An Equivariant Filter for Spacecraft Nonlinear Relative Navigation with Range and Bearing Measurements

Gil Serrano; Bruno J. Guerreiro; Pedro Lourenço; Rita Cunha

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arXiv · 2609.13094

An Equivariant Filter for Spacecraft Nonlinear Relative Navigation with Range and Bearing Measurements

Gil Serrano·Bruno J. Guerreiro·Pedro Lourenço·Rita Cunha

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Abstract

Relative navigation is a fundamental task in space proximity operations and autonomous rendezvous. The nonlinear relative orbital dynamics are equivariant and admit a semidirect product Lie group symmetry. This property is used to design an Equivariant Filter (EqF). The filter estimates the relative position and velocity between a chaser spacecraft and a target by lifting the filter dynamics to the group, while respecting the underlying geometry of the problem. Simulations demonstrate the filter's performance and effectiveness.

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Gil Serrano, Bruno J. Guerreiro, Pedro Lourenço, Rita Cunha. 2026-09-11. An Equivariant Filter for Spacecraft Nonlinear Relative Navigation with Range and Bearing Measurements. https://arxiv.org/abs/2609.13094

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