In view of the large output noise and low precision of the MEMS (Micro-Electro-Mechanical System) gyroscope, the virtual gyroscope technology is used to fuse the data to improve its output precision. However, the traditional virtual gyroscope technology has poor dynamic compensation effect. Therefore, a virtual gyroscope technology with high precision dynamic filtering is proposed. First of all, the high accuracy model of the real dynamic angular rate based on Taylor formula is established. And the random error model of the MEMS gyroscope array is improved based on the real angular rate modeling results. The Kalman filter is designed for dynamic data fusion to improve the dynamic compensation precision of the virtual gyroscope. The test results show that the 1σ standard deviation of the estimation error of the proposed method is 2 times lower than the 1σ standard deviation of the direct KF model’s dynamic estimation error, and it is nearly 8 times lower than the 1σ standard deviation of the static random error of the single gyroscope and the compensation accuracy is improved with the increase of the real angular rate modeling order.

Aiming at the problem of large navigation errors for unmanned vehicle based on MEMS inertial navigation systems(MEMS-INS, MINS) due to low output accuracy of MEMS inertial sensors, a redundant MINS is designed and a high precision positioning algorithm is proposed. In redundant MINS, the output of the redundant gyroscopes is estimated by the improved virtual gyro algorithm based on improved current statistical model and interacting multiple model Kalman filter (ICS-IMMKF). The weighted fusion algorithm is used to fuse the redundant accelerometer information, thus the virtual micro inertial navigation system (Virtual-MINS) is obtained. In the process of vehicle positioning based on virtual MINS, the centripetal acceleration is solved based on the kinematic constraints. Combined with the navigation information of Virtual-MINS and odometer (OD), the difference of centripetal acceleration and velocity are used as observation, and a Virtual-MINS/OD positioning algorithm based on kinematic nonholonomic constraints (NHC/Virtual-MINS/OD) is proposed. The simulation results show that the ICS-IMMKF algorithm can achieve high precision fusion of redundant gyro. In the test, azimuth maneuver is not constrained by the ground, therefore the ICS-IMMKF algorithm can obtain the azimuth rate with high precision. The experimental results show that the root mean square (RMS) of the East and North positioning errors, as well as the RMS of pitch, roll and azimuth estimation error based on the NHC/Virtual-MINS/ OD positioning algorithm are reduced to 34.15%, 22.65%, 55.11%, 64.93% and 41.37% of the NHC/#1-MINS/OD positioning algorithm, respectively. The method will provide a solution for high-precision positioning when GNSS fails.

The application of the Micro Electro-mechanical System (MEMS) inertial measurement unit has become a new research hotspot in the field of inertial navigation. In order to solve the problems of the poor accuracy and stability of MEMS sensors, the redundant design is an effective method under the restriction of current technology. The redundant data processing is the most important part in the MEMS redundant inertial navigation system, which includes the processing of abnormal data and the fusion estimation of redundant data. A developed quality index of the MEMS gyro measurement data is designed by the parity vector and the covariance matrix of the distributed Kalman filtering. The weight coefficients of gyros are calculated according to this index. The fault-tolerant fusion estimation of the redundant data is realized through the framework of the distributed Kalman filtering. Simulation experiments are conducted to test the performance of the new method with different types of anomalies.

In view that traditional dynamic Allan variance (DAVAR) method is difficult to make a good balance between dynamic tracking capabilities and the confidence of the estimation. And the reason is the use of a rectangular window with the fixed window length to intercept the original signal. So an improved dynamic Allan variance method was proposed. Compared with the traditional Allan variance method, this method can adjust the window length of the rectangular window adaptively. The data in the beginning and terminal interval was extended with the inverted mirror extension method to improve the utilization rate of the interval data. And the sliding kurtosis contribution coefficient and kurtosis were introduced to adjust the length of the rectangular window by sensing the content of shock signal in terminal interval. The method analyzed the window length change factor in different stable conditions and adjusted the rectangular window’s window length according to the kurtosis, sliding kurtosis contribution coefficient. The test results show that the more the kurtosis stability threshold was close to 3, the stronger the dynamic tracking ability of DAVAR would be. But the kurtosis stability threshold was too close to 3, there was a misjudgement in kurtosis analysis of signal stability, resulting in distortion of DAVAR analysis results. When using the improved DAVAR method, the kurtosis stability threshold can be close to 3 to improve the tracking ability and the estimation confidence in stable interval. Therefore, it solved the problem that the dynamic Allan variance tracking ability and confidence level were difficult to take into account, and also solved the problem of misjudgement in the stability analysis of kurtosis.

In view of the large output noise and low precision of the Micro-electro-mechanical Systems (MEMS) gyroscope, the virtual gyroscope technology was used to fuse the data of the MEMS gyroscope to improve its output precision. Random error model in the conventional virtual gyroscopes contained an angular rate random walk and angle random walk ignoring other noise items and the virtual gyroscope technology can not compensate all random errors of MEMS gyroscope. So, the improved virtual gyroscope technology based on the autoregressive moving average (ARMA) model was proposed. First, the conventional virtual gyroscope technology was used to model the random error of three MEMS gyroscopes, and the data fusion was carried out by a Kalman filter to get the output of the virtual gyroscope. After that, the ARMA model was used to model the output of the virtual gyroscope, the random error model was improved with the ARMA model, and the Kalman filter was designed based on the improved random error model for data fusion of the MEMS gyroscopes. The experimental results showed that the $1\sigma$ standard deviation of the output of the virtual gyroscope based on the ARMA model was 1.4 times lower than that of the conventional virtual gyroscope output.

The application of the micro-electro-mechanical system inertial measurement unit has become a new research hotspot in the field of inertial navigation. In order to solve the problems of the poor accuracy and stability of micro-electro-mechanical system sensors, redundant design is an effective method under the restriction of current technology. Redundant data processing is the most important part in the micro-electro-mechanical system redundant inertial navigation system, which includes the processing of anomaly data and the fusion estimation of redundant data. To further improve the reliability of the micro-electro-mechanical system redundant inertial measurement unit, an anomaly detection, isolation, and recognition method for data anomalies is proposed. The relationship between the parity space method detection function and the deterioration degree of anomaly data is mathematically deduced. The parity space method detection functions of different anomalies are analyzed, and five indicators are designed to quantitatively analyze the detection function values. According to these indicators, the detection and recognition method are proposed. The new method is tested by a series of simulation experiments.