New Error-Bounds With NLOS TOA Localization and the Applications

Non-line-of-sight (NLOS) localization has been a focus in mobile communications over the years. Many ways have been proposed to solve this problem. Among them, wide-band localization with time-of-arrival (TOA) technique can achieve high accuracy. For TOA, if no prior information of NLOS ranging error is provided, the received signal from NLOS path will not affect the localization accuracy. In contrast, if the prior distribution of ranging error is known, maximum a posteriori can be used to leverage the NLOS signals for less localization error, which can be expressed by the Bayesian Cramer-Rao lower bound (B-CRLB). Though existing works have provided the B-CRLB applicable to some distributions, it is not compatible to general applications. To address this research gap, we derive and propose a new B-CRLB that can be applied to arbitrary statistical distributions. In particular, we provide the closed-form expressions of the bounds for three specific distributions of Gaussian, exponential and Erlang. Numerical simulations are performed to verify the effectiveness and potential application of the proposed new lower-bounds.