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

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.

💡 Research Summary

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The paper addresses the long‑standing challenge of accurate extended‑pose estimation for inertial navigation systems (INS) when only inertial measurements are available, which inevitably leads to drift due to sensor noise, biases, and unknown initial conditions. To mitigate this, the authors propose a novel cascade observer architecture that cleanly separates translational dynamics from rotational kinematics while preserving the geometric structure of attitude evolution on the special orthogonal group SO(3).

The first stage embeds the INS dynamics into a 15‑dimensional linear time‑varying (LTV) model. By expressing position (p_B), velocity (v_B) and the rotation matrix in body coordinates, and by introducing an auxiliary unconstrained vector (z_B = \operatorname{vec}(R^\top)), the original nonlinear system is rewritten as
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