IEEE Transactions on Wireless Communications | 2019
Characterizing the Impact of SNR Heterogeneity on Time-of-Arrival-Based Localization Outage Probability
Abstract
In localization, an outage occurs if the positioning mean squared error (MSE) exceeds a pre-defined threshold $\\epsilon _{\\mathrm{ th}}$ . For time-of-arrival-based localization, a key factor affecting the MSE is the relative positions of the anchors with respect to the target location. From a design point of view, characterizing the distribution of the MSE over an ensemble of anchor locations as seen from the perspective of a target is essential for providing probabilistic performance guarantees against outage. To solve this difficult problem, previous works have assumed all anchor-target links to have the same SNR (i.e., SNR homogeneity), which neglects the impact of link distance variation on the SNR and the positioning error; for instance, under an inverse-square law pathloss model, the outage probability can differ by orders of magnitude when compared with the homogeneous SNR assumption. In this paper, we derive an approximate expression for the MSE distribution under an inverse-square law pathloss model when the anchors are uniformly distributed around a target. Through simulations, we verify that our approximation can be used to estimate the number of anchors needed so that the outage probability is below 1%.