A Framework of Finite-Model Kalman Filter with Case Study: MVDP-FMKF Algorithm

Abstract

Kalman filtering techniques have been widely used in many applications; however, standard Kalman filters for linear Gaussian systems usually cannot work well or even diverge in the presence of large model uncertainty. To resolve this problem occurred frequently in practical applications, where it is expensive to have large number of high-cost experiments or even impossible to obtain the exact system model, motivated by our previous pioneering work on finite-model adaptive control, a framework of finite-model Kalman filtering is introduced in this contribution, which supposes that the large model uncertainty may be restricted by a finite set of known models, and the known models can be very different from each other, and the number of known models can be flexibly chosen so that the uncertain model may always be approximated by one of the known models. Within the presented framework of finite-model Kalman filter, according to the idea of adaptive switching via minimizing vector distance principle, a simple finite-model Kalman filter, termed as MVDP-FMKF, has been mathematically formulated and illustrated by extensive simulations.