ADAPTIVE FILTERING

Applications of the Kalman filter in orbit determination problems have sometimes encountered a difficulty which has been referred to as divergence. The phenomenon is a growth in the residuals; the state and its estimate diverge. This problem can often be traced to insufficient accuracy in modeling the dynamics used in the filter. Although more accurate modeling is an obvious solution, it is often an impractical, and sometimes an impossible, one. Model errors are here approximated by a white, Gaussian noise input, and its covariance (Q) is determined so as to produce consistency between residuals and their statistics. In this way, realtime feedback is provided from the residuals to the filter gain. Onset of divergence produces an increase in the filter gain and the adaptive filter is able to continue tracking. This scheme has a probabilistic interpretation. Under certain conditions the estimate of Q produces the most probable finite sequence of residuals. © 1969.