KALMAN FILTERING ERROR DUE TO INACCURACY IN FILTERS INITIAL CONDITION

It is a very well known fact that the initial condition of the optimal linear Kalman filter has to be set af the mean value of the system in itial state. In this paper, we have derived an expression for the filt ering error in the case when this condition is not satisfied. Both con tinuous- and discrete-time domain filter are considered. The obtained results are simple and elegant and clearly indicate the effect of the erroneous filter's initial condition. An example is included in order to demonstrate the results obtained.