Target tracking with explicit control of filter lag
W.J. Murray, John Edward Gray · 2002
Presents a method of gain adjustment for an alpha-beta filter when data points are lost or when the tracking interval changes. The steady-state position and velocity lags are first derived for a step acceleration input. The standard predictor-corrector forms of the filter equations are algebraically rearranged into two uncoupled difference equations; one equation for the smoothed position and one for smoothed velocity. The equations are then solved for the smoothed estimates using the method of undetermined coefficients. The solution is shown to consist of the input acceleration, transient terms and steady-state lags. The transient terms counteract the effects of the steady-state lags until the time determined by the filter's lag time. The steady-state lags are used for optimal adjustment of filter gains for aperiodic track conditions. For a varying track update interval, the filter gains which preserve a nominal periodic filter lag are derived. Such gain selection preserves the nominal lags associated with the constant tracking interval regardless of how the update interval varies. An example demonstrates the improvement in performance from using this approach.