Mark Briers

Fast particle smoothing: if I had a million particles

We propose efficient particle smoothing methods for generalized state-spaces models. Particle smoothing is an expensive O(N2) algorithm, where N is the number of particles. We overcome this problem by integrating dual tree recursions and fast multipole techniques with forward-backward smoothers, a new generalized two-filter smoother and a maximum a posteriori (MAP) smoother. Our experiments show that these improvements can substantially increase the practicality of particle smoothing.

Efficient Block Sampling Strategies for Sequential Monte Carlo Methods

Sequential Monte Carlo (SMC) methods are a powerful set of simulation-based techniques for sampling sequentially from a sequence of complex probability distributions. These methods rely on a combination of importance sampling and resampling techniques. In a Markov chain Monte Carlo (MCMC) framework, block sampling strategies often perform much better than algorithms based on one-at-a-time sampling strategies if “good” proposal distributions to update blocks of variables can be designed. In an SMC framework, standard algorithms sequentially sample the variables one at a time whereas, like MCMC, the efficiency of algorithms could be improved significantly by using block sampling strategies. Unfortunately, a direct implementation of such strategies is impossible as it requires the knowledge of integrals which do not admit closed-form expressions. This article introduces a new methodology which by-passes this problem and is a natural extension of standard SMC methods. Applications to several sequential Bayesian inference problems demonstrate these methods.

A rao-blackwellised unscented Kalman filter

The Unscented Kalman Filter oflers sign

Multi-target out-of-sequence data association: Tracking using graphical models

- cant improvements in the estimation of non-linear discrete- time models in comparison to the Extended Kalman Fil- ter 1121. In this paper we use a technique introduced by Casella and Robert (2), known as Rao-Blackwellisation, to calculate the tractable integrations that are found in the Unscented Kalman Filter: We show that this leads to a re- duction in the quasi-Monte Carlo variance, and a decrease in the computational complexity by considering a common tracking problem.

Multipath track association for over-the-horizon radar using Lagrangian relaxation

When performing data fusion, one often measures where targets were and then wishes to deduce where targets currently are. There has been recent research on the processing of such out-of-sequence data. This research has culminated in the development of a number of algorithms for solving the associated tracking problem. This paper reviews these different approaches in a common Bayesian framework and proposes an architecture that orthogonalises the data association and out-of-sequence problems such that any combination of solutions to these two problems can be used together. The emphasis is not on advocating one approach over another on the basis of computational expense, but rather on understanding the relationships among the algorithms so that any approximations made are explicit. Results for a multi-sensor scenario involving out-of-sequence data association are used to illustrate the utility of this approach in a specific context.

Bayesian visual tracking with existence process

Over-the-horizon radar (OTHR) uses the refraction of high frequency radiation through the ionosphere in order to detect targets beyond the line-of-sight horizon. The complexities of the ionosphere can produce multipath propagation, which may result in multiple resolved detections for a single target. When there are multipath detections, an OTHR tracker will produce several spatially separated tracks for each target. Information conveying the state of the ionosphere is required in order to determine the true location of the target and is available in the form of a set of possible propagation paths, and a transformation from measured coordinates into ground coordinates for each path. Since there is no a-priori information as to how many targets are in the surveillance region, or which propagation path gave rise to which track, there is a joint target and propagation path association ambiguity which must be resolved using the available track and ionospheric information. The multipath track association problem has traditionally been solved using a multiple hypothesis technique, but a shortcoming of this method is that the number of possible association hypotheses increases exponentially with both the number of tracks and the number of possible propagation paths. This paper proposes an algorithm based on a combinatorial optimisation method to solve the multipath track association problem. The association is formulated as a two-dimensional assignment problem with additional constraints. The problem is then solved using Lagrangian relaxation, which is a technique familiar in the tracking literature for the multidimensional assignment problem arising in data association. It is argued that due to a fundamental property of relaxations convergence cannot be guaranteed for this problem. However, results show that a multipath track-to-track association algorithm based on Lagrangian relaxation, when compared with an exact algorithm, provides a large reduction in computational effort, without significantly degrading association accuracy.

Super-resolution in practice: the complete pipeline from image capture to super-resolved subimage creation using a novel frame selection method

Most object tracking approaches either assume that the number of objects is constant, or that information about object existence is provided by some external source. Here, we show how object existence can be rigorously integrated within the Bayesian single and multiple object tracking framework. We provide a general treatment that impacts as little as possible on existing tracking algorithms, so that software can be reused, and that allows implementation with Kalman filters, extended Kalman filters, particle filters, etc. We apply the proposed framework to colour-based tracking of multiple objects.

Decentralized predictive sensor allocation

We present a complete super-resolution system using a camera, that is assumed to be on a vibrating platform and continually capturing frames of a static scene, that have to be super-resolved in particular regions of interest. In a practical system the shutter of the camera is not synchronised with the vibrations it is subjected to. So, we propose a novel method for frame selection according to their degree of blurring and we combine a tracker with the sequence of selected frames to identify the subimages containing the region of interest. The extracted subimages are subsequently co-registered using a state of the art sub-pixel registration algorithm. Further selection of the co-registered subimages takes place, according to the confidence in the registration result. Finally, the subimage of interest is super-resolved using a state of the art super-resolution algorithm. The proposed frame selection method is of generic applicability and it is validated with the help of manual frame quality assessment.

Two-dimensional assignment with merged measurements using Lagrangian relaxation

We present a method of dynamic coalition formation (DCF) in sensor networks to achieve well-informed sensor-target allocations. Forecasts of target movements are incorporated when choosing sensor states, as is a memory of target observation. The algorithm can be run in a centralized or decentralized configuration; the latter relies on local message passing in the form of the max-sum algorithm. We show how the DCF algorithm has been applied to synthetic and real data.

Fixed-lag sequential Monte Carlo data association

Closely spaced targets can result in merged measurements, which complicate data association. Such merged measurements violate any assumption that each measurement relates to a single target. As a result, it is not possible to use the auction algorithm in its simplest form (or other two-dimensional assignment algorithms) to solve the two-dimensional target-to-measurement assignment problem. We propose an approach that uses the auction algorithm together with Lagrangian relaxation to incorporate the additional constraints resulting from the presence of merged measurements. We conclude with some simulated results displaying the concepts introduced, and discuss the application of this research within a particle filter context.