Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations (Q1377315)

The paper proposes two approaches for nonlinear and nonnormal filters based on Monte Carlo simulation techniques: (MA1) The first Monte Carlo approach uses random draws directly from the appropriate conditional distributions; (MA2) The second Monte Carlo approach utilizes rejection sampling to get random draws based on the transition equation and the conditional densities obtained from the measurement equations. The main advantages of the filters based on (MA1) and (MA2) methods are the simplicity of computer programming, the absence of ad hoc assumptions, and a good experimental behaviour in comparison to other nonlinear filters that use numerical integration, Monte Carlo integration with importance sampling or Gibbs sampling. Furthermore, the proposed new filters can be extended directly to prediction and smoothing algorithms. Monte Carlo experiments with linear and nonlinear state-space models are realized in order to point out the statistical merits of the proposed filters.