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>

Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review

“…This tuning is often achieved by implementing Expectation-Maximisation (EM) algorithms [183]. The latter consists of a two-stage procedure, where the state of the system is estimated, and then covariance parameters are updated on an iterative basis [184], [185], [186], [187], [188], [189].…”

A Stochastic Expectation Maximization Algorithm for the Estimation of Wastewater Treatment Plant Ammonium Concentration

“…In addressing this challenge, we have chosen a modeling approach similar to Lukasse [15] and Stentoft [16], but with a significant difference: the utilization of a non-linear and non-gaussian model using a Particle Filter (PF) [4]. The PF offers distinctive advantages over the EKF and KF, particularly when dealing with non-linearity and complex, uncertain systems [19]. Its proficiency in modeling non-linear and non-Gaussian systems is invaluable for predicting N H + 4 concentrations over a 24-hour horizon with non-parametric confidence intervals.…”

“…An alternative strategy is the use of sequential Monte Carlo methods to address diverse distribution forms, such as the Ensemble Kalman Filter and Smoother (EnKF and EnKS) [21], [22] or the Particle Filter and Particle Smoother (PF and PS) [4], [23]. Chau et al [19] compared the use of EKF, EnKF and PF for parameter estimation in nonlinear models. Following their conclusion, we choose to employ the Particle Filter combined with a backward smoother (BS) with the Monte-Carlo Expectation Maximization (MCEM) method [24], a stochastic extension of the EM tailored for nonlinear systems.…”

“…The BS algorithm operates by propagating PF estimates backward in time, accounting for both the system dynamics and observations. A detailed description of the PF and BS can be found in [4], [23], [19], [25]. The Monte-Carlo Expectation Maximization (MCEM) [24] algorithm iteratively estimates model parameters.…”