Neyman-Pearson detection in sensor networks with dependent observations

Résumé

In this thesis, within the context of sensor networks, we are interested in the distributed detection problem under the Neyman-Pearson formulation and conditionally dependent sensor observations. In order to exploit all the detection potential of the network, the literature on this issue has faced optimal distributed detection problems, where optimality usually consists in properly designing the parameters of the network with the aim of minimizing some cost function related to the overall detection performance of the network. However, this problem of optimization has usually constraints regarding the possible physical and design parameters that we can choose when maximizing the detection performance of the network. In many applications, some physical and design parameters, for instance the network architecture or the local processing scheme of the sensor observations, are either strongly constrained to a set of possible design alternatives or either cannot be design variables in our problem of optimization. Despite the fact that those parameters can be related to the overall performance of the network, the previous constraints might be imposed by factors such as the environment where the network has to be deployed, the energy budget of the system or the processing capabilities of the available sensors. Consequently, it is necessary to characterize optimal decentralized detection systems with various architectures, different observation processes and different local processing schemes. The mayor part of the works addressing the characterization of distributed detection systems have assumed settings where, under each one of the possible states of our phenomenon of interest, the observations are independent across the sensors. However, there are many practical scenarios where the conditional independence assumption is violated because of the presence of different spatial correlation sources. In spite of this, very few works have faced the aforementioned characterizations under the same variety of settings as under the conditional independence assumption. Actually, when the strategy of the network is not an optimization parameter, under the assumption of conditionally dependent observations the existing literature has only obtained asymptotic characterizations of the detection performance associated with parallel networks whose local processing rules are based on amplify-and-relay schemes. Motivated by this last fact, in this thesis, under the Neyman-Pearson formulation, we undertake the characterization of distributed detection systems with dependent observations, various network architectures and binary quantization rules at the sensors. In particular, considering a parallel network randomly deployed along a straight line, we derive a closed-form error exponent for the Neyman-Pearson fusion of Markov local decisions when the involved fusion center only knows the distribution of the sensor spacings. After studying some analytical properties of the derived error exponent, we carry out evaluations of the closed-form expression in order to assess which kind of trends of detection performance can appear with increasing dependency and under two well-known models of the sensor spacing. These models are equispaced sensors with failures and exponentially spaced sensors with failures. Later, the previous results are extended to a two-dimensional parallel network that, formed by a set of local detectors equally spaced on a rectangular lattice, performs a Neyman-Pearson test discriminating between two di erent two-dimensional Markov causal fields defined on a binary state space. Next, under conditionally dependent observations and under the Neyman-Pearson set up, this thesis dissertation focuses on the characterization of the detection performance of optimal tandem networks with binary communications between the fusion units. We do so by deriving conditions under which, in an optimal tandem network with an arbitrary constraint on the overall probability of false alarm, the probability of misdetection of the system, i.e. at the last fusion node of the network, converges to zero as the number of fusion stages approaches infinity. Finally, after extending this result under the Bayesian set up, we provide two examples where these conditions are applied in order to characterize the detection performance of the network. From these examples we illustrate different dependence scenarios where an optimal tandem network can or cannot achieve asymptotic perfect detection under either the Bayesian set up or the Neyman-Pearson formulation. -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------