Reflection Map Construction: Enhancing and Speeding Up Indoor Localization

This paper introduces an indoor localization method that utilizes fixed reflector objects within the environment, leveraging a base station (BS) or users equipped with Angle of Arrival (AoA) and Time of Arrival (ToA) measurement capabilities. The localization process consists of two phases. In the offline phase, using specific strategy effective reflector points within a specific region are identified. In the online phase, a maximization problem is solved to locate users based on BS measurements and information gathered during the offline phase. Through analysis and simulation results, we demonstrate that with the same number of training points, the performance of the proposed localization technique surpasses that of fingerprint-based techniques. Additionally, we show that localizing an unknown user does not require a large number of training points throughout the entire environment; it is sufficient to place these training points on the boundary of the environment. We introduce the reflectivity parameter (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{r}$ </tex-math></inline-formula>), which quantifies the average number of first-order reflection paths from the transmitter to the receiver, and demonstrate its impact on localization accuracy. The log-scale accuracy ratio (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{a}$ </tex-math></inline-formula>) is defined as the logarithmic function of the localization area divided by the localization ambiguity area, serving as an indicator of accuracy. We show that in scenarios where the Signal-to-Noise Ratio (SNR) approaches infinity, and without a line of sight (LoS) link, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{a}$ </tex-math></inline-formula> is upper-bounded by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n_{r} \log _{2}\left ({{1 + \frac {\mathrm {Vol}({\mathcal {S}}_{A})}{\mathrm {Vol}({\mathcal {S}}_{\epsilon }({\mathcal {M}}_{s}))}}}\right)$ </tex-math></inline-formula>, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Vol}({\mathcal {S}}_{A})$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Vol}({\mathcal {S}}_{\epsilon }({\mathcal {M}}_{s}))$ </tex-math></inline-formula> represent the areas of the localization region and the area containing all reflector points with a probability of at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1 - \epsilon $ </tex-math></inline-formula>, respectively.