Regularized LTI system identification in the presence of outliers: A variational EM approach

Abstract

Regularized system identification of linear time invariant systems in the presence of outliers is investigated. The finite impulse response (fir) model and the Gaussian scale mixture are chosen to be the system model and the noise model, respectively. Two special cases of the noise model are considered: the well-known Student’s t distribution and a proposed G-confluent distribution. Both the fir model parameter and the latent variables in the noise model are treated as parameters of our statistical model and moreover, the scale of the noise variance is treated as a hyper-parameter besides the hyper-parameters used to parameterize the priors of the impulse response and the latent variables. Then a variational expectation–maximization algorithm is proposed for inference of the parameters and hyper-parameters of the statistical model, and the algorithm is guaranteed to converge to a stationary point. Monte Carlo numerical simulations show that when the relative size of outliers is small, the proposed approach performs comparably to a state-of-the-art method and when the relative size of outliers and/or the occurrence probability of outliers is large, the proposed approach outperforms the state-of-the-art method.