Blind Received Signal Strength Difference Based Source Localization With System Parameter Errors

The problem of passive source localization has been extensively studied due to its many applications in signal processing and wireless communications. Signal strength-based localization methods have the advantages of low cost and simple implementation. In this paper, blind source localization with unknown transmit power and unknown path loss exponent is considered based on the received signal strength difference (RSSD). A nonlinear RSSD-based model is formulated for systems perturbed by noise. Solutions obtained using conventional least squares methods suffer from significant performance degradation as they only consider errors in the data vector. Thus, an extended total least squares (ETLS) method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relationship between the observation matrix and data vector. The nonlinear and nonconvex RSSD-based localization problem is then transformed to an ETLS problem with fewer constraints. This is transformed to a convex semidefinite programming (SDP) problem using relaxation. The corresponding ETLS-SDP method is extended to the case with an unknown path loss exponent to jointly estimate the unknown source location and path loss exponent without resorting to transmit power estimation which is sensitive to errors. The mean squared error of the proposed ETLS method is obtained and the corresponding Cramér-Rao lower bound (CRLB) is derived as a performance benchmark. Performance results are presented that show that the RSSD-based ETLS-SDP method attains the CRLB for a sufficiently large signal-to-noise ratio (SNR).