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Outlier-Resistant Fusion for Multi-static Positioning using 5G NR Signals

Maximiliano Rivera Figueroa, Jannis Held, Pradyumna Kumar Bishoyi, Marina Petrova

Abstract

Indoor positioning faces ongoing challenges due to complex propagation conditions, such as multipath propagation, signal blockages, and intrinsic target characteristics that substantially impact measurement reliability and positioning accuracy. Existing methods, in particular Least Squares (LS), frequently struggle to maintain robustness when confronted with unreliable observations caused by multipath interactions and extended targets. In this work, we propose an outlier-resistant algorithm designed to mitigate the impact of outlier measurements and accurately estimate the position of an extended target in multipath-rich environments. We develop a two-step algorithm in which an initial coarse position estimate is obtained using the angle-of-arrival (AoA) and subsequently refined using the Cauchy loss function to suppress outliers. The numerical results confirm that the proposed algorithm improves robustness and accuracy, outperforming existing benchmark methods, such as Iterative Reweighted Least Squares (IRLS), LS, and Huber loss function, and achieving a positioning error of less than $70$ cm in $90\%$ of cases. Its effectiveness in mitigating multipath effects is further assessed by comparing tracking performance in cluttered and empty room scenarios.

Outlier-Resistant Fusion for Multi-static Positioning using 5G NR Signals

Abstract

Indoor positioning faces ongoing challenges due to complex propagation conditions, such as multipath propagation, signal blockages, and intrinsic target characteristics that substantially impact measurement reliability and positioning accuracy. Existing methods, in particular Least Squares (LS), frequently struggle to maintain robustness when confronted with unreliable observations caused by multipath interactions and extended targets. In this work, we propose an outlier-resistant algorithm designed to mitigate the impact of outlier measurements and accurately estimate the position of an extended target in multipath-rich environments. We develop a two-step algorithm in which an initial coarse position estimate is obtained using the angle-of-arrival (AoA) and subsequently refined using the Cauchy loss function to suppress outliers. The numerical results confirm that the proposed algorithm improves robustness and accuracy, outperforming existing benchmark methods, such as Iterative Reweighted Least Squares (IRLS), LS, and Huber loss function, and achieving a positioning error of less than cm in of cases. Its effectiveness in mitigating multipath effects is further assessed by comparing tracking performance in cluttered and empty room scenarios.
Paper Structure (10 sections, 16 equations, 4 figures, 1 algorithm)

This paper contains 10 sections, 16 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Position Estimation in Multi-static Systems
  4. Proposed Solution
  5. Finding the Optimal Position
  6. Complexity Analysis
  7. Performance Evaluation
  8. Setup and Scenarios
  9. Simulation Results and Discussion
  10. Conclusions

Figures (4)

  • Figure 1: From top to bottom: (a) QD raytracer illustration, (b) Indoor scenario. The blue line is the path of the target; the red squares indicate the gNBs, and the crossed rectangles represent objects placed in the room.
  • Figure 2: From top to bottom: (a) CDF of the position error of \ref{['problem:P1']}, which uses one transmitter at a time, and \ref{['problem:P2']}, which employs a round-robin approach to fuse all measurements. (b) Positioning error comparison between the proposed algorithm and benchmarks. PPR: Proposed RR.
  • Figure 3: Root mean square error (RMSE) of the position estimation as a function of $\alpha$ (top) and $\eta$ (bottom).
  • Figure 4: From top to bottom: (a) Tracking performance on the proposed scenario, (b) Tracking performance for an empty room scenario.