Emitter localization using received-strength-signal data

This paper considers a scenario in which signals from an emitter at an unknown location are received at a number of different collinear locations. The receiver can determine the received signal strength, but no other parameters of the signal. Postulating a log-normal transmission model with a constant but unknown path loss exponent and, also, an unknown transmit power and known noise variance, the paper shows how the localization problem can be solved, along with estimating the parameters appearing in the log-normal transmission model, given enough measurements at different points. The log-normal transmission model parameters can be determined first. An algorithm based on construction of a Gram matrix is proposed to estimate the path loss exponent and transmit power parameters from the received noisy power measurements. Since the estimated parameters are biased due to the nonlinearity of the model and constraints, a pattern-matching algorithm is also proposed to remove the bias in the estimates. The distances corresponding to the different received signal strength measurements can then be bounded, and finally the location estimation is formulated as a convex optimization problem where the estimated distances are used as the new measurements. Simulation results are finally provided to assess the efficacy of the proposed methods in the parameter and location estimation.