Semi-analytic solution of ECA filter with position and velocity measurements

Kalman filter for Constant Acceleration and Exponentially Correlated Acceleration target maneuver models with position and velocity measurements (CA-PVM) are dealt with. For Constant Acceleration target maneuver model analytical solution of the covariance and gain matrices is derived with new normalization that reduces the filter parameters from eight to five. The asymptotic behavior of the filter is presented. For the Exponentially Correlated Acceleration target maneuver model semianalytic solutions of the covariance and gain are presented by a combination of explicit formulas and graphical correction factors, thus demonstrating the structure of the solution and the performance of the filter. The analytical results, correction factors and the asymptotes are presented in graphical form for various values of the measurement noises level, target's acceleration level and of target's correlation time.