ALPF-GLRT based fault detection method for small faults applied to redundant IMUs

Since small faults exhibit a very close magnitude to sensor noises, the probability of missing detection (PMD) in existing methods will increase sharply in the presence of small faults. To address such a problem, this paper proposes a novel fault detection method for small faults applied to redundant IMUs. First, this method introduces an adaptive low-pass filter (ALPF) into the general likelihood ratio test (GLRT) by filtering the parity residuals of the GLRT model, thereby reducing the disturbance of sensor noises on fault detection. Subsequently, since the introduction of ALPF leads to the changes of the parity residual statistics, the covariance of parity residual should be recalculated at the respective sample instant. Lastly, to theoretically prove the superiority of the proposed method for small faults, the minimum detection bias (MDB) is derived and calculated, thereby validating that the MDB of the proposed method is lower than that of the conventional GLRT method. As indicated from the simulation results, the PMD of the proposed method decreases significantly for small faults compared with the GLRT method and the Monte Carlo PMD of the proposed method is 0.1% under the fault with the magnitude of 1 sigma, which demonstrates the effectiveness of the proposed method.