We analyze the statistical properties of the coverage of a one-dimensional path induced by a two-dimensional nonhomogeneous random sensor network. Sensor locations form a nonhomogeneous Poisson process and sensing area for the sensors are circles of random independent and identically distributed radii. We first characterize the coverage of a straight-line path by the nonhomogeneous one-dimensional Boolean model. We then obtain an equivalent M t /G t /∞, queue whose busy period statistics is the same as the coverage statistics of the line. We obtain k -coverage statistics for an arbitrary point and a segment on the x -axis. We provide upper and lower bounds on the probability of complete k -coverage of a segment. We illustrate all our results for the case of the sensor deployment having a “Laplacian” intensity function.

We consider a network of spatially distributed sensors deployed to track the intensity of a diffusing source whose location is fixed, but unknown. The sensors make discrete time concentration measurements and communicate them to a fusion center. We propose a recursive algorithm that can be used at the fusion center, which takes in the latest concentration measurements as input and produces an estimate for the source location and latest intensity as the output. The performance of the algorithm is verified through simulations.

We develop generalized method of moments estimators to estimate the parameters of a two-dimensional Boolean random field from measurements made on the coverage process induced on a straight line in the field. This is distinct from earlier studies e.g. P. Hall (1988), I. Molchanov and D. Stoyan (2004), where the parameters of a two-dimensional Boolean field are obtained from the coverage properties of a two-dimensional set. This problem has applications in radio-active field monitoring.

In a sensor network, the points in the operational area that are suitably sensed are a two-dimensional spatial coverage process. For randomly deployed sensor networks, typically, the network coverage of two-dimensional areas is analyzed. However, in many sensor network applications, e.g., tracking of moving objects, the sensing process on paths, rather than in areas, is of interest. With such an application in mind, we analyze the coverage process induced on a one-dimensional path by a sensor network that is modeled as a two-dimensional Boolean model. In the analysis, the sensor locations form a spatial Poisson process of density \lambda and the sensing regions are circles of i.i.d. random radii. We first obtain a strong law for the fraction of a path that is k{\hbox{-}}{\rm sensed}, i.e., sensed by (\geq k) sensors. Asymptotic path-sensing results are obtained under the same limiting regimes as those required for asymptotic coverage by a two-dimensional Boolean model. Interestingly, the asymptotic fraction of the area that is 1-sensed is the same as the fraction of a path that is 1-sensed. For k = 1, we also obtain a central limit theorem that shows that the asymptotics converge at the rate of \Theta(\lambda^{1/2}) for k = 1. For finite networks, the expectation and variance of the fraction of the path that is k{\hbox{-}}{\rm sensed} is obtained. The asymptotics and the finite network results are then used to obtain the critical sensor density to k{\hbox{-}}{\rm sense} a fraction \alpha_{k} of an arbitrary path with very high probability is also obtained. Through simulations, we then analyze the robustness of the model when the sensor deployment is nonhomogeneous and when the paths are not rectilinear. Other path coverage measures like breach, support, "length to first sense,? and sensing continuity measures like holes and clumps are also characterized. Finally, we discuss some generalizations of the results like characterization of the coverage process of m{\hbox{-}}{\rm dimensional} "straight line paths? by n{\hbox{-}}{\rm dimensional}, n > m, sensor networks.

We analyze the statistical properties of the coverage of a one-dimensional path induced by a two dimensional non homogeneous random sensor network. Sensor locations form a non homogeneous Poisson process and coverage area of each sensor is a circle of random i.i.d. radius. We first describe the one-dimensional coverage process on the line and describe an equivalent time-inhomogeneous Mt/Gt/infin queue whose busy period statistics will be equal to the coverage statistics of the line. We also obtain properties like conditional forward and backward hole-lengths. Additional results for the case of fixed coverage radius are obtained. We also obtain some numerical results for a deployment that has a 'Laplacian' intensity function.