Kalman Filter-Based Integrity Monitoring Against Sensor Faults
Kalman Filter-Based Integrity Monitoring Against Sensor Faults
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DOI：
10.2514/1.59480
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发表时间：
2013-03-01
影响因子：
2.6
通讯作者：
Pervan, Boris
中科院分区：
文献类型：
--
作者：
Joerger, Mathieu;Pervan, Boris
本文提出了一种新的基于卡尔曼滤波器的线性动态系统传感器故障检测方法。与现有的顺序故障检测算法相比，所提出的方法能够直接评估的完整性风险，这是一个未检测到的故障导致状态估计误差超过预定义的可接受范围的概率。新的方法也是计算效率和简单的实施。该算法的检测检验统计量的建立分三步进行。首先，当前和过去的时间卡尔曼滤波残差的加权范数被定义为广义非中心卡方分布的随机变量。其次，这些残差被证明是随机独立的状态估计误差。第三，当前时间和过去的时间残差被证明是相互独立的，所以基于卡尔曼滤波器的测试统计量可以递归地更新在真实的时间，通过简单地添加当前时间的残差贡献到以前计算的加权范数的过去的时间残差。卡尔曼滤波器为基础的完整性监测评估对最坏情况下的故障配置文件，这也是本文推导。最后，性能分析结果的飞机精密进场导航的一个例子中，从多星座卫星导航系统的差分测距信号进行滤波定位和载波相位周期模糊度估计的应用。
This paper introduces a new Kalman filter-based method for detecting sensor faults in linear dynamic systems. In contrast with existing sequential fault-detection algorithms, the proposed method enables direct evaluation of the integrity risk, which is the probability that an undetected fault causes state estimate errors to exceed predefined bounds of acceptability. The new method is also computationally efficient and straightforward to implement. The algorithm's detection test statistic is established in three steps. First, the weighted norms of current and past-time Kalman filter residuals are defined as generalized noncentrally chi-square distributed random variables. Second, these residuals are proven to be stochastically independent from the state estimate error. Third, current-time and past-time residuals are shown to be mutually independent, so that the Kalman filter-based test statistic can be recursively updated in real time by simply adding the current-time residual contribution to a previously computed weighted norm of past-time residuals. The Kalman filter-based integrity monitor is evaluated against worst-case fault profiles, which are also derived in this paper. Finally, performance analyses results are presented for an example application of aircraft precision approach navigation, where differential ranging signals from a multiconstellation satellite navigation system are filtered for positioning and carrier phase cycle ambiguity estimation.