Smoothing improvement ratio for α-β and α-β-γ tracking systems

This paper presents the optimal solution for the generalized, one-dimensional target tracking prediction and smoothing process. Closed form, steady state solutions for the α, α-β, and α-β-γ prediction tracker (parameters and performance) are shown to be dependent on the Tracking Index [1], a function of the track period, measurement noise and target maneuverability. An off-line smoothed track is obtained by combining two independent tracks: a forward filtered track and a backwards predicted track. The smoothing performances, Smoothing Improvement Ratio, and track combining weights are presented in closed form as functions of the α´s and β´s.