Steady‐state errors of an α‐β‐γ filter for radar tracking

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