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Robust Cislunar Navigation via LFT-Based $\mathcal{H}_\infty$ Filtering with Bearing-Only Measurements

Raktim Bhattacharya

TL;DR

The paper addresses autonomous cislunar navigation under strongly nonlinear CR3BP dynamics with bearing-only optical measurements. It introduces a Linear Fractional Transformation (LFT) framework to model nonlinear CR3BP dynamics and range-weighted sensing, and designs a full-order H-infinity observer to guarantee L2 performance despite bounded uncertainties. The robust observer is synthesized via salahmuuning of structured uncertainties and LPV representation, with simulations on Near Rectilinear Halo Orbits showing bounded estimation errors and smooth position tracking using flight-representative sensors. The work demonstrates a viable, robust onboard navigation approach for NRHO missions, reducing reliance on ground-based tracking and precise clocks while maintaining performance during comms gaps and occultations.

Abstract

This paper develops a robust estimation framework for cislunar navigation that embeds the Circular Restricted Three-Body Problem (CR3BP) dynamics and bearing-only optical measurements within a Linear Fractional Transformation (LFT) representation. A full-order $\mathcal{H}_\infty$ observer is synthesized with explicit $\mathcal{L}_2$ performance bounds. The formulation yields a nonlinear estimator that operates directly on the governing equations and avoids reliance on local linearizations. Dominant nonlinearities are expressed as structured real uncertainties, while measurement fidelity is represented through range-dependent weighting with Earth-Moon distances reconstructed from line-of-sight geometry. The sensing architecture assumes passive star-tracker-class optical instruments, eliminating the need for time-of-flight ranging or precision clocks. Simulations demonstrate bounded estimation errors and smooth position tracking over multiple orbital periods, with the largest deviations observed in the out-of-plane states, consistent with the stiffness of the vertical dynamics and the limitations of angle-only observability. Application to a Near Rectilinear Halo Orbit (NRHO) illustrates that the framework can achieve robust onboard navigation with bounded estimation errors with flight-representative sensors.

Robust Cislunar Navigation via LFT-Based $\mathcal{H}_\infty$ Filtering with Bearing-Only Measurements

TL;DR

The paper addresses autonomous cislunar navigation under strongly nonlinear CR3BP dynamics with bearing-only optical measurements. It introduces a Linear Fractional Transformation (LFT) framework to model nonlinear CR3BP dynamics and range-weighted sensing, and designs a full-order H-infinity observer to guarantee L2 performance despite bounded uncertainties. The robust observer is synthesized via salahmuuning of structured uncertainties and LPV representation, with simulations on Near Rectilinear Halo Orbits showing bounded estimation errors and smooth position tracking using flight-representative sensors. The work demonstrates a viable, robust onboard navigation approach for NRHO missions, reducing reliance on ground-based tracking and precise clocks while maintaining performance during comms gaps and occultations.

Abstract

This paper develops a robust estimation framework for cislunar navigation that embeds the Circular Restricted Three-Body Problem (CR3BP) dynamics and bearing-only optical measurements within a Linear Fractional Transformation (LFT) representation. A full-order observer is synthesized with explicit performance bounds. The formulation yields a nonlinear estimator that operates directly on the governing equations and avoids reliance on local linearizations. Dominant nonlinearities are expressed as structured real uncertainties, while measurement fidelity is represented through range-dependent weighting with Earth-Moon distances reconstructed from line-of-sight geometry. The sensing architecture assumes passive star-tracker-class optical instruments, eliminating the need for time-of-flight ranging or precision clocks. Simulations demonstrate bounded estimation errors and smooth position tracking over multiple orbital periods, with the largest deviations observed in the out-of-plane states, consistent with the stiffness of the vertical dynamics and the limitations of angle-only observability. Application to a Near Rectilinear Halo Orbit (NRHO) illustrates that the framework can achieve robust onboard navigation with bounded estimation errors with flight-representative sensors.

Paper Structure

This paper contains 13 sections, 35 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Cislunar Dynamics and Sensing Characteristics
  3. The CR3BP Model
  4. Design of Robust Navigation Observer
  5. Background on LFT Modeling of Nonlinear Systems
  6. LFT Modeling of CR3B Dynamics
  7. LFT Models of Onboard Sensing System
  8. Synthesis of Robust $\mathcal{H}_\infty$ Observer
  9. Simulation Results
  10. Simulation Setup
  11. Computation of $r_1$ and $r_2$ from Line-of-Sight Vectors
  12. Observer Implementation and Results
  13. Conclusions

Figures (5)

  • Figure 1: Cislunar Rotating Reference Frame, with $E$ (Earth), $M$ (Moon), and $s$ (Satellite).
  • Figure 2: LFT Representation of Nonlinear Systems.
  • Figure 3: System interconnection for designing and implementing proposed estimators.
  • Figure 4: LFT interconnection for designing robust $\mathcal{H}_\infty$ estimator.
  • Figure 5: Estimation errors using the proposed robust $\mathcal{H}_\infty$ observer.