Strapdown INS/GPS Integrated Navigation Using Geometric Algebra

A strapdown inertial navigation system (INS)/global positioning system (GPS) integrated navigation Kalman filter in terms of geometric algebra (GA) is proposed. Two error models, i.e., the additive GA error (AGAE) model and the multiplicative GA error (MGAE) model, are developed on the ground of the GA-based strapdown INS model. The AGAE model describes the navigation error by means of perturbation. In contrast, the MGAE model which is indirectly derived from the AGAE one, can physically represent the difference between the computed frame and the true frame. Subsequently, one Kalman filter is constructed on the basis of the MGAE model of the strapdown INS and the error model of GPS. A variety of simulations are carried out to test the proposed Kalman filter. The results show that the Kalman filter can reduce the navigation error remarkably.