Generalized Derivation of The EKF Based Inertial Navigation Error Dynamics

Abstract This work complements the various approaches to compute the error dynamics of the inertial navigation process. In contrast to work published earlier, the actual derivation of the navigation error model is based on the Jacobian derivative as used for the extended Kalman filter, with emphasis on a similarity transformation of the error state vector. Based on this similarity transformation, various features can be achieved which have a practical relevance for the implementation of an actual navigation system. The approach given is applicable to a wide field of filtering problems, especially in conjunction with the formulation of the extended Kalman filter. A simplified example is given and the filtering results based on real flight data with an unmanned helicopter are provided. The derivation of a more precise navigation error model concludes the paper.