ABSTRACT
This chapter focuses on filtering (state estimation) and prediction theory related to state space models. There are several reasons for considering state space models. The primary reason is probably that the process described by the system equation of the state space model is a (first-order) Markov process. Furthermore, the state space formulation contains a measurement equation which allows for a rather flexible structure of the observations. The chapter describes some estimation methods, such as state interpolation, state filtering, and state prediction, which are needed for estimating parameters in the stochastic differential equations. It shows how the embedded parameters of the linear and nonlinear continuous-discrete state space models can be estimated using a maximum likelihood method. The chapter also discusses the applications of non-linear filters.
