Maximum likelihood parameter estimation for a high-dimensional system by particle-based filters

Abstract

Particle-based filters are applied to estimate poorly-known parameters in an oceanic thermohaline circulation model. The model is a stochastic partial differential equation that conceptually represents the Atlantic meridional overturning circulation. It exhibits rapid transitions between strong (temperature-dominated) and weak (salinity-dominated) circulations, and its stability depends on a stochastic term in the equation.Accurate estimation of the variance of the random term is critical in characterizing the circulation system, and the Maximum Likelihood Estimation is utilized via particle-based filters to estimate the parameter. The performance of different types of particle-based filters such as the Sequential Importance Resampling filter, Ensemble Kalman filter, and Maximum entropy filter are compared by the results of parameter estimation of the intermediate ocean model. The results show that all the three filters correctly estimate the stochastic parameter and, more importantly, suggest that particle-based filters are a promising tool for parameter estimation for high-dimensional systems.