Fundamental Properties and Optimal Gains of a Steady-State Velocity Measured α-β Tracking Filter

This paper clarifies the steady-state properties and performance of an α-β filter for moving target tracking using both position and velocity measurements. We call this filter velocity measured α-β (VM-α-β) filter. We first derive the stability condition and steady-state predicted errors as fundamental properties of the VM-α-β filter. The optimal gains for representative motion models are then derived from the Kalman filter equations. Theoretical and numerical analyses verify that VM-α-β filters with these optimal gains realize more accurate tracking than conventional α-β filters when the filter gains are relatively large. Our study reveals the conditions under which the predicted errors of the VM-α-β filters are less than those of conventional α-β filters. Moreover, numerical simulations clarify that the variance of the tracking error of the VM-α-β filters is approximately 3/4 of that of the conventional α-β filters in realistic situations, even when the accuracy of the position/velocity measurements is the same.