Optimal Continuity Allocation for a Tightly-coupled KF-based GNSS/IMU Navigation System with Redundant IMUs

Abstract

This paper introduces an optimal continuity allocation algorithm for a tightly-coupled Kalman-filter (KF)-based Global Navigation Satellite System (GNSS) and multiple Inertial Measurement Units (IMUs) integrated navigation system. Beyond our recent work on the integrity and continuity algorithm of a KF-based GNSS and a single IMU navigation system, the method proposed in this paper enables IMU sensor exclusion while assuring total continuity and integrity requirements under redundant IMU sensor configuration. Two filtering scenarios in the presence of redundant IMU sensors are considered: 1) individual filters that utilize state estimates from a single set of filters at a time, and uses other filters as backup solutions, and 2) a decentralized filter where all the parallel local filters process each IMU sensor measurement and local estimates are subsequently fused in a master filter to achieve the global estimations. First, an analytical equation that can evaluate the continuity risk probability under each filter scenario is derived. Second, based on the fact that sub-filters within the decentralized filter share the same GNSS measurements with different IMU sensors, an inter-filter correlation between test statistics of the decentralized filter is considered to tightly allocate continuity to each monitor. Inter-filter correlation is quantified recursively by the KF, and the monitor thresholds are determined from the formulated joint distributions by the inter-filter correlation. Lastly, a minimum bounding protection level (PL) is determined by optimally allocating continuity risk to each monitor. Continuity allocation considering the correlation significantly improves the overall availability by lowering the continuity burden of each monitor. Simulation results show the benefits of utilizing redundant IMU in terms of system availability and the benefits of taking into account the exact inter-filter correlation for the case of a decentralized filter when allocating continuity requirements for each monitor.