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Optimal Sensing Precision for Celestial Navigation Systems in Cislunar Space using LPV Framework

Eliot Nychka, Raktim Bhattacharya

TL;DR

This work tackles robust onboard celestial navigation in cislunar space by casting the nonlinear CR3BP dynamics as a linear parameter-varying (LPV) system and designing observers with guaranteed estimation error bounds. It introduces two convex optimization formulations to jointly optimize the LPV observer gain and the per-sensor precision, ensuring a user-specified bound on the estimation error in either the $\mathcal{H}_2$ or $\mathcal{H}_\infty$ sense. The approach yields a sensor-precision vector $\beta$ (with $\kappa_i = \sqrt{\beta_i}$ or $\sqrt{\beta_i/\gamma}$) and an observer gain $L = X^{-1}Y$ from LMIs that enforce $\|G_{\bar w \rightarrow \epsilon}(s,\rho)\|_p < \gamma$ for all admissible $\rho$ in a convex polytope. Simulation on the CR3BP-based cislunar model demonstrates that the observers can achieve accurate positioning with minimal sensing, providing theoretical guarantees and practical guidance for hardware design in deep-space navigation.

Abstract

This paper introduces two innovative convex optimization formulations to simultaneously optimize the H2/Hinf observer gain and sensing precision, and guarantee a specified estimation error bound for nonlinear systems in LPV form. Applied to the design of an onboard celestial navigation system for cislunar operations, these formulations demonstrate the ability to maintain accurate spacecraft positioning with minimal measurements and theoretical performance guarantees by design.

Optimal Sensing Precision for Celestial Navigation Systems in Cislunar Space using LPV Framework

TL;DR

This work tackles robust onboard celestial navigation in cislunar space by casting the nonlinear CR3BP dynamics as a linear parameter-varying (LPV) system and designing observers with guaranteed estimation error bounds. It introduces two convex optimization formulations to jointly optimize the LPV observer gain and the per-sensor precision, ensuring a user-specified bound on the estimation error in either the or sense. The approach yields a sensor-precision vector (with or ) and an observer gain from LMIs that enforce for all admissible in a convex polytope. Simulation on the CR3BP-based cislunar model demonstrates that the observers can achieve accurate positioning with minimal sensing, providing theoretical guarantees and practical guidance for hardware design in deep-space navigation.

Abstract

This paper introduces two innovative convex optimization formulations to simultaneously optimize the H2/Hinf observer gain and sensing precision, and guarantee a specified estimation error bound for nonlinear systems in LPV form. Applied to the design of an onboard celestial navigation system for cislunar operations, these formulations demonstrate the ability to maintain accurate spacecraft positioning with minimal measurements and theoretical performance guarantees by design.
Paper Structure (12 sections, 2 theorems, 30 equations, 3 figures)

This paper contains 12 sections, 2 theorems, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Specific Contributions
  3. Problem Formulation
  4. Brief Overview of LPV Systems
  5. LPV Observer Design
  6. Optimal Sensing Precision for $\mathcal{H}_2$-LPV Observers
  7. Optimal Sensing Precision for $\mathcal{H}_\infty$-LPV Observers
  8. Results
  9. Representation of Cislunar Dynamics in LPV Form
  10. Simulation Results
  11. Conclusions
  12. Acknowledgment

Key Result

Theorem 1

The optimal sensing precision and observer gain for an LPV estimator with $\|G_{ \bar{w} \rightarrow \epsilon}(s,\rho)\|_2<\gamma$ is given by the convex optimization problem where the optimal sensing precision $\kappa_i = \sqrt{\beta_i}$, and $L := X^{-1}Y$.

Figures (3)

  • Figure 1: Earth-Moon resonant orbits in cislunar space for tracking resident space objects (RSOs).
  • Figure 2: Optimal sensing precision $\kappa$.
  • Figure 3: Results for observers in cislunar space.

Theorems & Definitions (8)

  • Remark
  • Remark
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark
  • Remark