Analytical solution of α-β-Γ tracking filter with a noisy jerk as correlated target maneuver model

An analysis of a discrete constant gain α-β-Γ tracking filter where target acceleration is correlated in time is presented in the frequency domain. The steady-state gain solution for the same tracking filter was given by C.C. Arcasoy (1996) where the maneuver correlation coefficient θ was assumed to be zero. The target was assumed to be moving with constant acceleration motion. The closed-formed results for estimating optimum steady-state position, velocity, and acceleration of the target are given along with the code for a simple program that computes the gains for a given tracking index as a function of maneuver correlation coefficient. The gain can be calculated from the solution of the constant coefficient quartic equation for given system parameters that is in the same form as that given by Arcasoy. The stability analysis of the optimal tracking filter yields the selection of the quartic equation root.