Symmetry preserving nonlinear observer for attitude estimation with magnetometer only.

Area of Science:

• Aerospace Engineering
• Control Systems Theory
• Nonlinear Dynamics

Background:

• Nano-satellite attitude determination is crucial for mission success.
• Limited sensor availability, such as only a Three-Axis Magnetometer (TAM), poses significant challenges.
• Observability issues hinder accurate estimation of attitude and angular velocity.

Purpose of the Study:

• To design a nonlinear symmetry observer for nano-satellite attitude determination using solely TAM data.
• To address data limitations and observability problems through a nested filter approach.
• To simultaneously estimate attitude and angular velocity with enhanced accuracy.

Main Methods:

• A two-nested-filter approach is employed.
• The first filter estimates the magnetic field derivative using an extended Kalman filter.
• The second filter utilizes magnetic field and its derivative with invariant observers under Lie group actions.
• Invariant error dynamic equations are derived for observer design.
• Periodic Riccati differential equations are used for tuning observer performance.

Main Results:

• Successful simultaneous estimation of attitude and angular velocity was achieved.
• The proposed observer compensates for data scarcity and resolves observability issues.
• Validation through simulation demonstrated the observer's effectiveness.
• Exponential stability of the observer was mathematically proven.

Conclusions:

• The developed nonlinear symmetry observer provides a robust solution for nano-satellite attitude determination with limited sensors.
• The nested filter strategy effectively overcomes data limitations and observability challenges.
• The methodology offers a reliable and stable approach for precise attitude and angular velocity estimation in nano-satellites.