## 1 Introduction  
Micro-electro-mechanical system inertial measurement unit (MEMS IMU) has the advantages of being low cost, small volume, and lightweight, but low precision and poor stability are still problems that cannot be ignored. Many aircraft, cars, and satellites are beginning to use MEMS sensors [1; 2; 3; 4; 5]. Among them, most MEMS accelerators have already met the tactical and navigation grade requirements [6; 7]. However, only a few MEMS gyros can reach the level of tactical grade [1], and these tactical grade gyros are too expensive for common application. To improve the performance of MEMS IMU, a series of studies have been conducted to promote MEMS manufacturing technology. On the other hand, the improvement can also be achieved through reasonable designs and algorithms. Under the restriction of current manufacturing technology, a lot of research has been done to improve the performance of the MEMS system, and redundant design is the most effective approach to improve the accuracy and stability [8; 9; 10; 11; 12; 13]. Even for the tactical or navigation grade sensors, the redundant configuration can improve the performance substantially [14]. In the redundant inertial navigation system (RINS), the processing of redundant data is the most important link. It is divided into two parts: processing data anomalies and fusing redundant data. The motivation of this paper is to develop the anomaly diagnosis method, and improve the reliability of the MEMS RINS. The data anomalies are comprised of sensor faults and outliers. The faults refer to the failure and variation of sensor characteristics, which are probably caused by harsh environmental conditions,such as the moisture, extreme temperature, electromagnetic radiation, impact, and vibration [15]. These kind anomalies are related to the aging, damage, and performance degradation of the sensors, and they are generally irreversible hard failures. The definition of an outlier is an observation (or subset of observations) which appears to be inconsistent with the remainder of that set of data. The outliers in inertial measurement data arise because of instrument error, natural deviations, or changes in the behavior of systems. The outliers usually appear as the self-recovery and transient mutations [16]. For further analysis, the anomalies can be divided into more subcategories based on a different baseline. In this paper, anomaly patterns serve as evidence to choose anomaly solution methods. So we classify anomalies as short-duration auto-recovery anomalies and sustained anomalies. The former includes isolated outliers, small outlier patches, transient faults, etc., which refer to the anomalies that sustain a short duration and recover spontaneously. The short-duration auto-recovery anomalies can be corrected well with outlier eliminating methods. The latter includes large outlier patches, hard faults, permanent failures, etc. These kinds of anomalies can be subdivided by their different performance characteristics. The constant drift fault and multiplicative fault (variation of scale factor) can be repaired through re-calibration technology [17; 18]. For instance, the faulty sensors can be calibrated with the data of other types of navigation information or the fusion estimation signal without anomaly data. However, large outlier patches, noise failure, complete failure, and other hard faults are usually isolated directly. Overall, the reclassification of anomalies is shown in Figure 1.  
At present, most methods only divide the anomalies into faults and outliers to process. Due to the differences between faults and outliers, the countermeasures against them are carried out separately in different ways. To protect the output fusion signal from faults, the fault detection and isolation (FDI) methods can make the system continue working normally [19; 20; 21; 22]. The solution against the faults is to detect the measurement data in real time, isolate faulty sensors and discontinue using them.