The Asymptotic Optimality of a Bearings-only Tracking Filter with a High Rate of Noisy Measurement

An asymptotic form of a previously introduced discrete-time tracking filter, known as the shifted Rayleigh filter (Clark et al., 2005), is shown to have desirable asymptotic properties as the measurement rate is increased while the `information content´ of the measurements in any fixed period is held constant. In particular, a range of asymptotic filters, indexed by the sampling interval, produce estimates that are asymptotically optimal. The measurement and conditional distribution processes associated with these filters, when suitably modified, converge in distribution to the corresponding processes of an idealized continuous-time filter, which has the structure of a Kalman-Bucy filter