Observability Analysis of a Matrix Kalman Filter-Based Navigation System Using Visual/Inertial/Magnetic Sensors

A matrix Kalman filter (MKF) has been implemented for an integrated navigation system using visual/inertial/magnetic sensors. The MKF rearranges the original nonlinear process model in a pseudo-linear process model. We employ the observability rank criterion based on Lie derivatives to verify the conditions under which the nonlinear system is observable. It has been proved that such observability conditions are: (a) at least one degree of rotational freedom is excited, and (b) at least two linearly independent horizontal lines and one vertical line are observed. Experimental results have validated the correctness of these observability conditions.