In most autonomous vehicles the navigation subsystem is based on Inertial Navigation System (INS). Regardless of the INS grade, its navigation solution drifts in time. To avoid such a drift, the INS is fused with external sensor measurements. Recent publications show that the lever-arm, the relative position between the INS and aiding sensor, has influence on the navigation performance.
Most published research in this field is focused on INS/GNSS fusion with GNSS position updates only where performance and analytical observability analysis were made to examine the consequence of vehicle maneuvers on the estimation of the lever-arm states.
Yet, besides position updates, a variety of sensors measuring the vehicle velocity vector are available including GNSS and a Doppler velocity log. As in position measurements, when performing INS/velocity measurements fusion, the lever-arm must be taken account for. In this paper, an analytical observability and performance analysis for velocity measurements with lever-arm aided INS is derived for stationary conditions. The observable and unobservable subspaces are derived for two error-stets models: 1) a 12 error-state model (the position and lever-arm error-states are not included) yet the lever-arm is present in the measurement equation and 2) a 15 error-state model including the lever-arm error-states. The analytical closed form expressions are verified by numerical simulation.