Optimal design of α-β-(γ) filters

Optimal sets of the smoothing parameter (/spl alpha/, /spl beta/ and /spl gamma/) are derived for a sampled data target tracker. A constrained parameter optimization problem is formulated for specific 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 expressions for the steady state error and the sum of the square of the errors capturing the transient behavior are derived for a straight line trajectory where the target moves with constant acceleration and a circular trajectory with the target moving at constant speed. The constrained optimization includes, besides the maneuver errors, a metric of noise capacity strength, expressed by the mean square response of the filter to white noise. An optimal selection of /spl alpha/, /spl beta/ and /spl gamma/ parameters is provided for various penalties on the noise filtering.