The attitude determination problem from two reference vectors - a description of the triad algorithm and its attitude covariance matrix

Abstract

This article presents a description of the TRIAD algorithm, which utilizes two vector observations for determining a body three-dimensional attitude. This algorithm describes a deterministic form to calculate the attitude and it does not constitute the optimal solution for the problem, but can be implemented efficiently on computers. The Cartesian covariance matrix for this algorithm is also presented. This matrix calculation are addressed in details, resulting in a simple analytical formula based on two different sensor sets measurements in the body frame. The solutions presented are suited to implement highly integrated attitude determination systems that employ MEMS (Micro-Electro-Mechanical Systems) technology sensors and low cost microcontrollers.

Keywords

• Attitude determination
• Triad
• Covariance matrix