Steady‐state errors of an α‐β‐γ filter for radar tracking
Yoshio Kosuge, Masayoshi Ito, Takamitsu Okada, Seiji Mano · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 2002
Abstract Radar tracking filters estimate the true values for a target's motion, such as position and speed, using observed values for the target's position. An α‐β filter is a tracking filter for one‐dimensional space using a constant‐velocity linear motion model, and an α‐β‐γ filter is a tracking filter for one‐dimensional space using a uniformly accelerated motion model. Calculation formulas for the steady‐state variance for a target in constant‐velocity linear motion when sufficient time has passed since the initial value calculations have been reported for α‐β filters. However, for α‐β‐γ filters, although computational formulas for the steady‐state variance for a target in uniformly accelerated motion when there is a drive noise indicating vagueness in the motion model derived from the principles of a Kalman filter have been reported, a calculation formula for the steady‐state variance for a target in constant‐velocity linear motion has not been reported. In this paper the authors present a calculation formula for the steady‐state variance for a target in constant‐velocity linear motion for an α‐β‐γ filter. In addition, the authors show the conditions for the gains α, β, and γ for an α‐β‐γ filter that are necessary to have the variance be positive and meaningful. Furthermore, the authors show that this condition is identical to the condition for which the α‐β‐γ filter is stable. Finally, the authors demonstrate that the calculation formula for the variance in the error for an α‐β‐γ filter is an extension of the calculation formula for an α‐β filter. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(12): 65–79, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecjc.1129