In a parallel distributed detection system each local detector makes a decision based on its own observations and transmits its local decision to a fusion center, where a global decision is made. Given fixed local decision rules, in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. In this thesis, we propose a blind technique for the general distributed detection problem with multiple hypotheses. We start by formulating the optimal M-ary fusion rule in the sense of minimizing the overall error probability when the local decision rules are fixed. The optimality can only be achieved if the prior probabilities of hypotheses and parameters describing the local detector performance are known. Next, we propose a blind technique to estimate the parameters aforementioned as in most cases they are unknown. The occurrence numbers of possible decision combinations at all local detectors are multinomially distributed with occurrence probabilities being nonlinear functions of the prior probabilities of hypotheses and the parameters describing the performance of local detectors. We derive nonlinear Least Squares (LS) and Maximum Likelihood (ML) estimates of unknown parameters respectively. The ML estimator accounts for the known parametric form of the likelihood function of the local decision combinations, hence has a better estimation accuracy. Finally, we present the closed-form expression of the overall detection performance for both binary and M-ary distributed detection and show that the overall detection performance using estimated values of unknown parameters approaches quickly to that using their true values. We also investigate various impacts to the overall detection. The simulation results show that the blind algorithm proposed in this thesis provides an efficient way to solve distributed detection problems. / Thesis / Master of Applied Science (MASc)

Investigation of stains from crime scenes are commonly used in the search for criminals. At The National Laboratory of Forensic Science, where these stains are examined, a number of questions of theoretical and practical interest regarding the databases of DNA profiles and the strength of DNA evidence against a suspect in a trial are not fully investigated. The first part of this thesis deals with how a sample of DNA profiles from a population is used in the process of estimating the strength of DNA evidence in a trial, taking population genetic factors into account. We then consider how to combine hypotheses regarding the relationship between a suspect and other possible donors of the stain from the crime scene by two applications of Bayes’ theorem. After that we assess the DNA profiles that minimize the strength of DNA evidence against a suspect, and investigate how the strength is affected by sampling error using the bootstrap method and a Bayesian method. In the last part of the thesis we examine discrepancies between different databases of DNA profiles by both descriptive and inferential statistics, including likelihood ratio tests and Bayes factor tests. Little evidence of major differences is found.

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Ces travaux traitent du suivi de l'activité humaine à travers l'analyse en temps r éel de signaux physiologiques et d'accélé rométrie. Il s'agit de données issues de capteurs ambulatoires ; elles sont bruitées, ambigües, et ne représentent qu'une vision incomplète de la situation. De par la nature des données d'une part, et les besoins fonctionnels de l'application d'autre part, nous considérons que le monde des possibles n'est ni exhaustif ni exclusif, ce qui contraint le mode de raisonnement. Ainsi, nous proposons un raisonnement abductif à base de modèles interconnectés et personnalisés. Ce raisonnement consiste à manipuler un faisceau d'hypothèses au sein d'un cadre dynamique de contraintes, venues tant de l'observateur (en termes d'activités acceptables) que d'exigences non-fonctionnelles, ou portant sur la santé du sujet observé. Le nombre d'hypothèses étudiées à chaque instant est amené à varier, par des mécanismes de Pr édiction-Vérification ; l'adaptation du Cadre participe également à la mise en place d'un pilotage sensible au contexte. Nous proposons un système multi-agent pour représenter ces hypothèses; les agents sont organisés autour d'un environnement partagé qui leur permet d' échanger l'information. Ces échanges et, de manière générale, la détection des contextes d'activation des agents, sont régis par des filtres qui associent une action à des conditions. Le mode de raisonnement et l'organisation de ces agents hétérogènes au sein d'un cadre homogène confèrent au système expressivité, évolutivité et maîtrise des coûts calculatoires. Une implémentation utilisant des données réelles permet d'illustrer les qualités de la proposition. / This proposal deals with human activity monitoring, through the real-time analysis of both physiology data and accelerometry. These data come from ambulatory sensors ; they are noisy and ambiguous, and merely represent a partial and incomplete observation of the current si- tuation. Given the nature of the data on one hand, and the application's required features on the other hand, we consider an Open World of non-exclusive possible situations. This has a restrictive impact on the reasoning engine. We thus propose to use abductive reasoning, based on interconnected and personalized models. This way of reasoning consists in handling a beam of hypotheses, within a dynamic Frame of constraints which come both from the Observer (who defines acceptable situations) and from non-functional expectations, or relating to the observed person's health. The number of hy- potheses at each timestep is wont to vary, by means of Prediction-Verification schemes. The evolution of the Frame leads to context-sensitive adaptive control. We propose a multi-agent system to manage these hypotheses; the agents are organized around a shared environment which allows them to trade information. This interaction and the general detection of activation contexts for the agents are powered and regulated by condition- action filters. The way of reasoning and the organization of heterogeneous agents within a homogeneous Frame lead to a system which we claim to be expressive, evolutive and cost-efficient. An imple- mentation using real sensor data is presented to illustrate these qualities.