arbitrary length