With the development of high-precision safety–critical applications using global navigation satellite systems (GNSS), fault detection and exclusion (FDE) is indispensable to guaranteeing the integrity of a GNSS positioning and navigation system. Many FDE algorithms have been developed based on the standard Kalman filter (KF), assuming that GNSS measurements come with Gaussian uncorrelated white noise. The existence of colored noise in GNSS measurements, which is typical for positioning with low-cost receivers and in challenging environments will, however, degrade the performance of KF-based FDE algorithms. We proposed an FDE scheme based on improved KF considering colored noise (CKF) as a first-order autoregressive model to improve the FDE performance. The performance of the proposed CKF-based FDE algorithm was evaluated with an application to real-time kinematic positioning using a low-cost receiver. A CKF-based fault detection test, a fault identification test, a minimum detectable bias (MDB), error distribution, and positioning results were examined. The results showed that the CKF-based FDE can obtain realistic statistical information to improve integrity monitoring reliability. The fault detection test achieved a 17.83% improvement in FDE performance and a reduction in the false alarm rate, from 23.33 to 5.50%, compared with KF-based FDE. The tests also indicated that the CKF-based FDE can detect multiple faults with zero-miss detection. The fault identification test had an average improvement of 32.14%, and a more realistic MDB was obtained. The results of this study contribute to making objective decisions for the integrity monitoring of practical, precise GNSS positioning.

随着使用全球导航卫星系统（GNSS）的高精度安全关键型应用程序的发展，故障检测和排除（FDE）对于保证GNSS定位和导航系统的完整性是必不可少的。假设GNSS测量伴随着高斯不相关白噪声，则已经基于标准卡尔曼滤波器（KF）开发了许多FDE算法。GNSS测量中彩色噪声的存在（这通常是使用低成本接收器进行定位以及在具有挑战性的环境中进行的测量）会降低基于KF的FDE算法的性能。我们提出了一种基于改进KF的FDE方案，该方法将有色噪声（CKF）作为一阶自回归模型，以提高FDE性能。提出的基于CKF的FDE算法的性能已通过使用低成本接收器的实时运动定位应用进行了评估。检查了基于CKF的故障检测测试，故障识别测试，最小可检测偏差（MDB），误差分布和定位结果。结果表明，基于CKF的FDE可以获取现实的统计信息，从而提高完整性监控的可靠性。与基于KF的FDE相比，故障检测测试的FDE性能提高了17.83％，错误警报率从23.33降低到5.50％。测试还表明，基于CKF的FDE可以通过零失误检测来检测多个故障。故障识别测试平均改善了32.14％，并且获得了更逼真的MDB。