Optimal Configuration of Redundant Inertial Sensors Considering Lever Arm Effect

An optimal configuration for a redundant inertial measurement unit (RIMU) minimizing the lever arm effect and the constraints for the optimality are proposed. The proposed configuration provides the allocation of each sensor in an RIMU as well as the orientation, while conventional configurations, which do not consider the lever arm effect, suggest the orientation only. The orientation is fixed, so that the configuration may guarantee the best navigation performance, and the allocation of each sensor is determined for minimizing the lever arm effect and for the densest disposition of the structures. To qualify the navigation performance of a configuration, a novel figure of merit (FOM) indicating the worst navigation performance of an RIMU is proposed first. In general, an FOM, which indicates the averaged error covariance of all the estimation, is used as a navigation performance index. The proposed FOM, however, represents the worst error covariance, which contributes to the determination of a secure configuration against excessive noises. The optimal condition of the proposed FOM is also derived, in which case the proposed configuration guarantees the best navigation performance. Using the proposed FOM, the constraint for obtaining the optimal configuration, which guarantees the best navigation performance and minimizes the lever arm effect, is proposed. The effectiveness of the proposed method is confirmed via case studies and Monte Carlo simulations, which show that the RIMU with the proposed configuration sustains sufficiently high position accuracy in spite of the lever arm effect.