Parameter Estimation Of TVAR Model Under The α Stable Distributed Noise Conditions

Both non-Gaussian and non-stationary signal processing are the research focus in thecurrent signal processing field.Strictly, many signals are non-stationary random. In practical applications, however, asthe limitation of theoretical conditions, the signal analyses are only confined to stationarysignals until 1980s. Parametric model is a novel method applied to non-stationary randomsignals processing which uses time-varying parameters to represent non-stationary signals.Comparing to the methods assuming signals are stationary during some time periods, thismodel can make parameter estimation more accurate.Ordinarily, every signal processing algorithm is based on the Gaussian assumption.Since Gaussian assumption is considered to be feasible and can be proved by the central limittheorem in some cases. Moreover, Gaussian assumption can simplify signal processingsystem design greatly which makes it easy to do theoretical analysis. However, signals arenon-Gaussian and satisfy fractional lower a stable distribution in many practical applications.Therefore, it is required to use fractional lower statistics to design signal processingalgorithms.The original contribution of this thesis is that two time-varying parameters estimationalgorithms of the non-Gaussian signal TVAR model under a stable distributed noiseconditions are proposed. Related theories, such as a stable distribution and random signalparameter models, are introduced at first. Afterwards, a stable signal parameter model,time-varying parameter model of non-stationary random signals and corresponding parameterestimation algorithms are studies, followed by discussion on some application problems aboutTVAR model. In the end, combining signal processing theories and non-stationary randomsignal time-varying parameters model under a stable distributed conditions, the TVARmodel time-varying parameter estimation algorithms for non-stationary signals are studies.(1) By expanding the least p norm (LPN) method for stationary random signal modelparameter estimation under a stable distribution to non-stationary random signal, thetime-varying least p norm (TVLPN) algorithm for TVAR model time-varying parameterestimation is obtained.(2) By improving least mean square (LMS) algorithm for TVAR model parameterestimation under Gaussian conditions toαstable distributed conditions, the time-varying least mean square (TVLMP) algorithm for TVAR model time-varying parameter estimation isobtained.Simulation results show that our TVLPN and TVLMP algorithms are developed for bothGaussian conditions andαstable distributed conditions and have better robustnesscompared with the previous LPN and LMS algorithms.