Cooperative Received Signal Strength-Based Sensor Localization With Unknown Transmit Powers

• Published in: IEEE transactions on signal processing Vol. 61; no. 6; pp. 1389 - 1403
• Main Authors: Vaghefi, R. M., Gholami, M. R., Buehrer, R. M., Strom, E. G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Complexity theory; Computational complexity; cooperative sensor localization; Detection, estimation, filtering, equalization, prediction; Estimators; Exact sciences and technology; Information, signal and communications theory; linear least squares (LLS); Localization; maximum likelihood (ML); Maximum likelihood estimation; Networks; Nuisance; Optimization; path loss exponent (PLE); Position (location); Power measurement; Received Signal Strength (RSS); semidefinite programming (SDP); Sensors; Signal and communications theory; Signal processing algorithms; Signal, noise; Symmetric matrices; Telecommunications and information theory; transmit power; Wireless sensor networks; Performance evaluation; Non convex programming; Nuisance parameter; linear least squares (LLS); Data transmission; Power supply; Optimization; semidefinite programming (SDP); Relaxation; maximum likelihood (ML); Least squares method; Received Signal Strength (RSS); Target detection; Signal detection; Cramer Rao inequality; path loss exponent (PLE); transmit power; Computer simulation; cooperative sensor localization; Measurement sensor; Nonlinear problems; Algorithm; Computational complexity; Source localization; Signal processing; Maximum likelihood; Transmission loss; Sensor array
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2012.2232664

Cooperative localization (also known as sensor network localization) using received signal strength (RSS) measurements when the source transmit powers are different and unknown is investigated. Previous studies were based on the assumption that the transmit powers of source nodes are the same and perfectly known which is not practical. In this paper, the source transmit powers are considered as nuisance parameters and estimated along with the source locations. The corresponding Cramér-Rao lower bound (CRLB) of the problem is derived. To find the maximum likelihood (ML) estimator, it is necessary to solve a nonlinear and nonconvex optimization problem, which is computationally complex. To avoid the difficulty in solving the ML estimator, we derive a novel semidefinite programming (SDP) relaxation technique by converting the ML minimization problem into a convex problem which can be solved efficiently. The algorithm requires only an estimate of the path loss exponent (PLE). We initially assume that perfect knowledge of the PLE is available, but we then examine the effect of imperfect knowledge of the PLE on the proposed SDP algorithm. The complexity analyses of the proposed algorithms are also studied in detail. Computer simulations showing the remarkable performance of the proposed SDP algorithm are presented.