Poles and zeros of α-β and α-β-γ tracking filters

Discrete transfer functions for the α-β and α-β-γ Kalman tracking filters are presented. Filters for the update, as well as the prediction, estimates are considered. Root loci for the poles and zeros are presented, parameterised in the manoeuvring index. Closed-form solutions for the α-β-γ gains are given as functions of the manoeuvring index.