Optimal Design of α-β-γ Filters

Dirk Tenne，Tarunraj Singh
[ Link to psu.edu ]

Abstract – Optimal sets of the smoothing parameter (α, β and γ) are derived for a sampled data target tracker. A constrained parameter optimization problem is for-mulated for specic trajectories of the target, which includes the noise in the measurement, the steady state error and the transient response of the filter. This work considers two classes of target trajectories, circular and straight line maneuvers. Closed form ex-pressions for the steady state error and the sum of the square of the errors capturing the transient be-havior are derived for a straight line trajectory where the target moves with constant acceleration and a circular trajectory with the target moving at con-stant speed. The constrained optimization includes besides the maneuver errors a metric of noise capacity strength, expressed by the mean square response of the lter to white noise. An optimal selection of α, β and γ and parameters is provided for various penalties on the noise ltering.