Kalman filtering error due to inaccuracy in filter's initial condition

摘要

It is a very well known fact that the initial condition of the optimal linear Kalman filter has to be set at the mean value of the system initial state. In this paper, we have derived an expression for the filtering error in the case when thiscondition is not satisfied. Both continuous- and discrete-time domain filters 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 todemonstrate the results obtained.