## 1 Introduction
A set of FDI methods have already been applied in the RINS successfully, which includes the Chi-square test [23; 24], the network-based method [25], and the parity space method. The parity space method includes the optimal parity vector test (OPT) [26], the generalized likelihood test (GLT) [27; 28], and the singular value decomposition (SVD) method [21; 22; 29; 30; 31]. Among these methods, the methods based on the Chi-square test are subjected to the filtering algorithm performance. When the filtering performance is degraded or even diverged, the detection and isolation results are not reliable. The neural network-based methods are restricted by the heavy computing burden and the requirements for large samples. In the main, the parity space method is a good choice for the navigation system, but it cannot handle the situation of multi faults. As for the outliers, there are two approaches commonly used to deal with them: one is to improve filter functions, which alleviate the impact of outliers by setting the weighted matrix or correcting the covariance matrix at every sampling moment [32; 33; 34; 35]; another one is to replace the detected outlier points with mean values or the points from fitted curves [36; 37]. The methods introduced above can reduce the effect of anomalies to some degree, but there are still some problems. Firstly, the outliers in the measurement data, especially the outlier patches, are easily  
Figure 1: The classification of data anomalies. misdiagnosed as the faults, which will lead to an increase in the false alarm rate. The outliers will cause the detection function values to exceed the detection threshold, but there is no failure or damage in the sensor with outliers. Such misdiagnosis may induce a well-behaved sensor to be deactivated. Secondly, when the outlier eliminating methods and FDI methods are operating simultaneously, the practical performance may degrade, because the calculation burden will increase and the results of different methods will interfere with each other. For example, the outlier eliminating methods regard every anomaly point as an outlier. Since the deviation of anomaly points caused by sensor faults will be diminished after the outlier eliminating processing, the original statistical characteristics of the faults will change. As a result, the probability of correct detection (PCD) and the probability of correct isolation (PCI) will decline. Thirdly, the FDI methods cannot identify the patterns of anomalies. So the different modes of anomalies have to be handled in the same way. Deactivating sensors with hard faults is reasonable. However, some faulty sensors are not physically damaged and can continue to be used after correction, so traditional strategies can possibly result in the loss of available sensors. To solve the problems above, this paper proposed a diagnosis method for data anomalies in MEMS RINS. The SVD-based method is briefly reviewed, and the flaws of this method are analyzed. The improved SVD-based method is presented. The disadvantages of this method are analyzed and improved. To demonstrate the feasibility of recognizing a fault pattern by analyzing the detection function, the mathematical relation between the detection function and sensor faults is derived. Five indicators of detection are defined on the basis of the analysis of various anomalies. The anomaly recognition method is proposed according to these five indicators. The proposed method can detect faults and outliers simultaneously, so that, the mutual interference between outlier eliminating and fault detection can be removed. The anomalies can receive suitable and reasonable treatments based on the recognition results. The anomaly processing is simplified too. This paper is organized as follows: In Section 2, the SVD method is briefly reviewed, and the disadvantages are discussed and improved. To demonstrate the feasibility of using detection function values as the evidence for anomaly recognition, the relation between the detection function and anomalies is deduced.