On the a priori information in sequential estimation problems

In this paper, the effect of errors in the a priori information is studied when the sequential estimations are carried out on the states of linear systems disturbed by white noise. Four theorems are derived to describe the mutual relations among the three covariance matrices, namely the optimum, calculated, and actual covariance matrices, where the last two are based on the incorrect a priori information. By finding the upper bound for the variance of the actual estimate, performance of the Kalman filter is prescribed and the knowledge is utilized for design of the combined system of analog and digital filters. A phase-locked loop receiver is used as an example of analog filter and the considerable improvement on the estimation process is deduced by the theory and it is confirmed by the experimental simulation on the digital computer.