Analytical solution of alpha-beta-Gamma colored noise tracking filter with a noisy jerk as correlated target maneuver model

An analysis of a discrete constant gain alpha-beta-Gamma colored noise tracking filter where target acceleration is correlated in time is presented in the frequency domain. Recently, the steady-state gain solution for the same tracking filter was given in [1] where the maneuver correlation coefficient theta was assumed to be zero. The target was assumed to be moving with constant acceleration and was acted upon by a zero mean noise jerk which perturbs its constant acceleration motion [5]. In this work, the close-form results for estimating optimum steady-state position, velocity and acceleration of the target are given. 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 in [1,2,3]. The stability analysis of the optimal tracking filter yields the selection of the quartic equation root.