Synthesis of an optimal set of radar track-while-scan smoothing equations

Performance measures are described which realistically reflect both noise-reduction and maneuver-following capability of a radar track-while-scan (TWS) system. Illustrations are given which compare various smoothing equations on the basis of this performance measure. Finally, a set of position-and-velocity tracking equations is synthesized by a calculus-of-variations technique. The synthesized set is optimum for both position and velocity tracking within the given performance sense, in the class of all fixed parameter, linear tracking equations. The resulting optimally synthesized set characterizes the commonly termed "
\alpha-\beta
" tracker, with the important proviso that
\beta=\alpha^{2}/(2 - \alpha)
.