Positioning Algorithms for Wireless Sensor Networks

Position information is often one of the key requirements for a wireless sensor network (WSN) to function as intended. Due to drawbacks in using GPS or having to manually setting sensor positions, extracting the position information by means of the network itself has been extensively studied in the literature. In this approach, it is commonly assumed that there are a few sensor nodes with known positions, called reference nodes, and some type of measurements are taken between different nodes. During the last decade, a number of positioning algorithms have been proposed for the positioning problem. Evaluating the performance of various algorithms based on practical data is an important step in classifying different positioning methods. Paper A studies the performance of different approaches through real range measurements made by two ultra-wideband devices. The main result of Paper A is that no positioning algorithm uniformly shows the best performance in different situations. Paper B considers the positioning problem using received signal strength measurements when the channel parameters (transmit power and path-loss exponent) are unknown in sensor nodes. Assuming fixed values for the channel parameters, the positioning problem is formulated as finding a point in the intersection of a number of halfplanes (in a 2D network). The well-known approach projection onto convex sets (POCS) is employed to solve the problem. The proposed method gives a good coarse estimate for the positioning problem. In the literature, it has been shown that cooperation between reference nodes can improve the position estimate. To cope with difficulty in solving the optimal estimator in this type of network, which are mainly due to nonlinearity and nonconvexity issues, a two-step linear estimator is proposed in Paper C to solve the positioning problem. In the first step, a coarse estimate is obtained, and it is refined in the second step. For sufficiently high signal-to-noise-ratios, the proposed estimator attains the optimal performance; i.e., it attains the Cramér-Rao lower bound. Finally, Paper D formulates the positioning problem as a convex feasibility problem (CFP) for both non-cooperative and cooperative networks. To solve a CFP, two methods based on POCS and outer-approximation are employed (two geometric solutions). The properties of POCS for non-cooperative networks are reviewed and an upper-bound on the position error of POCS is proposed. Simulation results show that the positioning algorithms based on geometric solutions are more robust against non-line-of-sight compared to proposed statistical approaches such as nonlinear least squares.