Inertial Navigation Employing a Common-Frame Error Model

This paper examines an extension of previous common-frame theory in the state-error definition for inertial navigation systems (INS). In previous work, only body-frame errors were considered in relation to quantities such as biases from strapdown gyros. Reference-frame errors found in quantities such as the translational velocity have not been considered previously. The work here derives the full INS equations where an alternative vector state-error is defined using common coordinates over all vector-error realizations, thereby providing a true-to-life representation of the actual errors. The INS is analyzed through a stationary linear analysis to show that the fundamental frequencies are unchanged; however, there are now more coupling terms within the state matrix. The performance of the INS filter is then analyzed using a simulation.