Positive FIR System Identification using Maximum Entropy Prior

Abstract

Bayesian nonparametric methods have been introduced in a linear system identification paradigm to avoid the model and order selection problem. In this framework, a finite impulse response (FIR) model is considered, and the impulse response is realized as a zero-mean Gaussian process. The identification results mainly depend on a prior covariance (kernel) which has to be estimated from data. But the Gaussian prior assumption is inappropriate when the impulse response is constrained on an interval. This paper considers the positive FIR model identification problem using non Gaussian prior where a positive model denotes a system with the nonnegative impulse response. A suitable prior is selected as the maximum entropy prior when the impulse response has interval constraints. A truncated multivariate normal prior is shown to be the maximal entropy prior for positive FIR model identification. Simulation results demonstrate that the proposed prior shows significantly better robustness.