Analytic Solution of ECV Filter with Position and Velocity Measurements

This paper deals with target tracking of the exponentially correlated velocity filter with position and velocity measurements. Analytic solutions of covariance and gain are presented by closed-form formulas, thus demonstrating the structure of the solution and the performance of the filter. The asymptotic behavior of the filter's covariance and gain is presented. The results and the asymptotes are presented in analytic and graphical forms for various values of the measurement noise level and target's correlation time.