Strapdown Navigation Using Geometric Algebra: Modeling and Error Analysis

A strapdown inertial navigation system (SDINS) model and two comparable error models are developed using geometric algebra (GA). GA is a powerful representational and computational system for geometry. Rigid body motions can be represented by versor products in GA framework. Therefore, the navigation equation can be recast using GA. It turns out that the principle of strapdown navigation can be expressed in three continuous motor kinematic equations, which share a unitary form. Two error models, i.e. the additive and multiplicative GA error models, are developed. The SDINS and error models presented in this paper are supposed to benefit the prospective integrated navigation filter in terms of GA.