The alpha-beta-Gamma tracking filter with a noisy jerk as the maneuver model: Frequency domain solution

Abstract

An analysis of a discrete constant gain alpha-beta-Gamma tracking filter is presented in frequency domain. The target is assumed to be moving with constant acceleration and is acted upon by an uncorrelated zero noise jerk which perturbs its constant acceleration motion. Closed-formed results for estimating optimum steady-state position, velocity, and acceleration of the target are given along with the code for simple program that computes the gains for a given tracking index. While the results [2 and 4] are correct, the gains can be found in a much simpler manner. The stability analysis of the optimal tracking filter yields the selection of the quartic equation root.