Convex optimization algorithms for cooperative RSS-based sensor localization

To obtain a global solution for the source location estimates, the cost function of RSS-based sensor localization is relaxed as convex optimization problem which can be solved by interior point method. Weighted squared least square (WSLS) and weighted least square (WLS) based optimization functions are proposed to locate the source nodes. The corresponding semidefinite programming (SDP), second-order cone program (SOCP) and mixed SOC/SDP algorithms are designed by considering the known or unknown transmit powers. The computational complexity of the proposed algorithms is derived by analyzing the number of variables and equality constraints produced in the relaxation. The simulations show that the mixed SOC/SDP runs faster than the SDP, although the algorithms have the approximately equal accuracy performance. Whether the transmit power is known or not, the accuracy performance of the WLS-SDP is better than that of the WSLS-SDP and WSLS-SOC/SDP algorithms. However the computational complexity of the WLS-SDP is greatly larger than that of WSLS-SOC/SDP and WSLS-SDP due to a large number of variables.