A hybrid SS-TOA wireless geolocation based on path attenuation under imperfect path loss exponent

We consider the wireless geolocation using the time of arrival (ToA) of radio signals in a cellular setting. The main concern in this paper involves the effects of the error knowledge of the path loss exponent (PLE). We derive the asymptotic error performance of the maximum likelihood (ML) estimator under the imperfect PLE. We point out that a previous method provides inaccurate performance prediction and then present a new method based on the Taylor series expansion. Numerical examples illustrate that the Taylor analysis captures the bias and the error variance of the ML estimator under the imperfect PLE better than the conventional method. Simulation results also illustrate that in the threshold region, the ML estimator outperforms the MC estimator even in the presence of the PLE error. However, in the asymptotic region the MC estimator and the ML estimator with the perfect PLE outperform the ML estimator under the imperfect PLE.