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Reflection Map Construction: Enhancing and Speeding Up Indoor Localization

Milad Johnny, Shahrokh Valaee

TL;DR

This paper presents an indoor localization approach that exploits fixed environmental reflectors by combining an offline reflector-map construction stage with an online localization stage at a BS equipped with AoA/ToA capabilities. The offline phase identifies effective reflector points using far fewer measurements than fingerprint databases, while the online phase localizes the user by maximizing a likelihood-like function that leverages the reflector map and measurement uncertainties. The authors introduce a reflectivity parameter $n_r$ and define the log-scale accuracy ratio $R_a$, deriving an upper bound on $R_a$ in high-SNR non-LoS scenarios and relating localization performance to the size of the reflector-covering region ${\mathcal S}_{\epsilon}(\mathcal M_s)$. A fast pre-processing routine restricts the search area to a region ${\mathcal K}({\mathcal M_e})$, followed by a gradient-ascent optimization to obtain the user location, with simulations showing significant efficiency gains over fingerprinting and improved resilience to measurement noise. The framework supports practical deployment and suggests strategies, such as introducing precise artificial reflectors (e.g., corner reflectors or RIS) to increase $n_r$ and enhance localization accuracy without enlarging the reflector volume.

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 \(n_r \log_{2}\left(1 + \frac{\mathrm{Vol}(\mathcal{S}_A)}{\mathrm{Vol}(\mathcal{S}_ε(\mathcal{M}_s))}\right)\). Here, \(\mathrm{Vol}(\mathcal{S}_A)\) and \(\mathrm{Vol}(\mathcal{S}_ε(\mathcal{M}_s))\) represent the areas of the localization region and the area containing all reflector points with a probability of at least \(1 - ε\), respectively.

Reflection Map Construction: Enhancing and Speeding Up Indoor Localization

TL;DR

This paper presents an indoor localization approach that exploits fixed environmental reflectors by combining an offline reflector-map construction stage with an online localization stage at a BS equipped with AoA/ToA capabilities. The offline phase identifies effective reflector points using far fewer measurements than fingerprint databases, while the online phase localizes the user by maximizing a likelihood-like function that leverages the reflector map and measurement uncertainties. The authors introduce a reflectivity parameter and define the log-scale accuracy ratio , deriving an upper bound on in high-SNR non-LoS scenarios and relating localization performance to the size of the reflector-covering region . A fast pre-processing routine restricts the search area to a region , followed by a gradient-ascent optimization to obtain the user location, with simulations showing significant efficiency gains over fingerprinting and improved resilience to measurement noise. The framework supports practical deployment and suggests strategies, such as introducing precise artificial reflectors (e.g., corner reflectors or RIS) to increase and enhance localization accuracy without enlarging the reflector volume.

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 (), 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 () 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, is upper-bounded by \(n_r \log_{2}\left(1 + \frac{\mathrm{Vol}(\mathcal{S}_A)}{\mathrm{Vol}(\mathcal{S}_ε(\mathcal{M}_s))}\right)\). Here, \(\mathrm{Vol}(\mathcal{S}_A)\) and \(\mathrm{Vol}(\mathcal{S}_ε(\mathcal{M}_s))\) represent the areas of the localization region and the area containing all reflector points with a probability of at least , respectively.
Paper Structure (22 sections, 7 theorems, 65 equations, 11 figures)

This paper contains 22 sections, 7 theorems, 65 equations, 11 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Order of Reflections
  4. Finding Physical Locations of Environmental Reflectors
  5. User Placement Strategy for the Reflection Map Construction
  6. Effective Reflector Points Construction
  7. Localization Accuracy Lower Bound and Proposed Strategy
  8. Localization Accuracy Lower Bound
  9. Localization Strategy
  10. Pre-processing Technique
  11. Dividing the Space
  12. Sector-based Selection
  13. Defining Local Regions
  14. Final Localization Region
  15. Gradient Ascent Algorithm for Optimization
  16. ...and 7 more sections

Key Result

Lemma 1

Considering ${\bf p}_b=(0,0)$ and $c_0 \tau_i > \lvert{{\bf p}_u }\rvert$ the location of the corresponding reflector ${\bf p}_{s_i}=(x_{s_i},y_{s_i})$ can be calculated as follows: where $\phi$ represents the angle of the line connecting the transmitter to the receiver with respect to the x-axis.

Figures (11)

  • Figure 1: Block diagram of proposed indoor localization strategy
  • Figure 2: Part (a) illustrates a confined boundary environment, featuring a transmitter with two trajectory paths and a receiver located in a specific position. The transmitter can vary its location for signal transmission. For each transmitter location, a subset of reflector objects situated along the boundary of the environment becomes activated. In (b), the transmitter, when positioned along the boundary of the empty localization regions $\mathcal{R}_1$ and $\mathcal{R}_2$ can identify all the effective reflectors on these regions.
  • Figure 3: A convex RoL divided by $m$ vertical and $k$ horizontal lines, where each parallel line spaced by value $\delta$. The length of the side of RoL is at least $2~\max(m,n) \delta$.
  • Figure 4: Lower bound $\frac{\mathrm{Vol}(\mathcal{S}_u)}{\mathrm{Vol} \left({\mathcal{S}_{A}}\right)}$ as a function $\frac{ \mathrm{Vol}(\mathcal{S}_{A})}{\mathrm{Vol}\left({\mathcal{S}_{\epsilon}(\mathcal{M}_s)}\right)}$ for different values $n_r$.
  • Figure 5: Sub-figure (a) shows the layout of our environment consisting of an infinity number of reflector points which represent the set $\mathcal{S}_{\epsilon}(\mathcal{M}_s)$. Sub-figure (b) shows the location of test points.
  • ...and 6 more figures

Theorems & Definitions (18)

  • Lemma 1
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Definition 5
  • ...and 8 more