Bayesian Approach to Guidance in the Presence of Glint

Abstract

When tracking targets with radar, changes in target aspect with respect to the observer can cause the apparent centerofradarree ectionstowandersignie cantly. Theresulting noisy angleerrorsarecalledtargetglint. Glintmay severely affect the tracking accuracy, particularly when tracking largetargetsat shortranges (such as might occur in the e nal homing phase of a missile engagement ). The effect of glint is to produce heavy-tailed, time-correlated non-Gaussiandisturbancesontheobservations.ItiswellknownthattheperformanceoftheKalmane lterdegrades severely in the presence of such disturbances. We propose a random-sample-based implementation of a Bayesian recursive e lter. Thise lteris based on the Metropolis ‐Hastings algorithm and theGaussian sum approach. The key advantage of the e lter is that any nonlinear/non-Gaussian system and/or measurement models can be routinely implemented. Tracking performance of the e lter is demonstrated in the presence of glint. I. Introduction G LINTis dee nedasthe inherentcomponent oferrorin aradar’ s measurement of position or Doppler frequency of a complex target due to interference of the ree ections from different elements of the target. A complex target, such as an aircraft or tank, may be considered as being made up of a number of independent scattering elements. The radar return from such a target is the vector sum of the radar returns from each of the individual scatterers. As the relative position of the radar and the scatterers changes, the relative phase of the radar returns varies, causing large e uctuations in the combined signal. The change in relative phase of the signal returns causes a change in the apparent target center and, hence,the angular error measured by the radar. This angular noise or scintillation is called glint. Glint can cause the apparent location of the target to fall outside of its physical span (this can be simply demonstrated by analysis of a two-source target ). The linear displacement of the apparent target position due to glint varies inversely with range. As a rough guide, the standard deviation of the angular glint from an aircraft target is about kL/R, where L is the wing span of the target, R istherangetothetarget,and k isaconstanttakingavaluebetween 0.1 and 0.2 (Ref. 1). Glint is particularly troublesome for target tracking because it is a low-frequency effect, the bandwidth of the error typically being a few hertz. In Ref. 2, the correlation time tgc of the glint noise is shown to be approximately tgc o ¸ 3:4!aL