On the initialization of statistical optimum filters with application to motion estimation

The present paper is focusing on the initialization of statistical optimum filters for motion estimation in robotics. It shows that if certain conditions concerning the stability of a system are fulfilled, and some knowledge about the mean of the state is given, an initial error covariance matrix that is optimal with regard to the convergence behavior of the filter estimate might be analytically obtained. Easy algorithms for the n-dimensional continuous and discrete cases are presented. The applicability to non-linear systems is also pointed out. The convergence of a normal Kalman filter is analyzed in simulation using the discrete model of a theoretical example.