# Hybrid Nonlinear Observers for Inertial Navigation Using Landmark Measurements

## TL;DR

This paper introduces two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$ for inertial navigation, achieving global exponential stability and handling measurement biases, validated through simulations and experiments.

## Contribution

The paper presents novel hybrid nonlinear observers on $SE_2(3)$ with fixed and variable gains, extending to biased measurements, and demonstrating stability and performance improvements.

## Key findings

- Observers achieve global exponential stability.
- Variable gain observer outperforms fixed gain in accuracy.
- Experimental results confirm robustness and effectiveness.

## Abstract

This paper considers the problem of attitude, position and linear velocity estimation for rigid body systems relying on landmark measurements. We propose two hybrid nonlinear observers on the matrix Lie group $SE_2(3)$, leading to global exponential stability. The first observer relies on fixed gains, while the second one uses variable gains depending on the solution of a continuous Riccati equation (CRE). These observers are then extended to handle biased angular velocity measurements. Both simulation and experimental results are presented to illustrate the performance of the proposed observers.