Measurement While Drilling Research Articles

Analysis on the change characteristics of waveform during the transmission of continuous wave mud pulse signal

Continuous wave mud pulse transmission is the most widely used information transmission technology in measurement while drilling (MWD). The increase in transmission distance will cause the signal attenuation and deformation during transmission, the affecting exploration efficiency. The waveform change law of continuous mud pulse wave in the process of downhole transmission, this paper establishes a mathematical analysis model, focuses on the modulation form of continuous wave signal, physical mud characteristics, and drill pipe characteristics, and discusses the transmission rules of various characteristics on continuous pressure wave. A simulation system of drill pipe transmission pressure wave is constructed. The transmission characteristics of continuous wave signals under different modulation forms are discussed. The positive correlation between the amplitude attenuation and waveform distortion of pulse signals caused by increased gas holdup in the mud under bubbly flow patterns is analyzed. The numerical calculation and simulation analysis results show that the viscosity frequency characteristic of mud is the main factor affecting the attenuation of continuous wave signal. The surface roughness, size and other physical characteristics of drill pipe can affect the transmission speed and attenuation of signals in long-distance transmission. The signal is prone to distortion at the position of modulation phase change.

Design and numerical study of active cooling system of measurement while drilling for high temperature based on supersonic

Measurement while drilling (MWD) plays an important role in controlling well trajectory, improving drilling efficiency and saving drilling cost. In recent years, a large number of high-temperature wells have appeared, which makes the traditional MWD instruments no longer applicable. So far, no active cooling method has been successfully applied to MWD instruments for high-temperature oil and gas wells. This paper presents a new active cooling method for air drilling by utilizing the throttling and cooling of drilling gas, and the cooling system is designed. An axisymmetric numerical model of internal fluid is established, and different drilling gas flow channel design methods are discussed. The research results indicate that the wall temperature of the cooling section is much higher than the center fluid temperature, but lower than the ambient temperature, and can be used for active cooling of downhole drilling instruments. Compared with other design methods, the supersonic nozzle designed using the Bezier method has better parallelism of the gas in cooling section. The diffusion capability of straight wall diffuser is better than that of curved wall diffuser, and it can withstand greater back pressure. For straight wall diffuser, increasing the throat length and reducing the contraction and expansion angle can improve the diffusion capacity, but they also lead to a longer diffuser.

Chaotic Effect-Based Array Duffing Systems with Improved Nonlinear Restoring Force for Weak Signal Detection in Dynamic MWD.

In the process of dynamic Measurement While Drilling (MWD), the strong vibration and rapid rotation of the Bottom Hole Assembly (BHA) lead to multi-frequency and high-amplitude noise interference in the attitude measurement signal. The weak original signal and extremely low signal-to-noise ratio (SNR) are always the technical difficulties of dynamic MWD. To solve this problem, this paper uses the chaotic effect of the Duffing system, which takes the expression (-x3 + x5) as a nonlinear restoring force to detect the weak characteristic signal of downhole dynamic MWD. First of all, in order to meet the limit condition of the chaotic phase transition of the system output, the frequency value of the characteristic signal is reconstructed and transformed based on the variable scale theory. Then, in order to solve the influence of the initial phase of the characteristic signal on the detection accuracy, a detection model based on the array Duffing system is presented, and a frequency-detection scheme with all-phase coverage is given. Finally, another array Duffing system is designed for the parameter estimation of the characteristic signal. The critical value of chaotic phase transition is determined by adjusting the amplitude of the driving signal of the array Duffing system, and then the amplitude and phase parameters of the characteristic signal are synchronously estimated. The experimental results show that the proposed method can effectively extract the weak characteristic signal within the strong noise, and the SNR of the characteristic signal can be as low as -21 dB. Through the attitude calculation for the extracted characteristic signal, it can be seen that the proposed method can improve the accuracy of the inclination of the drilling tool significantly, which proves the feasibility and effectiveness of the method proposed in this paper.

Bottom hole pressure prediction based on hybrid neural networks and Bayesian optimization

Many scholars have focused on applying machine learning models in bottom hole pressure (BHP) prediction. However, the complex and uncertain conditions in deep wells make it difficult to capture spatial and temporal correlations of measurement while drilling (MWD) data with traditional intelligent models. In this work, we develop a novel hybrid neural network, which integrates the Convolution Neural Network (CNN) and the Gate Recurrent Unit (GRU) for predicting BHP fluctuations more accurately. The CNN structure is used to analyze spatial local dependency patterns and the GRU structure is used to discover depth variation trends of MWD data. To further improve the prediction accuracy, we explore two types of GRU-based structure: skip-GRU and attention-GRU, which can capture more long-term potential periodic correlation in drilling data. Then, the different model structures tuned by the Bayesian optimization (BO) algorithm are compared and analyzed. Results indicate that the hybrid models can extract spatial-temporal information of data effectively and predict more accurately than random forests, extreme gradient boosting, back propagation neural network, CNN and GRU. The CNN-attention-GRU model with BO algorithm shows great superiority in prediction accuracy and robustness due to the hybrid network structure and attention mechanism, having the lowest mean absolute percentage error of 0.025%. This study provides a reference for solving the problem of extracting spatial and temporal characteristics and guidance for managed pressure drilling in complex formations.

Real-time estimating method on rock strength via MWD of roofbolter and its application to in-situ grouting quality evaluation

Grouting reinforcement is an effective method for controlling fractured rock in the deeply buried roadways of coal mines. However, quantitatively evaluating the strength of grouted rock masses remains a challenge. The design of grouting reinforcement is primarily based on empirical knowledge. Consequently, this study proposes a real-time in-situ method for evaluating grouting quality using measure while drilling (MWD) based on a roofbolter. Initially, we validated the method through a numerical study using the discrete element method. Several 3D rock samples with varying crack densities were established and drilled numerically, demonstrating that the strength of fractured rock masses can be better estimated using the rock drillability index rather than drilling specific energy. Therefore, a model, known as the Pd–Rc model, was established to estimate rock strength based on the rock drillability index. Subsequently, an in-situ validation was conducted using a self-developed MWD testing system to assess the grouting quality in fractured rock masses. The results show that the strength of the rock mass increases by 38%, 56.0%, and 49.7%, respectively, after grouting, as observed in three boreholes. This method allows for quantitative estimation of grouting quality.

Application and Development of Fiber Optic Gyroscope Inertial Navigation System in Underground Space

Fiber Optic Gyroscope Inertial Navigation System (FOG-INS) is a navigation system using fiber optic gyroscopes and accelerometers, which can offer high-precision position, velocity, and attitude information for carriers. FOG-INS is widely used in aerospace, marine ships, and vehicle navigation. In recent years, it has also played an important role in underground space. For example, in the deep earth, FOG-INS can be used in directional well drilling, which can enhance recovery in resource exploitation. While, in shallow earth, FOG-INS is a high-precision positioning technique that can guide construction in trenchless underground pipelaying. This article extensively reviews the application status and latest progress of FOG-INS in underground space from three aspects—FOG inclinometer, FOG drilling tool attitude measurement while drilling (MWD) unit, and FOG pipe-jacking guidance system. First, measurement principles and product technologies are introduced. Second, the research hot spots are summarized. Finally, the key technical issues and future trends for development are put forward. The findings of this work are useful for further research in the field of FOG-INS in underground space, which not only provides new ideas and directions for scientific research, but also offers guidance for subsequent engineering applications.

Study on signal decomposition-based pump noise cancellation method for continuous-wave mud pulse telemetry

Continuous mud pulse telemetry is an advanced downhole data transmission technology in measurement while drilling (MWD) systems. However, various noise interference during transmission has resulted in continuous mud pulse telemetry often encountering difficulties in decoding under harsh working conditions, with the influence of pump noise being the most severe. On the bases of the narrowband signal characteristics of pump noise harmonics and a deep study of the variational mode decomposition (VMD) algorithm, this study proposes an improved version called constant center frequency VMD (CVMD), the mode function center frequencies of which are fixed in the initial state. The denoising performance of the proposed algorithm is thoroughly analyzed by simulating a series of continuous mud pulse signals with different noise intensities under stable/unstable mud pump conditions. Results demonstrate that the CVMD algorithm has an advantage over conventional filters because the former can maximize the preservation of useful information within the critical frequency band. Compared with the Kalman filter based on the same pump noise model, the CVMD algorithm has a higher signal-to-noise ratio, smaller mean square error, higher correlation with the ideal signal, and is also applicable when the pump state is unstable. In addition, the proposed method has been successfully applied to the processing of real-field experimental data transmitted over thousands of meters and disturbed by complex noise. Consequently, a distinctive waveform of the transmitted pulse is obtained, and powerful technical support is provided for the realization of continuous mud pulse downhole data transmission in harsh mud circulation environments.

Formation lithology predictions based on measurement while drilling (MWD) using gradient boosting algorithms

Many subsurface engineering applications require petrophysical and geomechanical properties as inputs for estimating the recoverable hydrocarbon volume and the reservoir deformation and properties' change during the life cycle of the production. Well log data plays a key role in estimating these reservoir properties, including volumes of minerals, Young's Modulus, and Poisson's Ratio. A conventional workflow using a multi-mineral petrophysical inversion model based on core-log integration requires an a priori rock-fluid model; therefore, it is often unavailable in reservoirs of complex minerals, such as carbonate or unconventional fields. In addition, most unconventional wells do not acquire Logging While Drilling (LWD) and/or wireline logs due to economic constraints or borehole instability reasons. Available measurements for these wells are typically Measurement While Drilling (MWD) Gamma Ray (GRMA) logs along with drilling dynamics measurements including Surface Weight-On-Bit (SWOB), Rate Of Penetration (ROP), Torque (TQA), Revolutions Per Minute (RPM), and the differential pressure. Thus, in this study, we demonstrate a machine learning approach, which does not require an a priori model, to predict formation lithologies based on conventional MWD and wireline well logs.We applied the Extreme Gradient Boosting Regression (XGBR) method to simultaneously predict the weight fractions of 5 minerals: QFM (Quartz-Feldspar-Mica), carbonate, clays, pyrite, and siderite from drilling dynamics measurements. The XGBR algorithm was tested with datasets from four adjacent wells in the Volve Field, located in the North Sea. A total of 10,575 data points were used to train and validate the model. The trained model was then applied to the blind test dataset of 10,446 data points from the same field. Lithology predictions from the trained model yield excellent results of weight concentrations with Root-Mean-Square Errors (RMSE) of 6.01 and 7.44% for training and test datasets, respectively. The prediction results agree with the lithology obtained from the Elemental Capture Spectroscopy (ECS) data as well as the dominant lithology record from rock cuttings. With the developed model, lithologic information and sonic logs of the formation could be predicted with MWD data, which could ultimately help optimize real-time drilling and completion operations in the field.

BILSTM-Based Deep Neural Network for Rock-Mass Classification Prediction Using Depth-Sequence MWD Data: A Case Study of a Tunnel in Yunnan, China

Measurement while drilling (MWD) data reflect the drilling rig–rock mass interaction; they are crucial for accurately classifying the rock mass ahead of the tunnel face. Although machine-learning methods can learn the relationship between MWD data and rock mechanics parameters to support rock classification, most current models do not consider the impact of the continuous drilling-sequence process, thereby leading to rock-classification errors, while small and unbalanced field datasets result in poor model performance. We propose a novel deep neural network model based on Bi-directional Long Short-Term Memory (BILSTM) to extract information-related sequences in MWD data and improve the accuracy of the rock-mass classification. Two optimization modules were designed to improve the model’s generalization performance. Stratified K-fold cross-validation was used for model optimization in small and unbalanced datasets. Model validation is based on the MWD dataset of a highway tunnel in Yunnan, China. Multiple metrics show that the prediction ability of the network is significantly better than those of a multilayer perceptron (MLP) and a support-vector machine (SVM), while the model exhibits an improved generalization performance. The accuracy of the network can reach 90%, which is 13% and 15% higher than the MLP and SVM, respectively.

MWD Data-Based Marble Quality Class Prediction Models Using ML Algorithms

Brønnøy Kalk AS operates an open pit mine in Norway producing marble, mainly used by the paper industry. The final product is used as filler and pigment for paper production. Therefore, the quality of the product has utmost importance. In the mine, the primary quality indicator, called TAPPI, is quantified through a laborious sampling process and laboratory experiments. As a part of digital transformation, measurement while drilling (MWD) data have been collected in the mine. The purpose of this paper is to use the recorded MWD data for the prediction of marble quality to facilitate quality blending in the pit. For this purpose, two supervised classification modelling algorithms such as conventional logistic regression and random forest have been employed. The results show that the random forest classification model presents significantly higher statistical performance, and it can be used as a tool for fast and efficient marble quality assessment.

Identification of Impact Frequency for Down-the-Hole Drills Using Motor Current Signature Analysis

In rotary-percussion drilling, the impact frequency is a crucial variable that is closely linked to operational factors that determine the efficacy of the drilling process, such as the rate of penetration, bit wear, and rock mass characteristics. Typical identification methods rely on complex simulation models or the analysis of different sensor signals installed on specially adapted setups, which are difficult to be implemented in the field. This paper presents a novel study where the impact frequency is identified by motor current signature analysis (MCSA) applied to an induction motor driving a DTH drilling setup. The analysis of the case study begins with the definition of characteristic drilling stages where the pressure and sound signals allow the detection of an impact frequency of 14.10 Hz, which is then used as a reference to validate three MCSA identification approaches. As a result of the analysis, the envelope approach is the most robust for nearly real-time implementations considering its simplicity and range of coverage. Experimental results provide evidence about the feasibility of the proposed MCSA methods to be integrated into Measurement-While-Drilling (MWD) systems to improve drilling condition monitoring and rock mass characterization.

Deep Learning for Intelligent Prediction of Rock Strength by Adopting Measurement While Drilling Data

Precise, rapid, and reliable prediction of rock strength parameters is of great significance for underground engineering. This paper presents a method for predicting rock strength parameters including the Poisson’s ratio (P), elastic modulus (E), and uniaxial compressive strength (UCS) based on computer drilling jumbo measurement while drilling (MWD) data. First, the distribution characteristics and correlation of MWD data are studied; second, a filtering method of MWD data is proposed, which reduces the influence of operational and mechanical factors; finally, an intelligent prediction model of rock mechanics parameters was established, 30 groups of test data were used for application, and the mean absolute percentage error (MAPE) of prediction results for P, E and UCS are 2.11%, 3.11%, and 2.9%, the determination coefficients (R2) are 0.4346, 0.8241, and 0.6616. Compared with the data before optimization, the accuracy of prediction results is improved significantly, it shows that the deep neural network model can accurately predict rock mass parameters.

Rock mass structural recognition from drill monitoring technology in underground mining using discontinuity index and machine learning techniques

A procedure to recognize individual discontinuities in rock mass from measurement while drilling (MWD) technology is developed, using the binary pattern of structural rock characteristics obtained from in-hole images for calibration. Data from two underground operations with different drilling technology and different rock mass characteristics are considered, which generalizes the application of the methodology to different sites and ensures the full operational integration of MWD data analysis. Two approaches are followed for site-specific structural model building: a discontinuity index (DI) built from variations in MWD parameters, and a machine learning (ML) classifier as function of the drilling parameters and their variability. The prediction ability of the models is quantitatively assessed as the rate of recognition of discontinuities observed in borehole logs. Differences between the parameters involved in the models for each site, and differences in their weights, highlight the site-dependence of the resulting models. The ML approach offers better performance than the classical DI, with recognition rates in the range 89% to 96%. However, the simpler DI still yields fairly accurate results, with recognition rates 70% to 90%. These results validate the adaptive MWD-based methodology as an engineering solution to predict rock structural condition in underground mining operations.

Real-Time Underreamer Vibration Predicting, Monitoring, and Decision-Making Using Hybrid Modeling and a Process Digital Twin

Summary In hole enlargement while drilling (HEWD) operations, underreamers are used extensively to enlarge the pilot hole. Reamer wipeout failure can cause additional bottomhole assembly (BHA) trips, which can cost operators millions of dollars. Excessive reamer shock and vibration are leading causes of reamer wipeout; therefore, careful monitoring of reamer vibration is important in mitigating such a risk. Currently, downhole vibration sensors and drilling dynamics simulations (DDSs) are used to comprehend and reduce downhole vibration, but vibration sensors cannot be placed exactly at the reamer to monitor the vibrations in real time. DDSs are difficult to calibrate and are computationally expensive for use in real time; therefore, the real-time reamer vibration status is typically unknown during drilling operations. A process digital twin using a hybrid modeling approach is proposed and tested to address the vibration issue. Large amounts of field data are used in advanced DDSs to calibrate the HEWD runs. For each HEWD section, calibrated DDSs are performed to comprehend the downhole vibration at the reamer and downhole vibration sensors. A surrogate regression model between reamer vibration and sensor vibration is built using machine learning. This surrogate model is implemented in a drilling monitoring software platform as a process digital twin. During drilling, the surrogate model uses downhole measurement while drilling (MWD) data as inputs to predict reamer vibration. Wipeout risk levels are calculated and sent to the operators for real-time decision-making to reduce the possibility of reamer wipeout. Large volumes of reamer field data, including field recorded vibration and reamer dull conditions were used to validate the digital twin workflow. Then, the process digital twin was implemented and tested in two reamer runs in the Gulf of Mexico. A downhole high-frequency sensor was placed 8 ft above the reamer cutting structure in one field run, and the recorded sensor vibration data and corresponding reamer dull conditions showed a very good match with the real-time digital twin predictions in a low-vibration scenario. Cases in high vibration are needed to fully validate the feasibility and accuracy of the digital twin. State-of-the-art downhole sensors, DDS packages, large amounts of field data, and a hybrid approach are the solutions to building, calibrating, and field testing the reamer digital twin to ensure its effectiveness and accuracy. Such a hybrid modeling approach can not only be applied to reamers but also to other critical BHA components.

A Bayesian Optimized Variational Mode Decomposition-Based Denoising Method for Measurement While Drilling Signal of Down-the-Hole Drilling

Measurement while drilling (MWD) emerges as a reliable technique for assessing rock mass properties. However, the measured MWD signals are often contaminated with noise, leading to distorted signals. To address this issue, this paper proposes a denoising method that utilizes variational mode decomposition (VMD) and wavelet soft thresholding (WST). The proposed method employs Bayesian optimization to adaptively determine the optimal VMD parameters. The decomposed modes are then further denoised using WST with appropriate thresholding and optimal wavelet decomposition levels. To validate the effectiveness of the proposed method, four synthetic signals with varying input signal-to-noise ratios (SNR) and two sets of measured MWD signals were evaluated. The results demonstrate the surpassing denoising efficiency of the proposed technique in terms of higher output SNR, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and lower RMSE values. Moreover, the denoised MWD signals show promising results, with reduced amplitude and volatility while preserving the characteristics of the original signals.

Investigation of pressure wave propagation and attenuation characteristics in managed pressure drilling by fast switching throttle valve

Pressure waves possess many significant applications in the oil and gas drilling engineering field, such as mud pulse telemetry (MPT) and measurement while drilling (MWD). The focus of this research is to study the pressure wave propagation and attenuation characteristics of wellbore liquid-phase flow in managed pressure drilling (MPD) by fast switching throttle valve (FSTV). First, a mathematical model of transient pressure wave propagation along the wellbore in both upstream and downstream directions is proposed in MPD by FSTV based on the one-dimensional transient flow theory. The model considering the frictional shear effect between the pipe walls is solved by utilizing the method of characteristics. Meanwhile, boundary conditions at the drill string inlet and annulus outlet, at the throttle valve, at the junction of drill bit, and at the reducer are adequately taken into account according to the actual situation of fluid flow. Second, a laboratory experiment of excited pressure waves in a vertical wellbore is conducted to measure the variation of the pressure fluctuation with different pump rates by FSTV. Comparing with the measurement result, the calculation result is discovered that the overall change is consistent, where the maximum absolute relative error at the peak of the pressure wave is only 4.5%. Finally, it further analyzes influential factors affecting the propagation and attenuation behaviors of wellbore pressure waves in liquid-phase flow based on the model. The results indicate that pressure waveforms present sinusoidal wave propagation, and pump rates, pressure wave speed, excitation time, fluid type, mud density, fluid viscosity, and borehole size exert varying degrees of influence on downhole pressure fluctuations. The proposed model achieves accurate quantitative interpretation and analysis of downhole pressure wave in MPD by FSTV, which has important significance for the realization of safe and efficient drilling.

Comparison Experimental Test on Feedback Degree of Single and Comprehensive Parameters of Measurement-While-Drilling Technology for Roof Bolter

The measurement-while-drilling (MWD) technology of roof bolter plays an important role in revealing roof rock lithology and roof structures, while the selection of MWD monitoring parameters is crucial for its effective application. Therefore, this study conducted experimental tests on the feedback degree of MWD parameters of roof bolter, mainly evaluating some single parameters and a comprehensive parameter of specific energy. Specific energy parameter was recognized as a better feedback parameter, while the results of this study showed that it did not reflect an absolute excellent feedback effect when the thrust energy contribution was small. Surprisingly, the torque single parameter reflected a good effect, which was also better than the single parameter of thrust, propulsion speed monitored. The research results provide a reference for the optimization of specific energy parameter in this case, and provide a data basis for the optimization of technical parameters of roof bolter WMD technology.

A Designed Calibration Approach for the Measurement-While-Drilling Instrument

The Measurement-While-Drilling (MWD) system, composed of a tri-axial magnetometer and a tri-axial accelerometer, is widely used in the Horizontal Directional Drilling machine in coal mines. This system can provide attitude information of each measuring point in the borehole, which will eventually allow the trajectory of the borehole to be drawn. The attitude information, however, showed a low-level accuracy, due to the sensor’s imperfection and mounting errors. The accuracy worsened when low-cost sensors were employed, as they had higher random noise. Therefore, an exploration of ways to eliminate the sensor imperfection and mounting tolerance as well as to suppress the noise is needed. In this paper, a feasible calibration approach was designed to address these issues. This new approach combined three foundational calibration algorithms, including the ellipsoidal fitting method, the planar fitting method, and the inner product invariance method. The traditional ellipsoidal fitting method and planar fitting method were optimized by using the recursive least square criterion and omitting the steps of sample data acquisition, respectively. In addition, the noise suppression method was involved in our approach to improve the calibration accuracy. The numerical simulation results showed that the number of sampling points decreased significantly, but the accuracy of the azimuthal angle and the pitch angle fully met the engineering requirements. The experimental results showed that the pitch angle error was reduced by less than 0.5°, and the azimuth error was also reduced by less than 2.5°. It should be noted that this new approach could be implemented without the help of other expensive auxiliary equipment.

Physics-Based Observers for Measurement-While-Drilling System in Down-the-Hole Drills

Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this context must be designed and conditioned for operating in harsh conditions, imposing trade-offs between the complexity, cost, and reliability of the measurement system. This paper presents a methodology for integrating physics-based observers into an MWD system as an alternative to complement or replace traditional physical sensors. The proposed observers leverage mathematical models of the drill’s electrical motor and its interaction with dynamic loads to estimate the bit speed and torque in a Down-the-Hole rig using current and voltage measurements taken from the motor power line. Experiments using data collected from four test samples with different rock strengths show a consistent correlation between the rate of penetration and specific energy derived from the observed drilling variables with the ones obtained from standardized tests of uniaxial compressive strength. The simplicity of the setup and results validate the feasibility of the proposed approach to be evaluated as an alternative to reduce the complexity and increase the reliability of MWD systems.

An Attitude Improvement Method of FOG-Based Measurement-While-Drilling Utilizing Backtracking Navigation Algorithm

Directional drilling utilizes the measurement-while-drilling (MWD) to provide attitude for drilling bit. A traditional MWD system, consisting of magnetometers and accelerometers, relies on expensive and huge nonmagnetic drill collar (NMDC) to shield from magnetic interference to obtain accurate attitude angles. A fiber optic gyroscope-based MWD (FOG-based MWD) that is based on inertial navigation is an alternative survey scheme. But, random vibration environment of underground introduces high-amplitude random noise to the FOGs. Besides, the auxiliary measuring equipment [such as global position system (GPS)] will not be available in underground environments, which will bring massive attitude error under pure inertial navigation. Therefore, combined with the engineering application conditions, this article proposes a modified attitude precision improvement approach of the FOG-based MWD. First, an autoregressive moving average (ARMA) error model for FOG is established to restrain the random vibration environment interference of underground. Second, combined with the FOG error model, a continuous backtracking navigation error model is developed to improve the azimuth accuracy. Moreover, the continuous backtracking algorithm frame is designed to estimate the attitude. Finally, a semi-physical experiment and a drilling test verify that the error model has an obvious effect on reducing the amplitude of FOG random noise. The proposed backtracking algorithm make the azimuth angle achieve a high-level estimation in short time. The result of the drilling test shows that the azimuth has an improvement of 48.79%, as compared with the traditional zero velocity update (ZUPT).