An Alternative Derivation of the Kalman Filter Using the Quasi-likelihood Method
by
Yan-Xia Lin
University of Wollongong, Australia

The Kalman filter has many applications in information system, economics and sample surveys. The core issue of the Kalman filter is to obtain the gain matrix for different models. Traditionally, the gain matrix is derived based on the full knowledge of the probability structure of underlying model. Usually the probability structure is assumed to be normal or conditional normal. It raises an issue about determining the gain matrix if the true probability structure does not follow normal or conditional normal structure or if the exactly true probability structure is unknown. In this paper, we show that the gain matrix can be obtained through the quasi-likelihood method if the exactly probability structure of underlying system is unknown and the Kalman filter is a special application of the quasi-likelihood method.

Date received: June 29, 2003