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

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. In practical applications, it is expensive to have large number of high-cost experiments or even impossible to obtain an 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 paper. This framework presumes that large model uncertainty may be restricted by a finite set of known models which can be very different from each other. Moreover, the number of known models in the set can be flexibly chosen so that the uncertain model may always be approximated by one of the known models, in other words, the large model uncertainty is “covered” by the “convex hull” of the known models. Within the presented framework according to the idea of adaptive switching via the minimizing vector distance principle, a simple finite-model Kalman filter, MVDP-FMKF, is mathematically formulated and illustrated by extensive simulations. An experiment of MEMS gyroscope drift has verified the effectiveness of the proposed algorithm, indicating that the mechanism of finite-model Kalman filter is useful and efficient in practical applications of Kalman filters, especially in inertial navigation systems.