FIR Steady State Kalman Filter for Motion Estimation and Prediction

Motion models play an essential role in navigation and tracking applications. Constant velocity, constant acceleration, and periodic motion state space models are described. It is shown that the models are observable and controllable. The Kalman filter has been used in order to estimate or predict the position of moving objects. It is shown that a steady state always exists for these models, and steady state Kalman filters for estimation and prediction are derived. It is also shown that the Finite Impulse Response (FIR) form of the steady state Kalman filter always exists, and the FIR form of the steady state Kalman filters for estimation and prediction are derived. Estimation and prediction algorithms that combine the steady state Kalman filter and its FIR form are proposed. Simulation results show the satisfactory behavior of the proposed estimation and prediction algorithms.