Stability of a tracking filter based on an ?-?-? 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 filter that uses the Kalman filter. For calculating load reduction, tracking filters that use an α-β filter or an α-β-γ filter, which are simplified forms of the Kalman filter, are widely used. Here, the α-β filter is used to calculate the position and speed of a moving target and the α-β-γ 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 α-β filter is always stable when its gains α and β lie in the range from 0 to 1. However, there are no reports about the α-β-γ filter. In this paper, the stability of the α-β-γ filter is clarified when it is used as a tracking filter. It is shown that the α-β-γ filter, in contrast to the α-β filter, is not necessarily stable when its gains α, β, and γ lie in the range from 0 to 1. However, it is shown that three types of α-β-γ filters derived from the Kalman filters etc. are stable. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(5): 102–116, 2000