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.

Vertical drilling is the first stage of petroleum exploitation and directional well technology. The near-vertical attitude at each survey station directly determines the whole direction accuracy of the borehole trajectory. However, the attitude measurement for near-vertical wells has poor azimuth accuracy because the poor signal-to-noise ratio of radial accelerometers hardly obtains the correct horizontal attitude, especially the roll angle. In this paper, a novel near-vertical attitude measurement method was proposed to address this issue. The redundant micro-electromechanical system (MEMS) accelerometers were employed to replace the original accelerometers from MEMS inertial measurement unit (IMU)/magnetometers for calculating horizontal attitude under near-vertical conditions. In addition, a simplified four-position calibration method for the redundant accelerometers was proposed to compensate for the installation and non-orthogonal error. We found that the redundant accelerometers enhanced the signal-to-noise ratio to upgrade the azimuth accuracy at the near-vertical well section. Compared with the traditional method, the experiment results show that the average azimuth errors and roll errors are reduced from 34.45° and 27.09° to 5.7° and 0.61°, respectively. The designed configuration scheme is conducive to the miniaturized design and low-cost requirements of wellbore measuring tools. The proposed attitude measurement method can effectively improve the attitude accuracy of near-vertical wells.

With the development of positioning technology, location services are constantly in demand by people. As a primary location service pedestrian navigation has two main approaches based on radio and inertial navigation. The pedestrian navigation based on radio is subject to environmental occlusion leading to the degradation of positioning accuracy. The pedestrian navigation based on micro-electro-mechanical system inertial measurement unit (MIMU) is less susceptible to environmental interference, but its errors dissipate over time. In this paper, a chest card pedestrian navigation improvement method based on complementary correction is proposed in order to suppress the error divergence of inertial navigation methods. To suppress attitude errors, optimal feedback coefficients are established by pedestrian motion characteristics. To extend navigation time and improve positioning accuracy, the step length in subsequent movements is compensated by the first step length. The experimental results show that the positioning accuracy of the proposed method is improved by more than 47% and 44% compared with the pure inertia-based method combined with step compensation and the traditional complementary filtering combined method with step compensation. The proposed method can effectively suppress the error dispersion and improve the positioning accuracy.

The error model of Fiber Optic Gyro System is simpler than Mechnical gyro, Fiber Optic Gyro offer the advantage of an extremely broad bandwidth and additionally the presence of Random Walk in the output. In this paper, A Calibration Technique was developed to calibrate a fiber optic gyro strapdown inertial navigator using a low cost two-gimbal test-table. Accelerometer scale factor and bias and accelerometer and gyro misalignments are calibrated using measurements of the acceleration in the navigation frame after each rotation. A sequence of ten rotations has been chosen to stream-line the procedure. The validity of the model is tested in real fiber optic gyro system.