arXiv subjects

Daniel E. Clark

Publications and source records attributed to Daniel E. Clark.

10 recordsLinked to original sources

arXiv2019

On a representation of partially-distinguishable populations

A representation of heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. It is demonstrated that any instance of this representation where individuals are independent can be related to a point process on the set of probability measures on the individual state space. The introduction of the proposed representation is fully constructive which ensures the meaningfulness of the approach.

math.PR↗

arXiv2018

Fusion of finite set distributions: Pointwise consistency and global cardinality

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 analyse the variational principle underlying EMDs and show that the EMDs of finite set distributions do not necessarily lead to consistent fusion of cardinality distributions. Indeed, we demonstrate that these inconsistencies may occur with overwhelming probability in practice, through examples with Bernoulli, Poisson and independent identically distributed (IID) cluster processes. We prove that pointwise consistency of EMDs does not imply consistency in global cardinality and vice versa. Then, we redefine the variational problems underlying fusion and provide iterative solutions thereby establishing a framework that guarantees cardinality consistent fusion.

eess.SP↗

arXiv2017

Single-cluster PHD filter methods for joint multi-object filtering and parameter estimation

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 estimated separately to the multi-object estimation process, which can lead to systematic errors or overconfidence in the estimates. These parameters can be estimated jointly with the multi-object process based only on the sensor data using a single-cluster point process model. This paper presents novel results for joint parameter estimation and multi-object filtering based on a single-cluster second-order Probability Hypothesis Density (PHD) and Cardinalised PHD (CPHD) filter. Experiments provide a comparison between the discussed approaches using different likelihood functions.

math.ST↗

arXiv2017

A second-order PHD filter with mean and variance in target number

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 propagates the cardinality distribution in the number of targets, albeit for a greater computational cost. Introducing the Panjer point process, this paper proposes a second-order PHD filter, propagating the second-order moment (i.e. variance) of the number of targets alongside its mean. The resulting algorithm is more versatile in the modelling choices than the PHD filter, and its computational cost is significantly lower compared to the CPHD filter. The paper compares the three filters in statistical simulations which demonstrate that the proposed filter reacts more quickly to changes in the number of targets, i.e., target births and target deaths, than the CPHD filter. In addition, a new statistic for multi-object filters is introduced in order to study the correlation between the estimated number of targets in different regions of the state space, and propose a quantitative analysis of the spooky effect for the three filters.

stat.ME↗

arXiv2016

Bayesian data assimilation based on a family of outer measures

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 that this type of outer measure enables the introduction of intuitive concepts such as pullback and general data assimilation operations.

cs.IT↗

arXiv2016

Multi-object filtering with stochastic populations

While the design of automated knowledge-based sensor scheduling is relevant to many multi-target detection and tracking problems, tracking algorithms are rarely built for this purpose and their outputs provide little flexibility for the design of sensor policies. In this paper, we present an estimation framework for stochastic populations in the context of multi-target estimation problems. Fully probabilistic in nature, it allows for the evaluation of the population of targets through statistical moments, as well as the assessment of sensor observations through information-theoretical gain functions. We present a principled solution derived from this framework addressing challenging multi-target scenarios involving missed detections and false alarms, the filter for Distinguishable and Independent Stochastic Populations, which propagates information on previously-detected targets as well as yet-to-be-detected targets while maintaining track continuity.

stat.AP↗

arXiv2015

Spawning Models for the CPHD Filter

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 CPHD filter with spawning from the Finite Set Statistics framework. A Gaussian Mixture implementation of the CPHD filter with spawning is then presented, illustrated with three applicable spawning models on a simulated scenario involving two parent targets spawning a total of five objects. Results show that filter implementations with spawn models provide more accurate results when compared to a birth model implementation.

stat.ME↗

arXiv2015

A few calculus rules for chain differentials

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.

math.FA↗

arXiv2013

Faa di Bruno's formula for chain differentials

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 terms of partitions of the directions.

math.FA↗

arXiv2012

Faa di Bruno's formula for Gateaux differentials and interacting stochastic population processes

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 modelling systems of this nature. In order to do this, we derive a new result in variational calculus, Faa di Bruno's formula for Gateaux differentials. Using this result, we derive the Chapman-Kolmogorov equation and Bayes' rule for stochastic population processes with interactions and hierarchies. We illustrate the general approach through case studies in multi-target tracking, branching processes and renormalization.

math.FA↗