Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models

Abstract

<p style='text-indent:20px;'>This study aims at comparing simulation-based approaches for estimating both the state and unknown parameters in nonlinear state-space models. Numerical results on different toy models show that the combination of a Conditional Particle Filter (CPF) with Backward Simulation (BS) smoother and a Stochastic Expectation-Maximization (SEM) algorithm is a promising approach. The CPFBS smoother run with a small number of particles allows to explore efficiently the state-space and simulate relevant trajectories of the state conditionally to the observations. When combined with the SEM algorithm, this algorithm provides accurate estimates of the state and the parameters in nonlinear models, where the application of EM algorithms combined with a standard particle smoother or an ensemble Kalman smoother is limited.</p>