Mark R. Morelande

A Bayesian Approach to Multiple Target Detection and Tracking

This paper considers the problem of simultaneously detecting and tracking multiple targets. The problem can be formulated in a Bayesian framework and solved, in principle, by computation of the joint multitarget probability density (JMPD). In practice, exact computation of the JMPD is impossible, and the predominant challenge is to arrive at a computationally tractable approximation. A particle filtering scheme is developed for this purpose in which each particle is a hypothesis on the number of targets present and the states of those targets. The importance density for the particle filter is designed in such a way that the measurements can guide sampling of both the target number and the target states. Simulation results, with measurements generated from real target trajectories, demonstrate the ability of the proposed procedure to simultaneously detect and track ten targets with a reasonable sample size

An Information-Based Approach to Sensor Management in Large Dynamic Networks

This paper addresses the problem of sensor management for a large network of agile sensors. Sensor management, as defined here, is the process of dynamically retasking agile sensors in response to an evolving environment. Sensors may be agile in a variety of ways, e.g., the ability to reposition, point an antenna, choose sensing mode, or waveform. The goal of sensor management in a large network is to choose actions for individual sensors dynamically so as to maximize overall network utility. Sensor management in the multiplatform setting is a challenging problem for several reasons. First, the state space required to characterize an environment is typically of very high dimension and poorly represented by a parametric form. Second, the network must simultaneously address a number of competing goals. Third, the number of potential taskings grows exponentially with the number of sensors. Finally, in low-communication environments, decentralized methods are required. The approach we present in this paper addresses these challenges through a novel combination of particle filtering for nonparametric density estimation, information theory for comparing actions, and physicomimetics for computational tractability. The efficacy of the method is illustrated in a realistic surveillance application by simulation, where an unknown number of ground targets are detected and tracked by a network of mobile sensors.

Manoeuvring target tracking in clutter using particle filters

A particle filter (PF) is a recursive numerical technique which uses random sampling to approximate the optimal solution to target tracking problems involving nonlinearities and/or non-Gaussianity. A set of particle filtering methods for tracking and manoeuvering target in clutter from angle-only measurements is presented and evaluated. The aim is to compare PFs to a well-established tracking algorithm, the IMM-PDA-EKF (interacting multiple model, probabilistic data association, extended Kalman filter), and to provide an insight into which aspects of PF design are of most importance under given conditions. Monte Carlo simulations show that the use of a resampling scheme which produces particles with distinct values offers significant improvements under almost all conditions. Interestingly, under all conditions considered here,using this resampling scheme with blind particle proposals is shown to be superior, in the sense of providing improved performance for a fixed computational expense, to measurement-directed particle proposals with the same resampling scheme. This occurs even under conditions favourable to the use of measurement-directed proposals. The IMM-PDA-EKF performs poorly compared with the PFs for large clutter densities but is more effective when the measurements are precise.

Modeling of corneal surfaces with radial polynomials

We consider analytical modeling of the anterior corneal surface with a set of orthogonal basis functions that are a product of radial polynomials and angular functions. Several candidate basis functions were chosen from the repertoire of functions that are orthogonal in the unit circle and invariant in form with respect to rotation about the origin. In particular, it is shown that a set of functions that is referred herein as Bhatia-Wolf polynomials, represents a better and more robust alternative for modeling corneal elevation data than traditionally used Zernike polynomials. Examples of modeling corneal elevation are given for normal corneas and for abnormal corneas with significant distortion.

Analyzing the dynamic wavefront aberrations in the human eye

The optics of the human eye are not static in steady viewing conditions and exhibit microfluctuations. Previous methods used for analyzing dynamic changes in the eyes optics include simple Fourier-transform-based methods, which have been used in studies of the eyes accommodation response. However, dedicated tools for the analysis of dynamic wavefront aberrations have not been reported. We propose a set of signal processing tools, the combination of which uncovers aspects of the dynamics of eyes optical aberrations which were hidden from conventional analysis techniques. The methodology includes extraction of artifacts from potentially significant eye movements, filtering, optimal parametric signal modeling, and frequency and time-frequency representations. The exposition of the techniques and their advantages over traditional techniques is illustrated for real dynamic eye wavefront aberration measurements.

Detection and parameter estimation of multiple radioactive sources

Given an area where an unknown number of unaccounted radioactive sources potentially exist, and using gamma- radiation count measurements collected at known locations within this area, the problem is to estimate the number of sources as well as their locations and intensities. Two approaches are investigated. The first is based on the maximum likelihood estimation and the generalised maximum likelihood rule for multiple hypothesis testing. The second approach estimates the parameters and the number of sources in the Bayesian framework via Monte Carlo integration. Numerical analysis and the performance comparison of both approaches against the Cramer-Rao bound are carried out.

An Efficient Multi-Frame Track-Before-Detect Algorithm for Multi-Target Tracking

This paper considers the multi-target tracking (MTT) problem through the use of dynamic programming based track-before-detect (DP-TBD) methods. The usual solution of this problem is to adopt a multi-target state, which is the concatenation of individual target states, then search the estimate in the expanded multi-target state space. However, this solution involves a high-dimensional joint maximization which is computationally intractable for most realistic problems. Additionally, the dimension of the multi-target state has to be determined before implementing the DP search. This is problematic when the number of targets is unknown. We make two contributions towards addressing these problems. Firstly, by factorizing the joint posterior density using the structure of MTT, an efficient DP-TBD algorithm is developed to approximately solve the joint maximization in a fast but accurate manner. Secondly, we propose a novel detection procedure such that the dimension of the multi-target state no longer needs be to pre-determined before the DP search. Our analysis indicates that the proposed algorithm could achieve a computational complexity which is almost linear to the number of processed frames and independent of the number of targets. Simulation results show that this algorithm can accurately estimate the number of targets and reliably track multiple targets even when targets are in proximity.

A Computationally Efficient Particle Filter for Multitarget Tracking Using an Independence Approximation

Particle filter (PF) based multi-target tracking (MTT) methods suffer from the curse of dimensionality. Existing strategies to combat this assume posterior independence between target states, in order to then sample targets independently, or to perform joint sampling of closely spaced targets only. When many targets are in proximity, these strategies either perform poorly or are too computationally expensive. We make two contributions towards addressing these limitations. Firstly, we advocate an alternative view of the use of posterior independence which emphasizes the statistical effect of assuming posterior independence on the Monte Carlo (MC) approximation of posterior density. Our analysis suggests that assuming posterior independence can provide a better MC approximation of the prior distribution at the next time, and therefore the posterior at the next time, without regard for how sampling is performed. Secondly, we present a computationally efficient, measurement directed, joint sampling method to cope with the target coupling and measurement ambiguity when targets are near each other. Consequently, we develop a PF which employs posterior independence while sampling targets jointly. This PF is applicable to both the traditional thresholded and track-before-detect style pixelized models. Simulation results for a challenging tracking scenario show that the proposed PF substantially outperforms existing approaches.

Analysis of Kalman Filter Approximations for Nonlinear Measurements

A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its various approximations for the case of a nonlinear measurement equation with additive Gaussian noise. The KF is based on a Gaussian approximation to the joint density of the state and the measurement. The analysis metric is the Kullback-Leibler divergence of this approximation from the true joint density. The purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the KF and its variants in nonlinear scenarios. This is illustrated using a numerical example.

Radiological Source Detection and Localisation Using Bayesian Techniques

The problem considered in this paper is detection and estimation of multiple radiation sources using a time series of radiation counts from a collection of sensors. A Bayesian framework is adopted. Source detection is approached as a model selection problem in which competing models are compared using partial Bayes factors. Given the number of sources, the posterior mean is the minimum mean square error estimator of the source parameters. Exact calculation of the partial Bayes factors and the posterior mean is not possible due to the presence of intractable integrals. Importance sampling using progressive correction is proposed as a computationally efficient method for approximating these integrals. Previously proposed algorithms have been restricted to one or two sources. A simulation analysis shows that the proposed methods can detect and accurately estimate the parameters of four sources with reasonable computational expense.