Estimation, Decision and Applications to Target Tracking

This dissertation mainly consists of three parts. The first part proposes generalized linear minimum mean-square error (GLMMSE) estimation for nonlinear point estimation. The second part proposes a recursive joint decision and estimation (RJDE) algorithm for joint decision and estimation (JDE). The third part analyzes the performance of sequential probability ratio test (SPRT) when the log-likelihood ratios (LLR) are independent but not identically distributed. The linear minimum mean-square error (LMMSE) estimation plays an important role in nonlinear estimation. It searches for the best estimator in the set of all estimators that are linear in the measurement. A GLMMSE estimation framework is proposed in this disser- tation. It employs a vector-valued measurement transform function (MTF) and finds the best estimator among all estimators that are linear in MTF. Several design guidelines for the MTF based on a numerical example were provided. A RJDE algorithm based on a generalized Bayes risk is proposed in this dissertation for dynamic JDE problems. It is computationally efficient for dynamic problems where data are made available sequentially. Further, since existing performance measures for estimation or decision are effective to evaluate JDE algorithms, a joint performance measure is proposed for JDE algorithms for dynamic problems. The RJDE algorithm is demonstrated by applications to joint tracking and classification as well as joint tracking and detection in target tracking. The characteristics and performance of SPRT are characterized by two important functions—operating characteristic (OC) and average sample number (ASN). These two functions have been studied extensively under the assumption of independent and identically distributed (i.i.d.) LLR, which is too stringent for many applications. This dissertation relaxes the requirement of identical distribution. Two inductive equations governing the OC and ASN are developed. Unfortunately, they have non-unique solutions in the general case. They do have unique solutions in two special cases: (a) the LLR sequence converges in distributions and (b) the LLR sequence has periodic distributions. Further, the analysis can be readily extended to evaluate the performance of the truncated SPRT and the cumulative sum test

Multitarget tracking and terrain-aided navigation using square-root consider filters

Filtering is a term used to describe methods that estimate the values of partially observed states, such as the position, velocity, and attitude of a vehicle, using current observations that are corrupted due to various sources, such as measurement noise, transmission dropouts, and spurious information. The study of filtering has been an active focus of research for decades, and the resulting filters have been the cornerstone of many of humankind\u27s greatest technological achievements. However, these achievements are enabled principally by the use of specialized techniques that seek to, in some way, combat the negative impacts that processor roundoff and truncation error have on filtering. Two of these specialized techniques are known as square-root filters and consider filters. The former alleviates the fragility induced from estimating error covariance matrices by, instead, managing a factorized representation of that matrix, known as a square-root factor. The latter chooses to account for the statistical impacts a troublesome system parameter has on the overall state estimate without directly estimating it, and the result is a substantial reduction in numerical sensitivity to errors in that parameter. While both of these techniques have found widespread use in practical application, they have never been unified in a common square-root consider framework. Furthermore, consider filters are historically rooted to standard, vector-valued estimation techniques, and they have yet to be generalized to the emerging, set-valued estimation tools for multitarget tracking. In this dissertation, formulae for the square-root consider filter are derived, and the result is extended to finite set statistics-based multitarget tracking tools. These results are used to propose a terrain-aided navigation concept wherein data regarding a vehicle\u27s environment is used to improve its state estimate, and square-root consider techniques provide the numerical stability necessary for an onboard navigation application. The newly developed square-root consider techniques are shown to be much more stable than standard formulations, and the terrain-aided navigation concept is applied to a lunar landing scenario to illustrate its applicability to navigating in challenging environments --Abstract, page iii

Occlusion reasoning for multiple object visual tracking

Thesis (Ph.D.)--Boston UniversityOcclusion reasoning for visual object tracking in uncontrolled environments is a challenging problem. It becomes significantly more difficult when dense groups of indistinguishable objects are present in the scene that cause frequent inter-object interactions and occlusions. We present several practical solutions that tackle the inter-object occlusions for video surveillance applications. In particular, this thesis proposes three methods. First, we propose "reconstruction-tracking," an online multi-camera spatial-temporal data association method for tracking large groups of objects imaged with low resolution. As a variant of the well-known Multiple-Hypothesis-Tracker, our approach localizes the positions of objects in 3D space with possibly occluded observations from multiple camera views and performs temporal data association in 3D. Second, we develop "track linking," a class of offline batch processing algorithms for long-term occlusions, where the decision has to be made based on the observations from the entire tracking sequence. We construct a graph representation to characterize occlusion events and propose an efficient graph-based/combinatorial algorithm to resolve occlusions. Third, we propose a novel Bayesian framework where detection and data association are combined into a single module and solved jointly. Almost all traditional tracking systems address the detection and data association tasks separately in sequential order. Such a design implies that the output of the detector has to be reliable in order to make the data association work. Our framework takes advantage of the often complementary nature of the two subproblems, which not only avoids the error propagation issue from which traditional "detection-tracking approaches" suffer but also eschews common heuristics such as "nonmaximum suppression" of hypotheses by modeling the likelihood of the entire image. The thesis describes a substantial number of experiments, involving challenging, notably distinct simulated and real data, including infrared and visible-light data sets recorded ourselves or taken from data sets publicly available. In these videos, the number of objects ranges from a dozen to a hundred per frame in both monocular and multiple views. The experiments demonstrate that our approaches achieve results comparable to those of state-of-the-art approaches

Solution Approaches to the Three-index Assignment Problem

This thesis explores the axial Three-Index Assignment Problem (3IAP), also called the Multidimensional Assignment Problem. The problem consists in allocating n jobs to n machines in n factories, such that exactly one job is executed by one machine in one factory at a minimum total cost. The 3IAP is an extension of the classical two-dimensional assignment problem. This combinatorial optimisation problem has been the subject of numerous research endeavours, and proven NP-hard due to its inextricable nature. The study adopts an algorithmic approach to develop swift and e ective methods for solving the problem, focusing on balancing computational e ciency and solution accuracy. The Greedy-Style Procedure (GSP) is a novel heuristic algorithm for solving the 3IAP, guaranteeing feasible solutions in polynomial time. Speci c arrangements of cost matrices can lead to the generation of higher-quality feasible solutions. In addressing the 3IAP, analysing the tie-cases and the matrix ordering led to new variants. Further exploration of cost matrix characteristics has allowed two new heuristic classes to be devised for solving 3IAP. The approach focuses on selecting the best solution within each class, resulting in an optimal or a high-quality approximate solution. Numerical experiments con rm the e ciency of these heuristics, consistently delivering quality feasible solutions in competitive computational times. Moreover, by employing diverse optimisation solvers, we propose and implement two e ective methods to achieve optimal solutions for 3IAP in good CPU times. The study introduces two local search methods based on evolutionary algorithms to solve 3IAP. These approaches explore the solution space through random permutations and the Hungarian method. Building on this, a hybrid genetic algorithm that integrates these local search strategies has been proposed for solving the 3IAP. Implementing the Hybrid Genetic Algorithm (HGA) produces high-quality solutions with reduced computational time, surpassing traditional deterministic approaches. The e ciency of the HGA is demonstrated through experimental results and comparative analyses. On medium to large 3IAP instances, our method delivers comparable or better solutions within a competitive computational time frame. Two potential future developments and expected applications are proposed at the end of this project. The rst extension will examine the correlation between cost matrices and the optimal total cost of the assignment and will investigate the dependence structure of matrices and its inuence on optimal solutions. Copula theory and Sklar's theorem can help with this analysis. The focus will be on understanding the stochastic dependence of cost matrices and their multivariate properties. Furthermore, the impact of variations in cost distributions, is often modelled based on economic sectors. The second extension involves integrating variable costs de ned by speci c probability distributions, enhancing the comprehensive analysis of economic scenarios and their impact on the assignment problem. The study considers various well-de ned probability distributions and highlights more practical applications of the assignment problem in real-world economics. The project's original contribution lies in its algorithmic approach to investigating the 3IAP, which has led to the development of new, fast, and e cient heuristic methods that strategically balance computational speed and the accuracy of the solutions achieved

Structured learning of metric ensembles with application to person re-identification

Matching individuals across non-overlapping camera networks, known as person re-identification, is a fundamentally challenging problem due to the large visual appearance changes caused by variations of viewpoints, lighting, and occlusion. Approaches in literature can be categoried into two streams: The first stream is to develop reliable features against realistic conditions by combining several visual features in a pre-defined way; the second stream is to learn a metric from training data to ensure strong inter-class differences and intra-class similarities. However, seeking an optimal combination of visual features which is generic yet adaptive to different benchmarks is a unsoved problem, and metric learning models easily get over-fitted due to the scarcity of training data in person re-identification. In this paper, we propose two effective structured learning based approaches which explore the adaptive effects of visual features in recognizing persons in different benchmark data sets. Our framework is built on the basis of multiple low-level visual features with an optimal ensemble of their metrics. We formulate two optimization algorithms, CMCtriplet and CMCstruct, which directly optimize evaluation measures commonly used in person re-identification, also known as the Cumulative Matching Characteristic (CMC) curve.Comment: 16 pages. Extended version of "Learning to Rank in Person Re-Identification With Metric Ensembles", at http://www.cv-foundation.org/openaccess/content_cvpr_2015/html/Paisitkriangkrai_Learning_to_Rank_2015_CVPR_paper.html. arXiv admin note: text overlap with arXiv:1503.0154

Segregating Event Streams and Noise with a Markov Renewal Process Model

DS and MP are supported by EPSRC Leadership Fellowship EP/G007144/1