Parameter and uncertainty estimation in stochastic differential equation models with multi-rate data and nonstationary disturbances

Abstract

Updated methods are proposed for estimating model parameters and error-covariance matrices in stochastic differential equation (SDE) models. New expressions, based on the LAMLE (Laplace Approximation Maximum Likelihood Estimation) and LAB (Laplace Approximation Bayesian) SDE estimation methods are derived so that LAMLE and LAB can be used for systems with multi-rate data and nonstationary disturbances. The updated LAMLE method is tested using simulated data from a two-state continuous stirred tank reactor (CSTR) model. Comparisons are made with the results obtained using the continuous-time stochastic method (CTSM), confirming that the updated LAMLE algorithm provides reliable estimates for unknown model parameters, measurement noise variances, and process-error variances. In all situations tested, the updated LAMLE algorithm converged to reliable parameter and uncertainty estimates, while avoiding convergence difficulties encountered by CTSM in some situations. The updated LAMLE and LAB algorithms will be useful for parameter estimation in online models used in advanced process monitoring and control applications where multi-rate data and nonstationary disturbances are often encountered. Estimates of measurement noise variances and process-error variances will be helpful for state-estimator tuning.