A generalized state space model and its application to a set of extended kalman filter equations

Abstract

An existing generalization of the classical linear state space model providing for state dependant measurement error covariance matrix, is further extended. The measurement and state errors are considered correlated, and all related covariance matrices are state dependant. The corresponding Kalman filter equations are given which are applied to derive approximate filtering equations for a lore complicated non-linear dynamic model. Finally an example is given, where a non-linear time series model is linearized and its parameters estimated by optimizing a Gaussian likelihood criterion.

Keywords:

• state space model
• state dependant variance
• extended Kalman filter