Chun Yang and Andrey Soloviev, QuNav

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A popular method for integrity monitoring is solution separation originally developed for GPS/GNSS. When applied to multisensor integrated navigation in GPS/GNSS-degraded and denied environments, an inertial navigation system (INS) serves as a core sensor to provide the baseline solution while others offer aiding data to reduce the inertial drifts. To maintain the integrity of such an integrated solution, a decentralized estimator can be used in which an aiding sensor is processed by a separate filter to estimate the error states of INS and of its own. The individual filters are then combined into solution subsets designed in such a way that when a fault occurs, it can be timely detected, identified, and excluded. The optimal solution can be recovered from fault-free solution subsets when the individual filters are uncorrelated. However, non-zero correlation exists due to the simple fact that they rely on the same inertial data. For instance, at the system startup time, subset estimates are fully correlated, resulting in a singularity in the fusion weighting matrix. As a result, a test condition is sought to check on individual filters for cross-correlation. A scalar quantity, referred to as vector correlation index (VCI), is introduced to characterize the overall correlation between local filter estimates. Furthermore, a numerical issue may develop when the subset estimates become highly correlated and the weighting matrix, though short of being singular, has a large condition number, thus amplifying the effect of noise in measurement data. To address this issue, an adaptive fusion scheme is set forth in this paper in which a diagonal loading is applied to the weighting matrix to ensure the resulting condition number stays below a certain level while not altering the optimal weighting too much for minimal error covariance. In this paper, both simulation and experimental data are used to illustrate the adaptive fusion scheme with tradeoffs between complexity (adaptive tuning vs. fixed loading; singular values vs. individual state components) and performance (transient vs. steady state estimation errors). Experimental data include GNSS/Odometer/LiDAR (2D and 3D)/INS.