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Statistical dependencies between information sources are rarely known, yet in practical distributed tracking schemes, they must be taken into account in order to prevent track divergences. Chernoff fusion is well-known and universally accepted method that can address the problem of track fusion when the statistical dependence between the fusing sources is unknown. In this paper we derive the exact Chernoff fusion equations for Bernoulli Gaussian max filters. These filters have been recently derived in the framework of possibility theory, as the analog of the Bernoulli Gaussian sum filters. The main motivation for the possibilistic approach is that it effectively deals with imprecise mathematical models (e.g. dynamics, measurements) used in tracking algorithms. The paper also demonstrates the proposed possibilistic fusion scheme in the absence of knowledge about statistical dependence.

Contemporary undertakings provide limitless opportunities for widespread application of machine reasoning and artificial intelligence in situations characterised by uncertainty, hostility and sheer volume of data. The paper develops a valuation network as a graphical system for higher-level fusion and reasoning under uncertainty in support of the human operators. Valuations, which are mathematical representation of (uncertain) knowledge and collected data, are expressed as credal sets, defined as coherent interval probabilities in the framework of imprecise probability theory. The basic operations with such credal sets, combination and marginalisation, are defined to satisfy the axioms of a valuation algebra. A practical implementation of the credal valuation network is discussed and its utility demonstrated on a small scale example., Comment: 16 pages, 3 figures

The problem is area-restricted search for targets using an autonomous mobile sensing platform. Detection is imperfect: the probability of detection depends on the range to the target, while the probability of false detections is non-zero. The paper develops an intermittent information-driven search strategy, which combines fast and non-receptive displacement phase (ballistic phase) with a slow displacement sensing phase. Decisions where to move next, both in the ballistic phase and the slow displacement phase, are information-driven: they maximise the expected information gain. The paper demonstrates the efficiency of the proposed strategy in the context of a search for underwater targets: the searcher is an autonomous amphibious drone which can both fly and land or takeoff from the sea surface., Comment: 6 pages

The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory, where uncertainty is represented using {\em possibility} functions, rather than {\em probability} distributions. Possibility functions model the uncertainty in a non-additive manner, and have the capacity to deal with partial (incomplete) problem specification. Thus, the main advantage of the possibilistic Bernoulli filter, derived in this paper, is that it can operate even in the absence of precise measurement and/or dynamic model parameters. This feature of the proposed filter is demonstrated in the context of target tracking using multi-static Doppler shifts as measurements., Comment: 23 pages

The problem is target motion analysis (TMA), where the objective is to estimate the state of a moving target from noise corrupted bearings-only measurements. The focus is on recursive TMA, traditionally solved using the Bayesian filters (e.g. the extended or unscented Kalman filters, particle filters). The TMA is a difficult problem and may cause the algorithms to diverge, especially when the measurement noise model is imperfect or mismatched. As a robust alternative to the Bayesian filters for TMA, we propose the recently introduced possibility filter. This filter is implemented in the sequential Monte Carlo framework, and referred to as the possibility particle filter. The paper demonstrates its superior performance against the standard particle filter in the presence of a model mismatch, and equal performance in the case of the exact model match., Comment: 3 figures, keywords: Target motion analysis; bearings-only tracking; robust stochastic filtering; Monte Carlo estimation; possibility distribution

This paper considers the problem of localising a stationary signal source using a team of mobile agents which only take binary measurements. Background false detection rates and missed detection probabilities are incorporated into the framework. A Bayesian estimation algorithm that discretises the search environment is employed, and analytical convergence and consistency results for this are derived. Fisher Information is then used as a metric for the design of optimal agent geometries. Knowledge of the probability of detection as a function of the source and agent locations is assumed in the analysis, with special attention given to range-dependent functions. The behaviour of the algorithm under inexact knowledge of the probability of detection is also analysed. Finally, simulation results are presented to demonstrate the effectiveness of the algorithm., Comment: 17 pages, 4 Figures, Submitted to IEEE Transactions on Signal Processing

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method can be adapted for the purpose of practical implementation of these equations. In particular, we explore how sampling can be used to provide support points for the approximation of these outer measures. This step enables practical algorithms to be derived in the spirit of particle filters. The performance of the obtained algorithms is demonstrated in simulations and their versatility is illustrated through various examples.

This overview paper describes the particle methods developed for the implementation of the a class of Bayes filters formulated using the random finite set formalism. It is primarily intended for the readership already familiar with the particle methods in the context of the standard Bayes filter. The focus in on the Bernoulli particle filter, the probability hypothesis density (PHD) particle filter and the generalised labelled multi-Bernoulli (GLMB) particle filter. The performance of the described filters is demonstrated in the context of bearings-only target tracking application., Comment: 50 pages including 6 figures in Information Fusion, 2016

Using the measurements collected at a number of known locations by a moving binary sensor, characterised by an unknown threshold, the problem is to estimate the parameters of a biochemical source, continuously releasing material into the atmosphere. The solution is formulated in the Bayesian framework using a dispersion model of Poisson distributed particle encounters in a turbulent flow. The method is implemented using the importance sampling technique and successfully validated with three experimental datasets under different wind conditions., Comment: 6 pages, 3 figures

The paper derives the theoretical Cramer-Rao lower bound for parameter estimation of a source (of emitting energy, gas, aerosol), monitored by a network of sensors providing binary measurements. The theoretical bound is studied in the context of a source of a continuous release in the atmosphere of hazardous gas or aerosol. Numerical results show a good agreement with the empirical errors, obtained using an MCMC parameter estimation technique., Comment: 5 pages, 3 figures

Localisation of a source of a toxic release of biochemical aerosols in the atmosphere is a problem of great importance for public safety. Two main practical difficulties are encountered in this problem: the lack of knowledge of the likelihood function of measurements collected by biochemical sensors, and the plethora of candidate dispersion models, developed under various assumptions (e.g. meteorological conditions, terrain). Aiming to overcome these two difficulties, the paper proposes a likelihood-free approximate Bayesian computation method, which simultaneously uses a set of candidate dispersion models, to localise the source. This estimation framework is implemented via the Monte Carlo method and tested using two experimental datasets., Comment: 23 pages, 7 figures

The paper presents an approach to olfactory search for a diffusive emitting source of tracer (e.g. aerosol, gas) in an environment with unknown map of randomly placed and shaped obstacles. The measurements of tracer concentration are sporadic, noisy and without directional information. The search domain is discretised and modelled by a finite two-dimensional lattice. The links is the lattice represent the traversable paths for emitted particles and for the searcher. A missing link in the lattice indicates a blocked paths, due to the walls or obstacles. The searcher must simultaneously estimate the source parameters, the map of the search domain and its own location within the map. The solution is formulated in the sequential Bayesian framework and implemented as a Rao-Blackwellised particle filter with information-driven motion control. The numerical results demonstrate the concept and its performance., Comment: 11 pages, 7 figures

The paper evaluates the error performance of three random finite set based multi-object trackers in the context of pedestrian video tracking. The evaluation is carried out using a publicly available video dataset of 4500 frames (town centre street) for which the ground truth is available. The input to all pedestrian tracking algorithms is an identical set of head and body detections, obtained using the Histogram of Oriented Gradients (HOG) detector. The tracking error is measured using the recently proposed OSPA metric for tracks, adopted as the only known mathematically rigorous metric for measuring the distance between two sets of tracks. A comparative analysis is presented under various conditions., Comment: 6 pages, 3 figures

The problem of environmental monitoring using a wireless network of chemical sensors with a limited energy supply is considered. Since the conventional chemical sensors in active mode consume vast amounts of energy, an optimisation problem arises in the context of a balance between the energy consumption and the detection capabilities of such a network. A protocol based on "dynamic sensor collaboration" is employed: in the absence of any pollutant, majority of sensors are in the sleep (passive) mode; a sensor is invoked (activated) by wake-up messages from its neighbors only when more information is required. The paper proposes a mathematical model of a network of chemical sensors using this protocol. The model provides valuable insights into the network behavior and near optimal capacity design (energy consumption against detection). An analytical model of the environment, using turbulent mixing to capture chaotic fluctuations, intermittency and non-homogeneity of the pollutant distribution, is employed in the study. A binary model of a chemical sensor is assumed (a device with threshold detection). The outcome of the study is a set of simple analytical tools for sensor network design, optimisation, and performance analysis., Comment: 21 pages and 7 figures

The paper presents an algorithm for syndromic surveillance of an epidemic outbreak formulated in the context of stochastic nonlinear filtering. The dynamics of the epidemic is modeled using a generalized compartmental epidemiological model with inhomogeneous mixing. The syndromic (typically non-medical) observations of the number of infected people (e.g. visits to pharmacies, sale of certain products, absenteeism from work/study etc.) are used for estimation. The state of the epidemic, including the number of infected people and the unknown parameters of the model, are estimated via a particle filter. The numerical results indicate that the proposed framework can provide useful early prediction of the epidemic peak if the uncertainty in prior knowledge of model parameters is not excessive., Comment: Three figures