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Constructing Indoor Region-based Radio Map without Location Labels

Zheng Xing, Junting Chen

TL;DR

A signal subspace model with a sequential prior is constructed for the RSS data, and an integrated segmentation and clustering algorithm is developed, which is shown to find the globally optimal solution in a special case.

Abstract

Radio map construction requires a large amount of radio measurement data with location labels, which imposes a high deployment cost. This paper develops a region-based radio map from received signal strength (RSS) measurements without location labels. The construction is based on a set of blindly collected RSS measurement data from a device that visits each region in an indoor area exactly once, where the footprints and timestamps are not recorded. The main challenge is to cluster the RSS data and match clusters with the physical regions. Classical clustering algorithms fail to work as the RSS data naturally appears as non-clustered due to multipaths and noise. In this paper, a signal subspace model with a sequential prior is constructed for the RSS data, and an integrated segmentation and clustering algorithm is developed, which is shown to find the globally optimal solution in a special case. Furthermore, the clustered data is matched with the physical regions using a graph-based approach. Based on real measurements from an office space, the proposed scheme reduces the region localization error by roughly 50% compared to a weighted centroid localization (WCL) baseline, and it even outperforms some supervised localization schemes, including k-nearest neighbor (KNN), support vector machine (SVM), and deep neural network (DNN), which require labeled data for training.

Constructing Indoor Region-based Radio Map without Location Labels

TL;DR

A signal subspace model with a sequential prior is constructed for the RSS data, and an integrated segmentation and clustering algorithm is developed, which is shown to find the globally optimal solution in a special case.

Abstract

Radio map construction requires a large amount of radio measurement data with location labels, which imposes a high deployment cost. This paper develops a region-based radio map from received signal strength (RSS) measurements without location labels. The construction is based on a set of blindly collected RSS measurement data from a device that visits each region in an indoor area exactly once, where the footprints and timestamps are not recorded. The main challenge is to cluster the RSS data and match clusters with the physical regions. Classical clustering algorithms fail to work as the RSS data naturally appears as non-clustered due to multipaths and noise. In this paper, a signal subspace model with a sequential prior is constructed for the RSS data, and an integrated segmentation and clustering algorithm is developed, which is shown to find the globally optimal solution in a special case. Furthermore, the clustered data is matched with the physical regions using a graph-based approach. Based on real measurements from an office space, the proposed scheme reduces the region localization error by roughly 50% compared to a weighted centroid localization (WCL) baseline, and it even outperforms some supervised localization schemes, including k-nearest neighbor (KNN), support vector machine (SVM), and deep neural network (DNN), which require labeled data for training.
Paper Structure (37 sections, 9 theorems, 76 equations, 5 figures, 4 tables, 2 algorithms)

This paper contains 37 sections, 9 theorems, 76 equations, 5 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Subspace Model for the Region-based Radio Map
  4. Sequential Data Collection and the Graph Model
  5. Probability Model with a Sequential Prior
  6. Subspace Feature Extraction and Region Matching
  7. Subspace Feature via Maximum-Likelihood
  8. Matching Clusters to Physical Regions
  9. Clustering via Segmentation for Sequential Data
  10. Asymptotic Property for Small $\beta$
  11. Asymptotic Consistency for Large $N$
  12. The Property of the Deterministic Proxy $F_{k}(\tau_{k})$
  13. A Merge-and-Split Algorithm under the Proxy Cost
  14. Convergence and Optimality
  15. Merge-and-Split Clustering for Sequential Data
  16. ...and 22 more sections

Key Result

Proposition 1

As $\beta\to0$, we have uniformly for every sequence $\bm{\tau}$ satisfying the constraint (eq:P01-constraint).

Figures (5)

  • Figure 1: A $30\times16$$\text{m}^{2}$indoor area deployed with 21 sensors (blue icons) partitioned into 10 non-overlapping regions (green dashed rectangles), where the red circles refers to the reference region center.
  • Figure 2: a) Percentage of the sum of the first $d$ dominant eigenvalues of the covariance matrix of the data collected from Region 1. (b) Similarity scores $[0,1]$ between subspaces, where 0 means the two subspaces are orthogonal and 1 means identical.
  • Figure 3: Convergence of the proposed algorithms, where the curves marked with R represents the mean trajectories for 20 independent random initializations.
  • Figure 4: Verification of the unimodality, the flatness, and the monotonicity near boundary of the cost function.
  • Figure 5: (a) Region localization error of our method versus the time interval for collecting the training data. (b) Region localization error at each region, where the regions are arranged in an increasing order of their sizes.

Theorems & Definitions (18)

  • Remark 1
  • Proposition 1: Asymptotic Hardening
  • proof
  • Proposition 2: Asymptotic Consistency
  • proof
  • Proposition 3: Unimodality
  • proof
  • Proposition 4: Flatness
  • proof
  • Proposition 5: Monotonicity near Boundary
  • ...and 8 more