Estimating parameters of nonlinear systems using the elitist particle filter based on evolutionary strategies

Abstract

In this article, we present the elitist particle filter based on evolutionary strategies (EPFES) as an efficient approach for nonlinear system identification. The EPFES is derived from the frequently-employed state-space model, where the relevant information of the nonlinear system is captured by an unknown state vector. Similar to classical particle filtering, the EPFES consists of a set of particles and respective weights which represent different realizations of the latent state vector and their likelihood of being the solution of the optimization problem. As main innovation, the EPFES includes an evolutionary elitist-particle selection which combines long-term information with instantaneous sampling from an approximated continuous posterior distribution. In this article, we propose two advancements of the previously-published elitist-particle selection process. Further, the EPFES is shown to be a generalization of the widely-used Gaussian particle filter and thus evaluated with respect to the latter for two completely different scenarios: First, we consider the so-called univariate nonstationary growth model with time-variant latent state variable, where the evolutionary selection of elitist particles is evaluated for non-recursively calculated particle weights. Second, the problem of nonlinear acoustic echo cancellation is addressed in a simulated scenario with speech as input signal: By using long-term fitness measures, we highlight the efficacy of the well-generalizing EPFES in estimating the nonlinear system even for large search spaces. Finally, we illustrate similarities between the EPFES and evolutionary algorithms to outline future improvements by fusing the achievements of both fields of research.