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LEO Constellations as a Decentralized GNSS Network: Optimizing PNT Corrections in Space

Xing Liu, Xue Xian Zheng, José A. López-Salcedo, Tareq Y. Al-Naffouri, Gonzalo Seco-Granados

TL;DR

The paper proposes a decentralized onboard GNSS processing framework for large-scale LEO constellations by modeling the constellation as a time-varying spaceborne network and applying a momentum-accelerated gradient-tracking algorithm. This approach allows each satellite to estimate local orbit and clock states while exchanging compact information with neighbors, achieving convergence to a centralized benchmark despite dynamic topology. Numerical experiments with hundreds of satellites demonstrate centimeter-level orbit accuracy and sub-nanosecond clock synchronization, with significant reductions in communication requirements compared to centralized fusion. The results support autonomous, scalable navigation capabilities for future space systems built on onboard cooperative processing.

Abstract

With the rapid expansion of low Earth orbit (LEO) constellations, thousands of satellites are now in operation, many equipped with onboard GNSS receivers capable of continuous orbit determination and time synchronization. This development is creating an unprecedented spaceborne GNSS network, offering new opportunities for network-driven precise LEO orbit and clock estimation. Yet, current onboard GNSS processing is largely standalone and often insufficient for high-precision applications, while centralized fusion is challenging due to computational bottlenecks and the lack of in-orbit infrastructure. In this work, we report a decentralized GNSS network over large-scale LEO constellations, where each satellite processes its own measurements while exchanging compact information with neighboring nodes to enable precise orbit and time determination. We model the moving constellation as a dynamic graph and tailor a momentum-accelerated gradient tracking (GT) method to ensure steady convergence despite topology changes. Numerical simulations with constellations containing hundreds of satellites show that the proposed method matches the accuracy of an ideal centralized benchmark, while substantially reducing communication burdens. Ultimately, this framework supports the development of autonomous and self-organizing space systems, enabling high-precision navigation with reduced dependence on continuous ground contact.

LEO Constellations as a Decentralized GNSS Network: Optimizing PNT Corrections in Space

TL;DR

The paper proposes a decentralized onboard GNSS processing framework for large-scale LEO constellations by modeling the constellation as a time-varying spaceborne network and applying a momentum-accelerated gradient-tracking algorithm. This approach allows each satellite to estimate local orbit and clock states while exchanging compact information with neighbors, achieving convergence to a centralized benchmark despite dynamic topology. Numerical experiments with hundreds of satellites demonstrate centimeter-level orbit accuracy and sub-nanosecond clock synchronization, with significant reductions in communication requirements compared to centralized fusion. The results support autonomous, scalable navigation capabilities for future space systems built on onboard cooperative processing.

Abstract

With the rapid expansion of low Earth orbit (LEO) constellations, thousands of satellites are now in operation, many equipped with onboard GNSS receivers capable of continuous orbit determination and time synchronization. This development is creating an unprecedented spaceborne GNSS network, offering new opportunities for network-driven precise LEO orbit and clock estimation. Yet, current onboard GNSS processing is largely standalone and often insufficient for high-precision applications, while centralized fusion is challenging due to computational bottlenecks and the lack of in-orbit infrastructure. In this work, we report a decentralized GNSS network over large-scale LEO constellations, where each satellite processes its own measurements while exchanging compact information with neighboring nodes to enable precise orbit and time determination. We model the moving constellation as a dynamic graph and tailor a momentum-accelerated gradient tracking (GT) method to ensure steady convergence despite topology changes. Numerical simulations with constellations containing hundreds of satellites show that the proposed method matches the accuracy of an ideal centralized benchmark, while substantially reducing communication burdens. Ultimately, this framework supports the development of autonomous and self-organizing space systems, enabling high-precision navigation with reduced dependence on continuous ground contact.
Paper Structure (10 sections, 38 equations, 6 figures, 2 tables, 1 algorithm)

This paper contains 10 sections, 38 equations, 6 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Spaceborne GNSS Observation Equations
  3. Estimability and Identifiability Analysis of Model Parameters
  4. Network Model for LEO Onboard GNSS Processing
  5. Well-defined Decentralized Formulation
  6. Momentum-Accelerated Gradient Tracking with Orbit Dynamics
  7. Numerical Results
  8. Conclusion
  9. Submatrix Definitions of the Design Matrix
  10. Matrices Used for Rank-Deficiency Elimination

Figures (6)

  • Figure 1: Conceptual illustration of a LEO constellation viewed as a decentralized spaceborne GNSS network. LEO satellites (bright nodes) form a sparse, time-varying inter-satellite communication graph, while each LEO node receives signals from visible GNSS satellites.
  • Figure 2: LEO constellation communication topology across two time scales. Over short horizons, the topology is effectively invariant as links persist despite satellite motion; over longer horizons, the topology changes as satellites move out of range of previous neighbors and establish new links. This motivates modeling the optimization over a periodically invariant (piecewise static) graph sequence $\{\mathcal{G}^{(t)}\}^{T}_{t=1}$.
  • Figure 3: LEO orbit determination error under different processing strategies (meter).
  • Figure 4: LEO time synchronization error under different processing strategies (nanosecond).
  • Figure 5: Convergence behavior measured by MSD. We compare the vanilla GT method with its momentum-accelerated variant, a consensus-only variant, and the combined momentum$+$consensus scheme. The latter corresponds to our proposed method, while the others serve as ablations.
  • ...and 1 more figures