A Rao-Blackwellized particle filter to estimate the time-varying noise parameters in non-linear state-space models using alternative stabilized forgetting

The identification of slowly-varying noise parameters in non-linear state-space models constitutes a long-standing problem. The present paper addresses this task using the Bayesian framework and sequential Monte Carlo (SMC) methodology. The proposed approach utilizes an algebraic structure of the model so that the Rao-Blackwellization of the parameters can be performed, thus involving a finite-dimensional sufficient statistic for each particle trajectory into the resulting algorithm. However, relying on standard SMC methods, such techniques are known to suffer from the particle path degeneracy problem. To counteract this issue, it is proposed to use alternative stabilized forgetting, which compensates for the incomplete knowledge of a model of parameter variations by finding a compromise between possible predictive densities of the parameters. An experimental study proves the efficiency of the introduced Rao-Blackwellized particle filter (RBPF) compared to some recently proposed approaches.