A hybrid SS-ToA wireless NLoS geolocation based on path attenuation: Mobile position estimation

The mobile position estimation using time-of-arrival (ToA) is considered for the wireless NLoS geolocation exploring a signal strength (SS) based on path loss. As exploited the path attenuation, a hybrid SS-ToA approach indicates a performance improvement compared with the usual ToA method. To realize this prospect, it calls for an estimator to determine the mobile position from the time delay. In this paper, we show that the use of line-of-sight (LoS) time delay provides the same performance as that given by using both the LoS and non-LoS (NLoS) time delays. We then propose least squares (LS), weighted least squares (WLS) and maximum likelihood (ML) to estimate the mobile position. Theoretical performance of the LS and WLS is analyzed. It reveals that for different LoS time delay error variances, the LS error variance is larger than the WLS error variance, which is equal to the Cramér-Rao bound (CRB). Numerical results illustrate that the time delay performance analysis is accurate when the time delay estimate is close to its true value, i.e. for small time delay error variance. For high SNR and large effective bandwidth, the LS cannot provide the performance compared with the CRB, whereas the WLS and ML are statistically efficient.