Kalman filter and alpha-beta filters for radar tracking

This paper discusses the tracking filter that estimates the true values of the states of the target such as position and velocity by Cartesian coordinates with the target position used as the observation value of the radar. A typical example is a Kalman filter or an alpha-beta filter. A Kalman filter has a good tracking accuracy but a heavy computational load, whereas the alpha-beta filter has a light computational load and is practical, although it has a problem in tracking accuracy. If the alpha-beta with a light computational load has a tracking accuracy similar to the one for a Kalman filter, this filter becomes even more practical. Therefore, in this paper, the conditions are discussed where the alpha-beta filter can approximate a Kalman filter. In this paper, the radar coordinates, where the target position vector is one axis, is used for calculation of the smoothing values (estimated values of the states for target motion at the present sampling time). It is proven that the alpha-beta filter can approximate a Kalman filter if the angular velocity of the target and the rotation of the radar coordinates with the coordinate axis rotated with the target motion are infinitesimal and the process noise (a parameter indicating the ambiguity of the target motion model) is independent and the same between the coordinates. This result indicates that the alpha-beta filter can approximate a Kalman filter if the target is at a low speed, the target range is large, or the target is proceeding the radar in a straight line.