This paper presents two fault tolerance methods for decentralized Kalman filter with non-common states (DKF-NCS) for nonlinear systems. The DKF-NCS is used in a sensor network, where states are not uniform across all nodes. To detect and isolate faulty measurements, the ${\chi }^2$ test has been quite useful, where faulty measurements are detected based on the innovation error and innovation error covariance matrix. However, the innovation error and innovation error covariance matrix are dependent on the predicted state vector and its error covariance along with measurement model. The ${\chi }^2$ distribution test fails, if the predicted state vector is not consistent with its predicted error covariance matrix. Also, due to processing of set of measurements independently, fault detection happens more often in decentralized estimation compared to centralized estimation. Therefore, discarding the valid measurements based on ${\chi }^2$ detector may impact the performance of decentralized estimators significantly. To overcome this problem, we propose two adaptive fault tolerance methods. The first method handles faulty measurements at the assimilation step by applying weighted correction of the information and information matrix. The second method modifies the measurement noise matrix based on a closed-form solution, if fault is detected. These methods are validated using 100 simulation runs for a tracking problem. Overall, the proposed methods are demonstrated to be superior compared to the ${\chi }^2$ test and an existing adaptive extended Kalman filter.

本文提出了非线性系统的非共态分散卡尔曼滤波器（DKF-NCS）的两种容错方法。DKF-NCS 用于传感器网络，其中所有节点的状态并不统一。为了检测和隔离错误的测量，${\chi }^2$测试非常有用，其中基于创新误差和创新误差协方差矩阵检测错误测量。然而，创新误差和创新误差协方差矩阵取决于预测状态向量及其误差协方差以及测量模型。这${\chi }^2$如果预测的状态向量与其预测的误差协方差矩阵不一致，则分布测试失败。此外，由于独立处理一组测量，与集中估计相比，故障检测在分散估计中更频繁地发生。因此，丢弃基于的有效测量${\chi }^2$检测器可能会显着影响分散估计器的性能。为了克服这个问题，我们提出了两种自适应容错方法。第一种方法通过应用信息和信息矩阵的加权校正来处理同化步骤中的错误测量。如果检测到故障，则第二种方法基于封闭形式的解决方案修改测量噪声矩阵。这些方法使用 100 次模拟运行来验证跟踪问题。总体而言，所提出的方法被证明是优于${\chi }^2$ 测试和现有的自适应扩展卡尔曼滤波器。