Mixture Kalman ®lters

In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling and weighted resampling to complete the on-linè®ltering' task. We propose a special sequential Monte Carlo method, the mixture Kalman ®lter, which uses a random mixture of the Gaussian distributions to approximate a target distribution. It is designed for on-line estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used non-linear systems and also serve to approximate many others. Compared with a few available ®ltering methods including Monte Carlo methods, the gain in ef®ciency that is provided by the mixture Kalman ®lter can be very substantial. Another contribution of the paper is the formulation of many non-linear systems into conditional or partial conditional linear form, to which the mixture Kalman ®lter can be applied. Examples in target tracking and digital communications are given to demonstrate the procedures proposed.