Observability and Performance Analysis of Velocity Measurements with Lever Arm Aided INS

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.