Signal parameter estimation using fourth order statistics: multiplicative and additive noise environment

Abstract

Parameter estimation of various multi-component stationary and non-stationary signals in multiplicative and additive noise is considered in this paper. It is demonstrated that the parameters of complex sinusoidal signal, complex frequency modulated (FM) sinusoidal signal and complex linear chirp signal in presence of additive and multiplicative noise can be estimated using a new definition of the fourth order cumulant (FOC), and the computed accumulated FOC (AFOC). Analytical expressions for the FOC/AFOC of the above signals are derived. The concept of accumulated cumulant is introduced to handle the case of a non-stationary signal, for which the fourth order cumulant may be a function of both time and lag. Simulation study is carried out for all the three signals. In case of complex sinusoidal signals, the results of parameter estimation show that the proposed method based on the new definition of fourth order cumulant performs better than an existing method based on fourth order statistics. The proposed method can be employed for parameter estimation of non-stationary signals also as mentioned above. For comparison purpose, the Cramer-Rao (CR) bound expressions are derived for all the signals considered for parameter estimation. The simulation results for non-stationary signals are compared with the CR bounds.