To reduce the influence of MEMS gyroscope random errors on navigation systems, the improved variational mode decomposition-wavelet threshold de-noising (WTD) method is proposed in this paper. First, to suppress the endpoint effect caused by the signal truncation and Hilbert transform during decomposition, the triangular waveform matching method is used to search for the waveform which most matches the endpoints in the whole signal. Secondly, the grid search algorithm is used to select the optimal parameters for the extended signal to realize the optimal decomposition. Finally, all the components are analyzed to determine autocorrelation characteristics. According to the variance of the autocorrelation function, all the components can be divided into noise components, mixed components and signal components. The noise components are directly removed, and the mixed components are de-noised using the WTD method. Then, the signal components and the mixed components are reconstructed after de-noising. Analysis of simulation and measured data de-noising experiments proves the effectiveness of the proposed method. For the static signal, the mean square error (MSE) of the proposed method is reduced by 10.1% and the signal to noise ratio (SNR) is increased by 14.2%. For the dynamic signal, the MSE of the proposed method decreases by 16.9% and the SNR increases by 18.8%.

The magnetic gradient tensor system (MGTS) based on the fluxgate sensors array replaces partial differentials with the sensors reading difference to approximate the magnetic field gradient, but it introduces structural errors at the mean time. A good structure design with reasonable parameters can reduce structural errors and expand the theoretical detection range of the MGTS. From the analysis of the complete 18-uniaxial MGTS, five simplified structures of the MGTS were summarized, which include the plane cross, equilateral triangle, square, right-angle tetrahedron, and regular tetrahedron. The differential magnetic gradient tensor measurement matrixes of different structures were also provided, where we found the plane-cross structure produces the smallest structural error. Moreover, the theoretical detection limits expression of the MGTS to the magnetic dipole was derived. The detection limit boundary of the MGTS is related to the sensor’s accuracy, the array baseline distance, and the magnetization direction and magnetic moment magnitude of the source. In actual heading-line surveys, the magnetic moments of four typical small magnets were successfully estimated by the magnetic dipole positioning method, and the theoretical detection limits of the built plane-cross MGTS aiming at the four magnets were estimated. The results show that the estimation accuracy of the theoretical detection limits of MGTs is ±0.5 m.

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 positioning of multiple magnetic sources with different depths, distributions and magnetic moments is extremely difficult. The improved tilt angle for target area recognition can be well adapted to the self-adaptive fuzzy c-means (SAFCM) clustering algorithm for grid measurement of magnetic gradient tensors (MGT), which provides a feasible solution to solve the complex problem of multi-target inversion. First, we improve the tilt angle with the normalized source strengths and the tensor contraction, which can accurately identify the two-dimensional area boundary of objects with different buried depths regardless of the magnetization direction. The grid measurements of magnetic gradient tensor systems (MGTS) enable this process. Then, with the tensor spacial invariant relations, we calculate the source initial position coordinates corresponding to each node in the recognition area, thereby forming a dense point cloud in the space near the target real position. Finally, we introduce a penalty function into the clustering validity function to eliminate the monotonous decreasing trend of the cluster number optimization process, thus the SAFCM algorithm can accurately and automatically detect the number and position of centroids. The simulation shows that with the Gaussian noise of 0 mean and 5 nT/m variance, the targets number recognition accuracy of 20 magnetic dipoles is 97.6%, and the horizontal position and buried depth estimation accuracy is greater than 91.7% and 85.6% respectively. In the real survey areas of 2.1m×2.1m and 1.2m×1.2m, the coordinates’ estimation deviation of nine small magnets is less than 0.091m.

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.