The stability of a fiber optic gyroscope (FOG) in measurement while drilling (MWD) could vary with time because of changing temperature, high vibration, and sudden power failure. The dynamic Allan variance (DAVAR) is a sliding version of the Allan variance. It is a practical tool that could represent the non-stationary behavior of the gyroscope signal. Since the normal DAVAR takes too long to deal with long time series, a fast DAVAR algorithm has been developed to accelerate the computation speed. However, both the normal DAVAR algorithm and the fast algorithm become invalid for discontinuous time series. What is worse, the FOG-based MWD underground often keeps working for several days; the gyro data collected aboveground is not only very time-consuming, but also sometimes discontinuous in the timeline. In this article, on the basis of the fast algorithm for DAVAR, we make a further advance in the fast algorithm (improved fast DAVAR) to extend the fast DAVAR to discontinuous time series. The improved fast DAVAR and the normal DAVAR are used to responsively characterize two sets of simulation data. The simulation results show that when the length of the time series is short, the improved fast DAVAR saves 78.93% of calculation time. When the length of the time series is long ( $6\times {10}^5$ samples), the improved fast DAVAR reduces calculation time by 97.09%. Another set of simulation data with missing data is characterized by the improved fast DAVAR. Its simulation results prove that the improved fast DAVAR could successfully deal with discontinuous data. In the end, a vibration experiment with FOGs-based MWD has been implemented to validate the good performance of the improved fast DAVAR. The results of the experience testify that the improved fast DAVAR not only shortens computation time, but could also analyze discontinuous time series.

Aiming to improve survey accuracy of Measurement While Drilling (MWD) based on Fiber Optic Gyroscopes (FOGs) in the long period, the external aiding sources are fused into the inertial navigation by the Kalman filter (KF) method. The KF method needs to model the inertial sensors’ noise as the system noise model. The system noise is modeled as white Gaussian noise conventionally. However, because of the vibration while drilling, the noise in gyros isn’t white Gaussian noise any more. Moreover, an incorrect noise model will degrade the accuracy of KF. This paper developed a new approach for noise modeling on the basis of dynamic Allan variance (DAVAR). In contrast to conventional white noise models, the new noise model contains both the white noise and the color noise. With this new noise model, the KF for the MWD was designed. Finally, two vibration experiments have been performed. Experimental results showed that the proposed vibration noise modeling approach significantly improved the estimated accuracies of the inertial sensor drifts. Compared the navigation results based on different noise model, with the DAVAR noise model, the position error and the toolface angle error are reduced more than 90%. The velocity error is reduced more than 65%. The azimuth error is reduced more than 50%.

Under the high dynamic conditions, Global Navigation Satellite System (GNSS) signals produce great Doppler frequency shifts, which hinders the fast acquisition of signals. Inertial Navigation System (INS)-aided acquisition can improve the acquisition performance, whereas the accuracy of Doppler shift and code phase estimation are mainly determined by the INS precision. The relation between the INS accuracy and Doppler shift estimation error has been derived, while the relation between the INS accuracy and code phase estimation error has not been deduced. In this paper, in order to theoretically analyze the effects of INS errors on the performance of Doppler shift and code phase estimations, the connections between them are re-deduced. Moreover, the curves of the corresponding relations are given for the first time. Then, in order to have a better verification of the INS-aided acquisition, a high dynamic scenario is designed. Furthermore, by using the deduced mathematical relation, the effects of different grade INS on the GNSS (including Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS)) signal acquisition are analyzed. Experimental results demonstrate that the INS-aided acquisition can reduce the search range of local frequency and code phase, and achieve fast acquisition. According to the experimental results, a suitable INS can be chosen for the deeply coupled integration.

A segmented angular rate joint estimator for fusing the measurements in an inertial sensor array is presented with higher precision and lower calculation burden, which offers better performance to UAV(Unmanned Aerial Vehicle) navigation. In recent years, micro aerial vehicles are increasingly indispensable in various industries. Attitude control is crucial for normal flight, therefore the precision of angular rate measurement is the determinant for attitude calculation based on IMU. The rapid development of MEMS industry, in addition to heterogeneous sensors, has given birth to multiple methods for improving the precision and reliability of angular rate measurement using homogeneous sensors called inertial sensor array. Computing angular motion based on inertial sensor array including gyroscope and accelerometer triads is a joint optimal estimation process. Due to the scale effect of accelerometer array, it is also sensitive to the angular motion. Both of the 2 types of sensor can form a complementary filter at sensor level. In this paper, we have proposed EKF and LM framework for angular velocity estimate of inertial array system, and fused them in the form of subsection measurement to give full play to the characteristics of the two methods and two types of sensor. Monte-Carlo simulation shows that the precision of angular velocity estimate is improved by up to 4.57%, and the calculation amount of the algorithm is greatly reduced.