Identification of continuous time models using discrete time data

Abstract

Continuous-discrete stochastic state space models in the form of nonlinear partially observed Itô stochastic differential equations (SDE's) with measurement noise are advocated for modelling dynamic systems in continuous time using discrete time data. Such models provide a decomposition of the noise affecting the system into a process noise term and a measurement noise term, and this prediction error decomposition (PED) allows unknown parameters to be estimated from experimental data in a prediction error (PE) setting, which gives less biased and more reproductible results in the presence of significant process noise than the more commonly used output error (OE) setting. To facilitate the use of continuous-discrete stochastic state space models, a PE estimation scheme that features maximum likelihood (ML) and maximum a posteriori (MAP) estimation is presented along with a software implementation. To illustrate the superiority of PE estimation over OE estimation a case study is given, which demonstrates the higher sensitivity of OE estimates to process noise.