Multiple order, multiple-time constant self-adaptive tracking filter

The algorithm described provides simultaneous availability of the state estimates corresponding to many orders of filters through the use of the fading memory (discounted) averages of the residuals of each lower order to obtain the estimates of a higher order. These averages are also used to provide maneuver parameters at different levels in order to obtain a gracefully changing hybrid combination of the filter estimates. Further, as the state estimate of a higher order filter is generally better than that of the lower order, particularly in respect of bias errors during and after a maneuver period, continual re-initialization of the lower order filters, using the higher order estimate, is effected through the use of the relevant maneuver parameter, enabling the filter to settle down faster towards the steady state conditions after a maneuver. The self-adaptive use of the the higher order estimates during maneuver thus provides a good smoothing under steady state conditions combined with rapid maneuver following with minimal bias errors, even in low data rate radar systems.