David Salmond

Bayesian state estimation for tracking and guidance using the bootstrap filter

The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

Ground target modelling, tracking and prediction with road networks

A model for vehicle motion on a road network Is developed using an enumeration of feasible routes. Combined with a generic stochastic model of distance travelled, a predicted pdf of vehicle position is derived as a mixture. This approach allows prior information on vehicle intent and behaviour to be included via the mixture weights. Illustrative examples are given using a second-order linear-Gaussian model for vehicle road speed. The value of road map data is shown via a tracking example with poor quality measurements and a substantial period prior to sensor activation. The tracking algorithm is implemented using a standard particle filter. In particular, the scheme has potential for revealing the likely paths taken by the vehicle.

Particles and Mixtures for Tracking and Guidance

The guidance algorithm is the central decision and control element of a missile system. It is responsible for taking data from all available missile sensors, together with targeting information and generating a guidance demand. This is usually in the form of an acceleration demand that is passed to the autopilot.

PARAMETER ESTIMATION FOR TERMINAL GUIDANCE USING A DOPPLER BEAM SHARPENING RADAR.

During the terminal phase of an engagement an air to surface missile must ensure that it is on track to hit its target accurately and satisfy terminal conditions. This terminal guidance problem has been tackled for a missile carrying a Doppler beam sharpening (DBS) radar seeker. Emphasis is upon aspects affecting the trajectory shape which arise as a consequence of using measurements from a DBS sensor to remove an unknown error in the position of the target and a bias error in the velocity of the inertial navigation system (INS) carried by the missile. The conditions for high quality DBS imagery must be met and these are derived. It is shown that, by use of sequential estimation techniques, the uncertainty in the estimated spatial co-ordinates of the target’s position may be reduced to a few meters – compared with hundreds of meters if the measurements derived from only one image are processed independently in each time step. A theoretical bound on the performance of an estimator, as a function of image quality and trajectory shape, is given via computation of posterior Cramer-Rao lower bound (CRLB). Two novel estimators have been designed to overcome the heavily non-linear nature of the DBS measurement process and their performance is close to the CRLB.

A novel MCMC tracker for stressing scenarios

We propose a very generic Bayesian framework for the principled exploitation of probabilistic batch-learning technologies for real-time state estimation. To illustrate our concepts, we derive a nonlinear filtering/smoothing solution for a challenging case study in target tracking. We also demonstrate the application of Markov chain Monte Carlo (MCMC) sampling methods as a computational tool within our framework. Finally, we present simulation results, benchmarked against a comparable particle filter.

A Gaussian Mixture Filter for Near-Far Object Tracking

The near-far object tracking (NFOT) problem concerns the tracking of an extended object consisting of a set of resolvable sources that, due to finite sensor resolution, appears as a single point when at long range from the sensor. A Gaussian mixture filter for this problem is presented for the case of a linear object comprising a known number of sources. The filter structure is a combination of the probabilistic data association (PDA) filter and the multiple simultaneous measurement filter. The filter takes into account the uncertainty concerning the objects structure and orientation, as well as the presence of false alarms. Simulations for an open-loop pursuit scenario are presented that compare the performance of the filter with another Gaussian mixture filter that does not consider sensor resolution

Efficient particle filtering for multiple target tracking with application to tracking in structured images

For many dynamic estimation problems involving nonlinear and/or non-Gaussian models, particle filtering offers improved performance at the expense of computational effort. This paper describes a scheme for efficiently tracking multiple targets using particle filters. The tracking of the individual targets is made efficient through the use of Rao-Blackwellisation. The tracking of multiple targets is made practicable using Quasi-Monte Carlo integration. The efficiency of the approach is illustrated on synthetic data.

BAYESIAN PATTERN MATCHING TECHNIQUE FOR TARGET ACQUISITION

The following acquisition/selection problem is considered: a group of N targets is observed at time t0 and one of them is designated (targeting information). At some later time t1 the target group is again observed by a missile seeker. The targets are assumed to move as a group, as well as individually,between observation times and so have a dependent motion model. The detection probability at t1 is less than one, and so some of the targets may not be detected. It is also possible that some measurements received at t1 may not originate from targets. The problem is to estimate the state of the designated target at time t1, given the two sets of measurements, i.e., to recover the designated target. We employ a dependent target motionmodel within a multiple hypothesis framework. The motion of the targets is modeled as the result of two effects: a bulk component,which is common to all targets, and an individual contribution, which is independent from target to target. A closed-form solution is derived for the linear-Gaussian special case, and simulation examples illustrating the technique are presented.

Bayesian approach to avoiding track seduction

The problem of maintaining track on a primary target in the presence spurious objects is addressed. Recursive and batch filtering approaches are developed. For the recursive approach, a Bayesian track splitting filter is derived which spawns candidate tracks if there is a possibility of measurement misassociation. The filter evaluates the probability of each candidate track being associated with the primary target. The batch filter is a Markov-chain Monte Carlo (MCMC) algorithm which fits the observed data sequence to models of target dynamics and measurement-track association. Simulation results are presented.

Target selection with communicating observers

The problem of surface target selection and estimation for multiple communicating observers is addressed. Prior information is provided in the form of a targeting map, which includes the expected posi- tion and possibly other attributes of the targets of in- terest in the scenario. This map is available to all ob- servers. The observers process sensor measurements locally and send information occasionally to a fusion centre, which produces an (approximate) overall pos- terior pdf of one, or more, required targets from the targeting map. It is assumed that the targets are fixed during the (fairly brief) observation period. A multiple hypothesis algorithm for local processing and a (subop- timal) central fusion scheme have been derived from a Bayesian starting point. Key aspects of this algorithm are that it is robust to observers joining (or leaving) the group, and that it is scalable with the number of observers. Operation of the scheme is demonstrated via a simple two dimensional simulation using a batch filter (Iterated Least Squares) implementation.