Relative inertial navigation employing a common frame error definition

This paper expands upon a new paradigm for inertial navigation systems with applications to the relative navigation scenario. Historically, errors in filter applications using inertial navigation system equations have been previously defined from an abstract vector point-of-view. For example, the error in velocity has always been expressed using a straight difference of the truth minus the estimate without regard to each of the vector’s frame representations. In previous work, an alternative vector state-error is defined using common coordinates over all error vector realizations, thereby providing a true-to-life representation of the actual errors. In this work, this newly derived Geometric Extended Kalman Filter is applied to the relative navigation of inertially flying vehicles. Simulation results are shown to assess the performance of the new filter design compared with the standard Multiplicative Extended Kalman Filter.