Analytic Error Assessment of Gyro-Free INS

A gyro-free INS consists of at least six distributed accelerometers capable of obtaining linear and angular acceleration and thereby capable of functioning as a conventional INS. Most of the research in the gyro-free field focused on seeking optimal accelerometer configurations and less attention was given to deriving appropriate state-space models and analytical error assessment as in a conventional INS. In this paper, we aim to fill this gap by contributing to three aspects of gyro-free theory. Firstly, practical gyro-free kinematic equations of motion and corresponding error-state models fitting to any set of accelerometers configuration are derived. Secondly, an analytic error assessment of the North Channel dynamics is provided enabling insight on the parameters affecting the gyro-free INS position error. Thirdly, a comparison between INS and gyro-free INS is performed, based on the derived analytical expressions.