In this paper, we study optimal radar deployment for intrusion detection, with focus on network coverage. In contrast to the disk-based sensing model in a traditional sensor network, the detection range of a bistatic radar depends on the locations of both the radar transmitter and radar receiver, and is characterized by Cassini ovals. Furthermore, in a network with multiple radar transmitters and receivers, since any pair of transmitter and receiver can potentially form a bistatic radar, the detection ranges of different bistatic radars are coupled and the corresponding network coverage is intimately related to the locations of all transmitters and receivers, making the optimal deployment design highly non-trivial. Clearly, the detectability of an intruder depends on the highest SNR received by all possible bistatic radars. We focus on the worst-case intrusion detectability, i.e., the minimum possible detectability along all possible intrusion paths. Although it is plausible to deploy radars on a shortest line segment across the field, it is not always optimal in general, which we illustrate via counter-examples. We then present a sufficient condition on the field geometry for the optimality of shortest line deployment to hold. Further, we quantify the local structure of detectability corresponding to a given deployment order and spacings of radar transmitters and receivers, building on which we characterize the optimal deployment to maximize the worst-case intrusion detectability. Our results show that the optimal deployment locations exhibit a balanced structure. We also develop a polynomial-time approximation algorithm for characterizing the worse-case intrusion path for any given locations of radars under random deployment.
Worst-case coverage has been first studied in @cite_3 for a traditional sensor network. Polynomial-time algorithms are devised to find maximum breach and maximum support paths between two locations. An efficient algorithm is proposed in @cite_2 to solve the best-coverage problem raised in @cite_3 . In @cite_15 , efficient algorithms are developed to find the minimum exposure path in sensor networks. Localized algorithms are designed in @cite_7 to solve the minimum exposure path problem. A new coverage measure that captures both the best and worst-case coverage is studied in @cite_11 . The deployment problem to improve the maximal breach path is considered by @cite_5 @cite_0 . Barrier coverage is an intimately related problem to worst-case coverage. The concept of weak and strong barrier coverage has been introduced in @cite_8 , where critical condition of weak barrier coverage is obtained for random deployment. The critical condition of strong barrier coverage is derived in @cite_13 using percolation theory. An effective metric of barrier coverage quality is proposed in @cite_9 . @cite_10 studies constructing barrier by sensors with limited mobility after initial deployment. A novel full-view coverage model is proposed in @cite_14 for constructing barrier in camera sensor networks.
@cite_14 @cite_7 @cite_8 @cite_10 @cite_9 @cite_3 @cite_0 @cite_2 @cite_5 @cite_15 @cite_13 @cite_11
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In this paper, we propose and evaluate algorithms for solving the worst-case-coverage deployment problem in ad-hoc wireless sensor net works. The worst-case-coverage deployment problem is to deploy additional sensors in the wireless sensor field to optimize the worst-case coverage. We derive a duality theorem that reveals the close relation between the maximum breach path and the minimum Delaunay cut. The duality theorem is similar to the well-known max-flow-mm-cut theorem in the field of network optimization. The major difference lies in the fact that the object function we study in this paper is nonlinear rather than linear. Based on the duality theorem, we propose an efficient dual algorithm to solve the worst- case-coverage deployment problem. In addition, we propose a genetic algorithm for deploying a number of additional sensors simultaneously. We use analytical proofs and simulation results to justify the usage of the proposed approaches Proposing a new approach to barrier coverage in wireless sensor network.Modeling barrier coverage with stochastic edge-weighted graph.Finding an optimal solution for the network stochastic edge-weighted coverage graph.Comparing the performance of the proposed method with the greedy and optimal methods. Barrier coverage is one of the most important applications of wireless sensor networks. It is used to detect mobile objects are entering into the boundary of a sensor network field. Energy efficiency is one of the main concerns in barrier coverage for wireless sensor networks and its solution can be widely used in sensor barrier applications, such as intrusion detectors and border security. In this work, we take the energy efficiency as objectives of the study on barrier coverage. The cost in the present paper can be any performance measurement and normally is defined as any resource which is consumed by sensor barrier. In this paper, barrier coverage problem is modeled based on stochastic coverage graph first. Then, a distributed learning automata-based method is proposed to find a near optimal solution to the stochastic barrier coverage problem. The stochastic barrier coverage problem seeks to find minimum required number of sensor nodes to construct sensor barrier path. To study the performance of the proposed method, computer simulations are conducted. The simulation results show that the proposed algorithm significantly outperforms the greedy based algorithm and optimal method in terms of number of network barrier paths. We study the problem of achieving maximum barrier coverage by sensors on a barrier modeled by a line segment, by moving the minimum possible number of sensors, initially placed at arbitrary positions on the line containing the barrier. We consider several cases based on whether or not complete coverage is possible, and whether non-contiguous coverage is allowed in the case when complete coverage is impossible. When the sensors have unequal transmission ranges, we show that the problem of finding a minimum-sized subset of sensors to move in order to achieve maximum contiguous or non-contiguous coverage on a finite line segment barrier is NP-complete. In contrast, if the sensors all have the same range, we give efficient algorithms to achieve maximum contiguous as well as non-contiguous coverage. For some cases, we reduce the problem to finding a maximum-hop path of a certain minimum (maximum) weight on a related graph, and solve it using dynamic programming. Barrier coverage in visual camera sensor networks (visual barrier coverage) has important real-world applications like battlefield surveillance, environmental monitoring, and protection of government property. Cost-effective deployment, a fundamental issue of visual barrier coverage, considers how to deploy the fewest camera sensors along the barrier to detect intruders (e.g., capture faces) with desirable performance. Existing visual barrier coverage approaches like full-view coverage require numerous camera sensors for capturing intruders' faces deterministically for any trajectory and facing angle. However, intruders' trajectories and facing angles are bounded and deterministic intruder detection requires many camera sensors for rare intrusion cases. Certain practical applications can tolerate limited intrusion mis-detection given budget limitations. This paper proposes local face-view barrier coverage, a novel concept that achieves statistical barrier coverage in camera sensor networks leveraging intruders' trajectory lengths l along the barrier and head rotation angles δ. Using (l, δ) and other parameters, we derive a rigorous probability bound for intruder detection for local face-view barrier coverage via a feasible deployment pattern. Our detection probability bound and deployment pattern can guide practical camera sensor network deployments with camera sensor budgets. Extensive evaluations show that local face-view barrier coverage requires up to 50 fewer camera sensors than full-view barrier coverage.