Reflection Map Construction: Enhancing and Speeding Up Indoor Localization

Abstract: This paper introduces an indoor localization method using fixed reflector objects within the environment, leveraging a base station (BS) equipped with Angle of Arrival (AoA) and Time of Arrival (ToA) measurement capabilities. The localization process includes two phases. In the offline phase, we identify effective reflector points within a specific region using significantly fewer test points than typical methods. In the online phase, we solve a maximization problem to locate users based on BS measurements and offline phase information. We introduce the reflectivity parameter ((n_r)), which quantifies the typical number of first-order reflection paths from the transmitter to the receiver, demonstrating its impact on localization accuracy. The log-scale accuracy ratio ((R_a)) is defined as the logarithmic function of the localization area divided by the localization ambiguity area, serving as an accuracy indicator. We show that in scenarios where the Signal-to-Noise Ratio (SNR) approaches infinity, without a line of sight (LoS) link, (R_a) is upper-bounded by (n_r \log_{2}\left(1 + \frac{\mathrm{Vol}(\mathcal{S}A)}{\mathrm{Vol}(\mathcal{S}{\epsilon}(\mathcal{M}s))}\right)). Here, (\mathrm{Vol}(\mathcal{S}_A)) and (\mathrm{Vol}(\mathcal{S}{\epsilon}(\mathcal{M}_s))) represent the areas of the localization region and the area containing all reflector points with a probability of at least (1 - \epsilon), respectively.