Simon Maskell

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

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.

Cramer-Rao bounds for non-linear filtering with measurement origin uncertainty

We are concerned with the problem of tracking a single target using multiple sensors. At each stage the measurement number is uncertain and measurements can either be target generated or false alarms. The Cramer-Rao bound gives a lower bound on the performance of any unbiased estimator of the target state. In this paper we build on earlier research concerned with calculating Posterior Cramer-Rao bounds for the linear filtering problem with measurement origin uncertainty. We derive the Posterior Cramer-Rao bound for the multi-sensor, non-linear filtering problem. We show that under certain assumptions this measurement origin uncertainty again expresses itself as a constant information reduction factor. Moreover we discuss how these assumptions can be relaxed, and the complications that occur when they no longer hold. We present an example concerned with multi-sensor management. We show that by utilizing the Cramer-Rao bound we are able to determine the combination of sensors that will enable us to achieve the most accurate tracking performance. Simulation results, using a probabilistic data association filter confirm our predictions.

A Bayesian approach to fusing uncertain, imprecise and conflicting information

The Dezert-Smarandache theory (DSmT) and transferable belief model (TBM) both address concerns with the Bayesian methodology as applied to applications involving the fusion of uncertain, imprecise and conflicting information. In this paper, we revisit these concerns regarding the Bayesian methodology in the light of recent developments in the context of the DSmT and TBM. We show that, by exploiting recent advances in the Bayesian research arena, one can devise and analyse Bayesian models that have the same emergent properties as DSmT and TBM. Specifically, we define Bayesian models that articulate uncertainty over the value of probabilities (including multimodal distributions that result from conflicting information) and we use a minimum expected cost criterion to facilitate making decisions that involve hypotheses that are not mutually exclusive. We outline our motivation for using the Bayesian methodology and also show that the DSmT and TBM models are computationally expedient approaches to achieving the same endpoint. Our aim is to provide a conduit between these two communities such that an objective view can be shared by advocates of all the techniques.

Group Object Structure and State Estimation With Evolving Networks and Monte Carlo Methods

This paper proposes a technique for motion estimation of groups of targets based on evolving graph networks. The main novelty over alternative group tracking techniques stems from learning the network structure for the groups. Each node of the graph corresponds to a target within the group. The uncertainty of the group structure is estimated jointly with the group target states. New group structure evolving models are proposed for automatic graph structure initialization, incorporation of new nodes, unexisting nodes removal, and the edge update. Both the state and the graph structure are updated based on range and bearing measurements. This evolving graph model is propagated combined with a sequential Monte Carlo framework able to cope with measurement origin uncertainty. The effectiveness of the proposed approach is illustrated over scenarios for group motion estimation in urban environments. Results with challenging scenarios with merging, splitting, and crossing of groups are presented with high estimation accuracy. The performance of the algorithm is also evaluated and shown on real ground moving target indicator (GMTI) radar data and in the presence of data origin uncertainty.

A rao-blackwellised unscented Kalman filter

The Unscented Kalman Filter oflers sign

Social media and pharmacovigilance: A review of the opportunities and challenges

- 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.

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

Adverse drug reactions come at a considerable cost on society. Social media are a potentially invaluable reservoir of information for pharmacovigilance, yet their true value remains to be fully understood. In order to realize the benefits social media holds, a number of technical, regulatory and ethical challenges remain to be addressed. We outline these key challenges identifying relevant current research and present possible solutions.

A Single Instruction Multiple Data Particle Filter

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.

Littoral tracking using particle filter

Particle filters are often claimed to be readily parallelisable. However, the resampling step is non-trivial to implement in a fine-grained parallel architecture. While approaches have been proposed that modify the particle filter to be amenable to such implementation, this papers novelty lies in its description of a Single Instruction Multiple Data (SIMD) implementation of a particle filter that uses N processors to process N particles. The resulting algorithm has a time complexity of O((log N)2) when performing resampling using N processors. The algorithm has been implemented using C for Graphics (CG), a language that enables the heavily pipelined architecture of modern graphics cards to be used to imitate a SIMD processor. Initial results are presented.