Designing for a convergent adaptive Kalman filter in time-varying stochastic linear systems

Designing for a convergent adaptive Kalman filter (AKF) which can be used in time-varying stochastic linear systems is considered. A necessary condition which can guarantee the designed AKF is convergent is proposed and proved. This necessary condition can be satisfied by choosing appropriate gains. In fact, choosing the gains is just a procedure of designing a convergent AKF. The AKF designed by the above procedure is convergent and only correlative with coefficient matrices of the system. So, it adapts to deal with time-varying stochastic linear systems. At last, the findings in this paper are validated by some simulations.