Modelling of Non - Stationary Autoregressive Alpha Stable Processes with Particle Filters

In this work, we propose a novel method to model time-varying autoregressive impulsive signals, which possess skewed or symmetric Alpha Stable distributions. The main contribution of this work is its ability to model both the unknown autoregressive coefficients and the distribution parameters, where all of them are time-varying. This method is a generalization of previous work by the same authors where the modelling of time-varying autoregressive coefficients, under constant distribution parameters was performed merely for symmetric distributions. The proposed method is composed of a particle filter, by which the timevarying autoregressive coefficients and the distribution parameters can be estimated successfully. The performance of the proposed method is tested for different parameter values where the time variation of the autoregressive coefficients and the distribution parameters are considered to be sinusoidal or piecewise constant in time. The location parameter is taken to be either zero or a ramp waveform. The successful performance of the proposed method serves as a promising contribution in the modelling of impulsive signals, which are frequently seen in many areas, such as teletraffic in computer communications, radar and sonar applications and mobile communications.