[Paper Review] A simple global observer for attitude and gyro biases

Philippe Martin, Ioannis Sarras|arXiv (Cornell University)|Apr 13, 2016

Inertial Sensor and Navigation5 references3 citations

TL;DR

This paper proposes a geometry-free nonlinear observer for global attitude and gyro bias estimation using vector measurements and a triaxial rate gyro. It ensures global asymptotic convergence through a simple design with straightforward stability analysis, validated via detailed numerical simulation.

ABSTRACT

We consider the classical problem of estimating the attitude and gyro biases of a rigid body from vector measurements and a triaxial rate gyro. We propose a simple geometry-free nonlinear observer with guaranteed global asymptotic convergence and a straightforward stability analysis. The excellent behavior of the observer is illustrated on a detailed numerical simulation.

Motivation & Objective

• To address the challenge of estimating attitude and gyro biases in rigid body systems using limited sensor data.
• To develop a globally convergent observer without reliance on geometric assumptions or complex manifold structures.
• To ensure robust and stable estimation performance under realistic dynamic conditions.
• To provide a computationally simple yet effective solution for real-time attitude estimation applications.

Proposed method

• The observer uses vector measurements and triaxial rate gyro data as inputs to estimate attitude and gyro biases.
• It employs a nonlinear error dynamics formulation that ensures global asymptotic convergence.
• The design avoids geometric constraints by using a geometry-free approach, simplifying the observer structure.
• Stability is proven using Lyapunov analysis, ensuring convergence from any initial condition.
• The observer structure is minimal and does not require linearization or approximation of the attitude dynamics.
• The method is implemented and tested in a detailed numerical simulation to validate performance.

Experimental results

Research questions

• RQ1 Can a simple nonlinear observer achieve global convergence in attitude and gyro bias estimation without geometric assumptions?
• RQ2 How does the observer perform under realistic sensor noise and dynamic conditions?
• RQ3 What is the impact of the geometry-free design on stability and convergence properties?
• RQ4 Can the observer be implemented with minimal computational overhead while maintaining accuracy?

Key findings

• The proposed observer achieves global asymptotic convergence for both attitude and gyro bias estimation.
• The stability analysis is straightforward and relies on Lyapunov theory, ensuring robustness from any initial condition.
• The observer demonstrates excellent performance in numerical simulations, confirming its practical viability.
• The geometry-free design eliminates the need for complex manifold representations, simplifying implementation.
• The method maintains high accuracy even with noisy measurements, as shown in simulation results.
• The computational simplicity enables potential real-time deployment in embedded systems.