Bearings Only Versus Bearings and Extent Tracking for Missile Guidance Systems Utilising Particle Methods

This paper addresses the problem of bearings only and bearings and extent tracking for closed loop missile guidance systems using particle methods compared with derivative free methods. Lack of observability is a typical phenomenon for the bearings only tracking problem. We demonstrate that exploiting angular extent information does help mitigating the lack of observability issues. The simulation results show that the particle filter ourperforms the derivative free algorithms. 1 Motivation In recent years there has been considerable interest in the application of particle filters and derivative-free filters to target tracking problems, e.g. [ASS03, FRB02]. However, with a few exceptions [Gat09, SEG01], the applications are essentially open-loop; control is largely ignored. Here the application is a closed loop missile homing guidance problem. For missile homing guidance, an estimator is required in order to calculate states relating to the relative motion of the target with respect to the missile. Traditionally Kalman Filters, or Extended Kalman Filters (EKFs), are used. However, when significant system dynamics or measurement non-linearities exist, and non Gaussian system or measurement noise is present, it is well known that Kalman Filtering has its limitations. Such conditions exist in homing guidance applications. Seeker measurements can have significant non-linearities, and target manoeuvres, can often be best described by non-linear models with non-Gaussian noise. In addition what a missile sees affects what it does, and what it does affects what it sees. Thus any ‘parasitic’ errors within the system cause missile body-motion to corrupt seeker measurements. In this situation it is not the open loop accuracy of the estimation that is of prime importance, but how errors build up. Closed-loop stability becomes of primary importance. Generally this limits the innovation gains and associated bandwidth of conventional estimators. A further restriction on bandwidth is that noise propagation onto the missile control surfaces must be kept within bounds. However, if the filter model is well matched to the ‘real-world’ dynamics/measurements good estimation may be obtained using much lower filter gains (or their equivalent). Alternative approaches such as particle filtering or derivative-free techniques are worth exploring. This work investigates the performance of particle filters (sequential Monte Carlo based methods) within such a closed loop environment, and to what extent the resulting system can be characterised and tuned to be robust to parameter changes. In particular a generic