Characterizing performance of α-β-γ filters

The α-β-γ filter, a sampled data target tracker which can asymptotically track a constant acceleration target, is discussed in detail. The α, β, γ parameters are studied to characterize the stability of the filter and its performance viz its transient behavior. A closed-form equation for the mean square response of the system to white noise is derived. In addition, performance measures to gauge the transient response and the steady state tracking error are derived. The closed-form equations for the noise ratio and the transient and steady state error are exploited to optimally select the α, β, γ parameters. The resulting solutions are shown to reduce to some results presented in the literature for the α-β filter.