$\mathcal{H}_\infty$ Optimal Navigation in the Cislunar Space with LFT Models

Abstract

Navigation in the cislunar domain presents significant challenges due to chaotic and unmodeled dynamics, as well as state-dependent sensor errors. This paper develops a robust estimation framework based on Linear Fractional Transformation (LFT) models, and state estimation in $\mathcal{H}_\infty$ and $\mu$ synthesis framework to address these challenges. The cislunar dynamics are embedded into an LFT form that captures nonlinearities in the gravitational model and state-dependent sensor errors as structured uncertainty. A nonlinear estimator is then synthesized in the $\mathcal{H}_\infty$ sense to ensure robust performance guarantees in the presence of the stated uncertainties. Simulation results demonstrate the effectiveness of the estimator for navigation in a surveillance constellation.