A Hybrid SS–ToA Wireless NLoS Geolocation Based on Path Attenuation: ToA Estimation and CRB for Mobile Position Estimation

We propose a new hybrid wireless geolocation scheme that requires only one observation quantity, namely, the received signal. The attenuation model is explored herein to capture the propagation features from the received signal. Thus, it provides a more accurate approach for wireless geolocation. To investigate geolocation accuracy, we consider the time-of-arrival (ToA) estimation in the presence of path attenuation. The maximum-correlation (MC) estimator is revisited, and the exact maximum-likelihood (ML) estimator is derived to estimate the ToA. The error performance of the ToA estimates is derived using a Taylor expansion. It is shown that the ML estimate is unbiased and has a smaller error variance than the MC estimate. Numerical results illustrate that, for a low effective bandwidth, the ML estimator well outperforms the MC estimator. Afterward, we derive the CramÉr–Rao bound (CRB) for the mobile position estimation. The obtained result, which is applicable to any value of path loss exponents, gives a generalized form of the CRB for the ordinary geolocation approach. In seven hexagonal cells, numerical examples show that the accuracy of the mobile position estimation exploring the path loss is improved compared with that obtained by the usual geolocation.