Stability of a tracking filter based on an α-β-γ filter

The tracking filter in a radar estimates the true values of target motion parameters such as position, speed, etc., from the observed target location. A typical example is the tracking Biter that uses the Kalman Biter. For calculating load reduction, tracking filters that use an alpha-beta filter or an alpha-beta-gamma filter, which are simplified forms of the Kalman filter, are widely used. Here, the alpha-beta filter is used to calculate the position and speed of a moving target and the alpha-beta-gamma filter is used when the acceleration of the target is required. Stability is a requirement for useful tracking filters, and it is known that the alpha-beta filter is always stable when its gains alpha and beta lie in the range from 0 to 1. However, there are no reports about the alpha-beta-gamma filter. In this paper, the stability of the alpha-beta-gamma Biter is clarified when it is used as a tracking filter. It is shown that the alpha-beta-gamma filter, in contrast to the alpha-beta filter, is not necessarily stable when its gains alpha, beta, and gamma lie in the range from 0 to 1. However, it is shown that three types of alpha-beta-gamma filters derived from the Kalman filters etc. are stable. (C) 2000 Scripta Technica.