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DRL-Based Beam Positioning for LEO Satellite Constellations with Weighted Least Squares

Po-Heng Chou, Chiapin Wang, Kuan-Hao Chen, Wei-Chen Hsiao

TL;DR

This work tackles real-time, CSI-free positioning in dynamic multi-beam LEO satellite systems by coupling a reinforcement-learning policy with an augmented weighted least squares estimator. The proposed DQN-WLS framework learns beam weighting directly from uplink pilot responses and beam geometry, enabling robust localization under interference and GNSS-denied conditions while maintaining low computational complexity. Empirical results show a 99.3% reduction in mean positioning error relative to a geometry-based baseline, achieving a 0.395 m RMSE with near real-time inference, demonstrating strong potential for onboard, autonomous beam management in NTN/LEO deployments.

Abstract

In this paper, we propose a reinforcement learning based beam weighting framework that couples a policy network with an augmented weighted least squares (WLS) estimator for accurate and low-complexity positioning in multi-beam LEO constellations. Unlike conventional geometry or CSI-dependent approaches, the policy learns directly from uplink pilot responses and geometry features, enabling robust localization without explicit CSI estimation. An augmented WLS jointly estimates position and receiver clock bias, improving numerical stability under dynamic beam geometry. Across representative scenarios, the proposed method reduces the mean positioning error by 99.3% compared with the geometry-based baseline, achieving 0.395 m RMSE with near real-time inference.

DRL-Based Beam Positioning for LEO Satellite Constellations with Weighted Least Squares

TL;DR

This work tackles real-time, CSI-free positioning in dynamic multi-beam LEO satellite systems by coupling a reinforcement-learning policy with an augmented weighted least squares estimator. The proposed DQN-WLS framework learns beam weighting directly from uplink pilot responses and beam geometry, enabling robust localization under interference and GNSS-denied conditions while maintaining low computational complexity. Empirical results show a 99.3% reduction in mean positioning error relative to a geometry-based baseline, achieving a 0.395 m RMSE with near real-time inference, demonstrating strong potential for onboard, autonomous beam management in NTN/LEO deployments.

Abstract

In this paper, we propose a reinforcement learning based beam weighting framework that couples a policy network with an augmented weighted least squares (WLS) estimator for accurate and low-complexity positioning in multi-beam LEO constellations. Unlike conventional geometry or CSI-dependent approaches, the policy learns directly from uplink pilot responses and geometry features, enabling robust localization without explicit CSI estimation. An augmented WLS jointly estimates position and receiver clock bias, improving numerical stability under dynamic beam geometry. Across representative scenarios, the proposed method reduces the mean positioning error by 99.3% compared with the geometry-based baseline, achieving 0.395 m RMSE with near real-time inference.

Paper Structure

This paper contains 18 sections, 15 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Coordinate System and Beam Geometry
  4. Channel Model
  5. Observation Model
  6. Augmented Weighted Least Squares (WLS)
  7. Problem Formulation
  8. DQN-WLS Based Beam Positioning
  9. Markov Decision Process Formulation
  10. Network Architecture
  11. Training Procedure
  12. Simulation Results and Analysis
  13. Experimental Setup
  14. Convergence Behavior
  15. Positioning Visualization
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Training convergence of cumulative reward and positioning error for PPO, DDQN, DQN, and the proposed DQN-WLS.
  • Figure 2: Positioning visualization at Episode 1000 under identical beam geometry and noise conditions. The yellow star denotes the estimated UT position, and the black circle indicates the ground truth. Compared with the geometry-driven ALG-B and standard DQN, the proposed DQN-WLS aligns closely with the ground truth and yields the smallest residual error.