Identification of Time-Varying Autoregressive Systems Using Maximum a Posteriori Estimation

Time-varying systems and nonstationary signals arise naturally in many engineering applications, such as speech, biomedical, and seismic signal processing. Thus, identification of the time-varying parameters is of crucial importance in the analysis and synthesis of these systems. The present time-varying system identification techniques require either demanding computation power to draw a large amount of samples (Monte Carlo-based methods) or a wise selection of basis functions (basis expansion methods). In this paper, the identification of time-varying autoregressive systems is investigated. It is formulated as a Bayesian inference problem with constraints on the conditional and prior probabilities of the time-varying parameters. These constraints can be set without further knowledge about the physical system. In addition, only a few hyper parameters need tuning for better performance. Based on these probabilistic constraints, an iterative algorithm is proposed to evaluate the maximum a posteriori estimates of the parameters. The proposed method is computationally efficient since random sampling is no longer required. Simulation results show that it is able to estimate the time-varying parameters reasonably well and a balance between the bias and variance of the estimation is achieved by adjusting the hyperparameters. Moreover, simulation results indicate that the proposed method outperforms the particle filter in terms of estimation errors and computational efficiency.