A nonparametric Bayesian model for system identification based on a super-Gaussian distribution

In the acoustic signal processing applications of finite impulse response (FIR) system identification, it is important to develop the identification method that is robust to super-Gaussian noises. Moreover, the identification method that estimates the FIR coefficients and the order of the unknown system is required, because the order of the unknown system is unavailable in advance. Therefore, in this paper, we propose a nonparametric Bayesian (NPB) model for FIR system identification using a super-Gaussian likelihood and the beta-Bernoulli process. In the proposed NPB model, we employ the hyperbolic secant distribution for the likelihood function. Then, we derive the inference algorithm to simultaneously estimate the FIR coefficients and the order of the unknown system. Our inference algorithm based on a hybrid inference approach combining the majorization-minimization (MM) algorithm and the Gibbs sampler. The simulation results suggest that the proposed method outperforms the conventional identification algorithms in a super-Gaussian noise environment.