The adaptation of observation noise covariances and adaptive Kalman filtering

The application of Kalman-Bucy filters entails precise knowledge on the a priori noise covariances as well as the system parameters. In many practical cases, however, such precise knowledge is not available, and approximate values are usually used or assumed. It has been pointed out that incorrect covariances often cause severe inconsistency between the calculated error covariance and the actual one. Approaches of adaptive filtering have been studied by various researchers for mainly time-invariant systems. An iterative procedure for the adaptation of the assumed a priori observation-noise covariances of time-variable systems is investigated in this paper. The procedure proposed here computes at each iteration a necessary correction from the covariances of the innovation process, and adapt the noise covariances thereby. The calculated error covariance is shown to tend to the actual in the limit. Simulated examples show that initial choices of the a priori covariance do not seem to be crucial to the convergence. An approach to adaptive filtering is also proposed.