TDOA-based localization under uniform prior knowledge: Performance bounds and its efficient calculation

The emergence of a myriad of location-based services has imposed a key role on wireless localization systems. The accuracy of such systems can be enhanced by using prior information on the target location area, commonly available through a map or wireless system coverage area. In the map-aware localization context, performance limits have been mainly explored for Time-of-Arrival positioning systems. This paper presents performance bounds for Time-Difference-of-Arrival (TDOA) localization using a uniform prior information of the location area. In particular, the paper derives a closed-form approximation of the Ziv-Zakai lower bound (ZZB) and Bayesian Cramer-Rao lower bound (BCRB). The presented bounds are evaluated under different configurations and compared with the maximum a posteriori (MAP) estimator, which incorporates a priori information about the location area, and with the Cramer-Rao lower bound (CRB) and the maximum likelihood (ML) estimator, both without prior information. Numerical results show that the proposed ZZB and BCRB exploit the a priori knowledge to increase the localization accuracy and provide tighter performance lower bounds of a MAP estimator, and are properly matched to the actual limits of practical positioning systems. In addition, the proposed closed-form ZZB approximation allows us to avoid numerical evaluation of integrals needed to compute BCRB and exact ZZB, while maintaining similar accuracy and decreasing the computational complexity.