A General Nonlinear Observer Design for Inertial Navigation Systems with Almost Global Stability Guarantees

TL;DR

This paper introduces a nonlinear observer for inertial navigation that guarantees almost global stability by combining linear time-varying estimation with geometric attitude reconstruction, applicable to pose estimation with inertial and exteroceptive data.

Contribution

The paper presents a novel cascade observer design that separates translational and rotational dynamics, ensuring almost global stability for inertial navigation systems.

Findings

Observer achieves almost global asymptotic stability.

Explicit conditions for uniform observability are derived.

Simulation confirms effectiveness of the proposed method.

Abstract

This paper studies nonlinear observer design for rigid-body extended pose estimation using inertial measurements and generic exteroceptive sensing. The estimation problem is formulated as a cascade architecture that separates translational dynamics from rotational kinematics while preserving the geometric constraint of attitude evolution on $SO(3)$. By embedding the inertial navigation model into a Linear Time-Varying (LTV) representation, we construct an observer composed of a Kalman-Bucy-type estimator for translational states and an auxiliary unconstrained attitude variable, coupled with a nonlinear geometric reconstruction filter evolving on $SO(3)$. The cascade interconnection is analyzed within a nonlinear systems framework. We prove that uniform observability of the LTV subsystem guarantees almost global asymptotic stability of the overall nonlinear observer. For a benchmark GPS landmark aided configuration, explicit sufficient conditions on admissible trajectories are derived to ensure uniform observability. Simulation results illustrate the effectiveness of the proposed estimation framework.