Improved auxiliary particle filtering: applications to time-varying spectral analysis

Abstract

This paper addresses optimal estimation for time-varying autoregressive (TVAR) models. First, we propose a statistical model on the time evolution of the frequencies, moduli and real poles instead of a standard model on the AR coefficients, as it makes more sense from a physical viewpoint. Second, optimal estimation involves solving a complex optimal filtering problem which does not admit any closed-form solution. We propose a new particle filtering scheme which is an improvement over the so-called auxiliary particle filter. The hyperparameters timing the evolution of the model parameters are also estimated on-line to make the model robust. Simulations demonstrate the efficiency of both our model and algorithm.