Daniel Clark

Daniel Clark
Institut Mines-Télécom | telecom-sudparis.eu · Télécom SudParis

PhD

About

123
Publications
15,659
Reads
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3,612
Citations
Introduction
My research interests are in the development of the theory and applications of point processes, stochastic filtering, and information theory. I have has collaborated closely with government and industry on a number of projects demonstrating capability across a range of military applications.
Additional affiliations
September 2017 - present
Institut Mines-Télécom
Position
  • Maitre de Conferences
Description
  • Teaching and research
September 2007 - September 2017
Heriot-Watt University
Position
  • Professor (Associate)
Description
  • Teaching and research.
October 2006 - October 2007
University of Cambridge
Position
  • Research Associate
Description
  • Researcher
Education
February 2003 - October 2006
Heriot-Watt University
Field of study
  • Electrical Engineering
September 2001 - June 2002
University of Cambridge
Field of study
  • Computer Science
September 1997 - June 2001
The University of Edinburgh
Field of study
  • Mathematics

Publications

Publications (123)
Article
Full-text available
This article is focused on estimating a quantity of interest in the context of military impact assessment that we shall call adversarial risk. We formulate the adversarial risk as a function of the multiobject state describing a group of weapons, and propose two approaches to estimate it using multiobject filters. The first, optimal, approach is ta...
Article
Modern tracking problems require fast, scalable, and robust solutions for tracking multiple targets from noisy sensor data. In this article, an algorithm that has linear computational complexity with respect to the number of targets and measurements is presented. The method is based on the propagation of the first two factorial cumulants of a point...
Article
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This paper considers the problem of guiding an unknown number of controllable interceptors to rendezvous with the same target at the same time. It is assumed that the all of the interceptors and the target are described by linear dynamics with Gaussian noise, though the theory presented does not preclude more general models. This extends the work o...
Article
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Point processes are often described with functionals, such as the probability generating functional, the Laplace functional, and the factorial cumulant generating functional. These are used to facilitate modelling of different processes and to determine important statistics via functional differentiation. In information theory, generating functions...
Article
The number of nodes in sensor networks is continually increasing, and maintaining accurate track estimates inside their common surveillance region is a critical necessity. Modern sensor platforms are likely to carry a range of different sensor modalities, all providing data at differing rates, and with varying degrees of uncertainty. These factors...
Article
This paper presents the filter for Hypothesised and Independent Stochastic Populations (HISP), a multi-object joint detection/tracking algorithm derived from a recent estimation framework for stochastic populations, in the context of Space Situational Awareness. Designed for multi-object estimation problems where the data association between tracks...
Article
Full-text available
Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional solutions to the problem pose difficulties in scaling with the number of sensors due to the joint multi-sensor...
Article
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A recent trend in distributed multi-sensor fusion is to use random finite set filters at the sensor nodes and fuse the filtered distributions algorithmically using their exponential mixture densities (EMDs). Fusion algorithms which extend the celebrated covariance intersection and consensus based approaches are such examples. In this article, we an...
Article
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Surveillance activities with ground-based assets in the context of space situational awareness are particularly challenging. The observation process is indeed hindered by short observation arcs, limited observability, missed detections, measurement noise, and contamination by clutter. This paper exploits a recent estimation framework for stochastic...
Article
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Many multi-object estimation problems require additional estimation of model or sensor parameters that are either common to all objects or related to unknown characterisation of one or more sensors. Important examples of these include registration of multiple sensors, estimating clutter profiles, and robot localisation. Often these parameters are e...
Article
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The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD p...
Article
To circumvent the intractability of the usual Cardinalized Probability Hypothesis Density (CPHD) smoother, we present an approximate scheme where the population of targets born until and after the starting time of the smoothing are estimated separately and where smoothing is only applied to the estimate of the former population. The approach is ill...
Article
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A multi-target filtering algorithm is introduced based on recent works on the modelling of partially-distinguishable populations and on the representation of partial information. This framework enables practically-relevant aspects of multi-target systems to be modelled and embedded in a principled way, such as pre-existing knowledge about the popul...
Article
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A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is based on the measure of a supremum, hence combining additive and highly sub-additive components. It is shown tha...
Conference Paper
The necessity for maintaining surveillance in airborne environments is ever growing. Criminals and terrorists are finding new and elaborate means of attack, and small UAVs such as quadcopters and hexacopters could be a possible threat. Their small size and agile movement will make them difficult to detect. This work aims to determine whether or not...
Article
In its classical form, the cardinalized probability hypothesis density (CPHD) filter does not model the appearance of new targets through spawning, yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models. In this paper, we propose a principled derivation of the CP...
Article
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A way of representing heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. In particular, it is demonstrated that any instance of this representation where individuals are independent can be related to a point process on the s...
Article
Multiple-input multiple-output (MIMO) sonar systems offer new perspectives for area surveillance especially in complex environments where strong multipath and dense clutter can become very challenging. This study proposes a MIMO sonar system based scheme to tackle the difficult problem of harbour surveillance. An emphasis is put on recognition and...
Conference Paper
Full-text available
We consider geographically distributed sensor platforms with limited field of views (FoVs) networked together in order to cover a larger surveillance region. Each sensor has a partially overlapping FoV with its neighbours, and, collects both target originated and spurious measurements. We are interested in estimating the locations of the sensors in...
Chapter
The random finite set (RFS) approach, introduced by Mahler as finite set statistics (FISST), is an elegant Bayesian formulation of multitarget filtering based on RFS theory. This chapter describes the RFS approach to multitarget tracking. It focuses on RFS-based algorithms such as the probability hypothesis density (PHD), and cardinalized PHD (CPHD...
Conference Paper
Full-text available
Motivated by object tracking applications with networked sensors, we consider multi sensor state space models. Estimation of latent parameters in these models requires centralisation because the parameter likelihood depend on the measurement histories of all of the sensors. Consequently, joint processing of multiple histories pose difficulties in s...
Conference Paper
Motivated by object tracking applications with networked sensors, we consider multi sensor state space models. Estimation of latent parameters in these models requires centralisation because the parameter likelihood depend on the measurement histories of all of the sensors. Consequently, joint processing of multiple histories pose difficulties in s...
Article
Full-text available
We consider self-localisation of networked sensor platforms which are located disparately and collect cluttered and noisy measurements from an unknown number of objects (or, targets). These nodes perform local filtering of their measurements and exchange posterior densities of object states over the network to improve upon their myopic performance....
Conference Paper
Full-text available
In this work, we consider the front-end processing for an active sensor. We are interested in estimating signal amplitude and noise power based on the outputs from filters that match transmitted waveforms at different ranges and bearing angles. These parameters identify the distributions in, for example, likelihood ratio tests used by detection alg...
Conference Paper
Full-text available
In environments of scarce hygiene it is of primary importance to detect potentially harmful concentrations of pathogens in drinking water. In many situations, however, accurate analysis of water samples is prohibitively complex and often requires highly specialised apparatuses and technicians. In order to overcome these limitations, a method to emp...
Conference Paper
This paper investigates a sensor management scheme that aims at minimising the regional variance in the number of objects present in regions of interest whilst performing multi-target filtering with the PHD filter. The experiments are conducted in a simulated environment with groups of targets moving through a scene in order to inspect the behaviou...
Conference Paper
Full-text available
A formulation of the hypothesised filter for independent stochastic populations (hisp) is proposed, based on the concept of association measure, which is a measure on the set of observation histories. Using this formulation, a particle approximation is introduced at the level of the association measure for handling the exponential growth in the num...
Article
Full-text available
In the classical derivation, the CPHD (Cardinalized Probability Hypothesis Density) filter does not model the appearance of new targets through spawning. However, there are applications for which spawning models more appropriately account for new targets than birth models, with the caveat that they may create issues with computational tractability....
Article
Full-text available
This paper summarizes the core definitions and results regarding the chain differential for functions in locally convex topological vector spaces. In addition, it provides a few elementary calculus rules of practical interest, notably for the differentiation of characteristic functionals in various domains of physical science and engineering.
Article
Calibrating multiple cameras is a fundamental prerequisite for many Computer Vision applications. Typically this involves using a pair of identical synchronized industrial or high-end consumer cameras. This paper considers an application on a pair of low-cost portable cameras with different parameters that are found in smart phones. This paper addr...
Article
The SC-PHD filter is an algorithm which was designed to solve a class of multiple object estimation problems where it is necessary to estimate the state of a single-target parent process, in addition to estimating the state of a multi-object population which is conditioned on it. The filtering process usually employs a number of particles to repres...
Article
For many disciplines in natural sciences like biology, chemistry or medicine, the invention of optical microscopy in the late 1800's provided groundbreaking insight into biomedical mechanisms that were not observable before with the unaided eye. However, the diffraction limit of the microscope gives a natural constraint on the image resolution sinc...
Article
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This article introduces a multi-object filter for the resolution of joint detection/tracking problems involving multiple targets, derived from the novel Bayesian estimation framework for stochastic populations. Fully probabilistic in nature, the filter for Distinguishable and Independent Stochastic Populations (DISP) exploits two exclusive probabil...
Article
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Fluorescence microscopy is a technique which allows the imaging of cellular and intracellular dynamics through the activation of fluorescent molecules attached to them. It is a very important technique because it can be used to analyze the behavior of intracellular processes in vivo in contrast to methods like electron microscopy. There are several...
Article
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Methods for sensor control are crucial for modern surveillance and sensing systems to enable efficient allocation and prioritisation of resources. The framework of partially observed Markov decision processes enables decisions to be made based on data received by the sensors within an information-theoretic context. This work addresses the problem o...
Article
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Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object tracking and sensor registration. Given that using standard filtering approaches for state estimation from came...
Conference Paper
Full-text available
In this work, we consider a network of bearing only sensors in a surveillance scenario. The processing of target measurements follow a two-tier architecture: The first tier is com-posed of centralised processing clusters whereas in the second tier, cluster heads perform decentralised processing. We are interested in the first tier problem of locati...
Poster
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A Multi-target visual tracking (MTVT) algorithm is developed using the recently popular Random finite set (RFS)-based filters. RFS is used to naturally represent the varying number of non-ordered multi-target states and observations which is analogous to random vector for single target tracking. Finite set statistics (FISST), the study of statistic...
Conference Paper
Full-text available
We consider geographically dispersed and networked sensors col-lecting measurements from multiple targets in a surveillance region. Each sensor node filters the set of cluttered, noisy target measure-ments it collects in a sensor centric coordinate system and with imperfect detection rates. The filtered multi-target information is, then, communicat...
Article
Full-text available
The random finite-set formulation for multiobject estimation provides a means of estimating the number of objects in cluttered environments with missed detections within a unified probabilistic framework. This methodology is now becoming the dominant mathematical framework within the sensor fusion community for developing multiple-target tracking a...
Conference Paper
Recent generalisations of stochastic filtering methods to multi-object systems have become very popular for solving multi-target tracking problems over the last decade. However, there was previously no general means of introducing correlations between objects. In this article, we investigate generalisations of such multi-object filters for systems...
Conference Paper
Volterra series are used for modelling nonlinear systems with memory effects. The nth-order impulse response and the kernels in the series can be determined with Fréchet derivatives of Volterra series operators. Consequently, we can determine the kernels of composite systems by taking higher-order Fréchet derivatives of composite series. The genera...
Article
Full-text available
A new filter for independent stochastic populations is studied and detailed, based on recent works introducing the concept of distinguishability in point processes. This filter propagates a set of hypotheses corresponding to individuals in a population, using a version of Bayes' theorem for multi-object systems. Due to the inherent complexity of th...
Conference Paper
In the context of multi-target tracking application, the concept of variance in the number of targets estimated in specified regions of the surveillance scene has been recently introduced for multi-object filters. This article has two main objectives. First, the regional variance is derived for a multi-object representation commonly used in the tra...
Conference Paper
Full-text available
This short paper focuses on the structure of the data association problem and details a solution based on the introduction of distinguishability in the representation of a given stochastic population. This approach allows for the derivation of general filtering equations for independent stochastic populations. Based on these general equations, the...
Article
Full-text available
The probability generating functional (p.g.fl.) provides a useful means of compactly representing point process models. Cluster processes can be described through the composition of p.g.fl.s, and factorial moment measures and Janossy measures can be recovered from the p.g.fl. using variational derivatives. This article describes the application of...
Conference Paper
Photoactivated Localization Microscopy (PALM) is a technique which allows the localization of particles smaller than the resolution of the microscope and can be used to analyze intracellular particle motion. Images acquired with this technique, however, are noisy, which complicates particle detection, and tracking the particles is complicated due t...
Article
Full-text available
This paper determines the general formula for describing differentials of composite functions in terms of differentials of their factor functions. This generalises the formula commonly attributed to Faa di Bruno to functions in locally convex topological vector spaces. The result highlights the general structure of the higher-order chain rule in te...
Article
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Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order stat...
Article
Full-text available
This document contains the notes of some of the lectures given at the first summer school on Finite Set Statistics held in Edinburgh from July 22, 2013 to July 26, 2013. The notes are mostly self contained and are accessible to everyone.
Article
Tracking systems are based on models, in particular, the target dynamics model and the sensor measurement model. In most practical situations the two models are not known exactly and are typically parametrized by an unknown random vector θ. The paper proposes a Bayesian algorithm based on importance sampling for the estimation of the static paramet...
Article
Full-text available
This paper presents the first algorithm for simultaneous localization and mapping (SLAM) that can estimate the locations of both dynamic and static features in addition to the vehicle trajectory. We model the feature-based SLAM problem as a single-cluster process, where the vehicle motion defines the parent, and the map features define the daughter...
Article
Full-text available
In this paper, we consider the problem of Distributed Multi-sensor Multi-target Tracking (DMMT) for networked fusion systems. Many existing approaches for DMMT use multiple hypothesis tracking and track-to-track fusion. However, there are two difficulties with these approaches. First, the computational costs of these algorithms can scale factoriall...
Conference Paper
Full-text available
This paper considers the application of feature-based simultaneous localisation and mapping (SLAM) using a random finite sets (RFS) framework for an autonomous underwater vehicle. SLAM allows for reduction in localisation error by tracking features which provide a fixed external reference. The SLAM problem is addressed here using a single-cluster p...
Conference Paper
Mahler’s Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget detection and tracking problem by propagating a mean density of the targets in any region of the state space. However, when retrieving some local evidence on the target presence becomes a critical component of a larger process - e....
Conference Paper
Tracking algorithms are based on models: target dynamic and sensor measurement model. In most practical situations the two models are not known exactly and are typically parametrised by an unknown random vector θ. The paper proposes a Bayesian algorithm based on importance sampling for the estimation of θ. The input are detections/measurements coll...
Article
Full-text available
Recent work by Mullane, Vo, and Adams has re-examined the probabilistic foundations of feature-based Simultaneous Localization and Mapping (SLAM), casting the problem in terms of filtering with random finite sets. Algorithms were developed based on Probability Hypothesis Density (PHD) filtering techniques that provided superior performance to leadi...
Article
Full-text available
The standard formulation of the probability hypothesis density (PHD) and cardinalised PHD (CPHD) filters assumes that the target birth intensity is known a priori. In situations where the targets can appear anywhere in the surveillance volume this is clearly inefficient, since the target birth intensity needs to cover the entire state space. This p...
Article
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The paper formulates the problem of sequential Bayesian estima-tion of a compound state consisting of a multi-object dynamic state and a multi-sensor bias. The compound state is modelled by a dou-bly stochastic point process, where the multi-object bias is a parent, whereas the multi-object state is the offspring point process. The prediction and t...
Article
A general approach for Bayesian filtering of multi-object systems is studied, with particular emphasis on the model where each object generates observations independently of other objects. The approach is based on variational calculus applied to generating functionals, using the general version of Faa di Bruno's formula for Gateaux differentials. T...
Article
Full-text available
The superposition of two independent point processes can be described by multiplication of their probability generating functionals (p.g.fl.s). The inverse operation, which can be viewed as a deconvolution, is defined by dividing the superposed process by one of its constituent p.g.fl.s. The deconvolved process is computed using the higher-order ch...
Article
The problem of estimating interacting systems of multiple objects is important to a number of different fields of mathematics, physics, and engineering. Drawing from a range of disciplines, including statistical physics, variational calculus, point process theory, and statistical sensor fusion, we develop a unified probabilistic framework for model...
Conference Paper
In the investigation of multi-sensor fusion problems, it is commonly assumed that all the parameters necessary to transform the information from the sensors to a common frame are known. Imperfect knowledge of these registration parameters induce systematic biases which would inhibit the benefits of multisensor fusion. For example, they can result i...
Conference Paper
This paper introduces a general chain rule (GCR) for Gâteaux differentials/Gâteaux derivatives, and describes its consequences for multitarget detection and tracking. After describing the GCR and its specific form for functionals and functional derivatives, we use it to derive two new PHD filters: (1) a PHD filter for general models of target-gener...
Conference Paper
In extended target tracking, targets potentially produce more than one measurement per time step. In recent random finite set (RFS) approaches, the set of measurements obtained from an extended target is modelled as a point process. In this paper, we expand on the RFS approach to extended target tracking by considering a hierarchical point process...
Conference Paper
Estimating the position of an object from cameras is a key requirement in many computer vision and robotics applications. In sensor fusion applications, where we integrate data from multiple observations and cameras over time and estimate the uncertainty in the state estimate, a Bayesian approach is more applicable than the usual Maximum Likelihood...