## 1 Introduction  
Modern navigation systems are developing in the direction of multi-sensor and deep information fusion. GNSS (Global Navigation Satellite System) has all-weather absolute positioning capability, but it is vulnerable to interference. On the contrary, INS (Inertial Navigation System), which has excellent anti-interference ability, can only provide relative position information. Thus, they have strong complementarity in performance. Deeply integrated GNSS/INS systems take into account the advantages of both GNSS and INS, and implement the deepest information fusion between GNSS and INS at present. Compared with loose integration and tight integration, deep GNSS/INS integration not only has better ability of anti-noise and anti-interference [1, 2], but also can track weaker satellite signals [3] and acquire the temporarily occluded signals more quickly [4]. All of these advantages are attributed to the use of vector tracking loop [5]. The distinctive feature of vector tracking loop is that, after fusing GNSS and INS data, the navigation filter generates the locally predicted carrier frequency and code phase for each receiving channel to implement signal tracking. This kind of structure realizes the information exchange among the receiving channels, which is helpful for strong signals to assist the reception of weak signals. However, there is a serious problem that, when a receiving channel contains fault information, the information will spread to the remaining channels, thereby degrading the system performance. Therefore, timely detection and identification of faults are important for deep integration based on vector tracking loop. Based on the approximate system model, a chi-square test is able to detect faults in real time by monitoring the difference between the measurements and the estimates of Kalman filter [6]. In order to weaken the influence of the inaccurate system model on the results of chi-square detection, [PERSON] et al. propose a method of calculating the covariance of system model error in a stable period [7]. [PERSON] et al. derive methods to generate rigorous integrity and continuity bounds for chi-square test when the signal is time-varying [8]. An integrated detection algorithm of combining particle filter and fuzzy inference system is presented by [PERSON] et al. [9]. The residuals which are generated by particle filter are used as the inputs of fuzzy inference system to output the different anomaly levels. However, its performance is limited due to the high computational load of particle filter. Wavelet transformation which can extract characteristic values from fault data is a powerful mathematical tool for fault diagnostics owing to its multi-resolution capability [10]. [PERSON] et al. study the method of detecting faults by employing the adaptive neural fuzzy inference algorithm [11], which allows real-time model-free residual analysis from Kalman filter estimates, and obtains better detection results than chi-square detection. The machine learning method SVM (Support Vector Machine) that has the ability to predict test statistics based on prior knowledge is applied in fault detection [12]. SVM cannot provide the accuracy of predicted value. However, another machine learning method named GPR (Gaussian Process Regression) is able to provide both the prediction of unknown input and the variance of prediction. The detection method of using GPR to predict the innovation of Kalman filter is shown to be especially effective in detecting gradual faults [13]. The above-mentioned methods can detect whether the GNSS receiver has faults or not, but they cannot identify the internal faults of GNSS. The whole GNSS is simply isolated from the integrated navigation system when an abnormality is detected in GNSS. In fact, the GNSS receiver contains multiple receiving channels to process satellite signals. In abnormal situations, the integrity of the integrated navigation system is maintained by just removing the fault channels from GNSS receiver, so that the system can keep working normally.