L1 norm and sliding window IRLS based gravity acceleration estimation method for rotary steerable system

Abstract

The application discloses a kind of based on L1 norm and sliding window IRLS gravity acceleration estimation method of rotary steering system, for the rotary steering system in approximate single-axis high-speed rotation, strong vibration and severe impact coexist, different types of sensor noise presents Gaussian-Laplacian mixed characteristics, leading to the problem of traditional L2 norm method estimation precision decline, insufficient robustness, the method of the present application will three-dimensional gravity acceleration estimation decoupled into three independent scalar L1 norm optimization sub-problems, iteratively solve using IRLS algorithm, and introduce based on the double convergence criterion of dual principle to ensure its finite time convergence.The method realizes the efficient, robust real-time estimation of gravity acceleration in the drilling downhole with limited computing resources, significantly improves the accuracy and reliability of the rotary steering system attitude measurement under complex drilling conditions.

Description

Technical Field

[0001] This invention relates to the field of rotary steering systems for directional drilling, and more particularly, to a method for estimating gravity acceleration in rotary steering systems based on the L1 norm and sliding window IRLS, for achieving high-precision gravity vector extraction and attitude calculation in downhole environments with strong vibration and severe impact. Background Technology

[0002] Rotary Steerable Systems (RSS) are core equipment in modern intelligent directional drilling. They achieve precise wellbore trajectory control through multi-sensor fusion and closed-loop control. In this system, the accuracy of attitude estimation directly affects the wellbore trajectory control effect. The book *Rotary Steerable Drilling Technology*, edited by Sun Mingxin, published by China University of Petroleum Press, March 2009, 1st edition, pp. 7-14, discloses that a typical rotary steerable drilling system includes a downhole rotary steerable drilling tool system, a measurement and uplink communication system, a surface monitoring system, and a downlink communication system. In Measurement While Drilling (MWD) environments, accelerometers installed on the drill collar are typically used to provide a gravity reference vector. However, in actual downhole environments, accelerometer measurement signals are subject to interference from various factors. First, the high-speed rotation of the drill string around its axis causes the lateral gravity component to exhibit rapid periodic changes, resulting in uneven observability across the three axes within a finite time window, which increases the difficulty of estimation. Second, strong vibrations and severe impacts during drilling contaminate accelerometer measurements, causing accelerometer noise to deviate significantly from the Gaussian distribution and instead exhibit a heavy-tailed Laplace characteristic, i.e., forming a Gaussian-Laplace mixed noise. Finally, geological changes lead to non-stationarity in the statistical characteristics of noise, making it difficult to establish an accurate noise model.

[0003] To address these challenges, researchers have proposed a series of methods for estimating gravity acceleration. Existing methods utilize correlation analysis to suppress non-gravitational acceleration; however, these methods implicitly rely on assumptions of statistical stationarity and rotational synchronicity. Under significant non-stationary conditions caused by strong shocks and formation changes, rotationally synchronized non-gravitational acceleration is difficult to effectively distinguish through correlation calculations, thus affecting estimation accuracy. While methods based on weighted moving averages and improved Kalman filtering achieve gravity acceleration estimation under strong vibration conditions, in actual drilling operations, acceleration measurements are often contaminated by significant vibrations and shocks. Such shock-induced non-gravitational acceleration is difficult to effectively characterize using Gaussian noise or colored noise models, thus undermining the basic applicability of filtering methods. Although existing methods differ in their implementation, they all essentially rely on minimizing estimation errors in the L2 norm sense. These methods have some effectiveness in specific scenarios, but they generally face problems such as strong reliance on Gaussian noise assumptions, difficulty in suppressing sparse shock interference, high computational complexity, unsuitability for real-time downhole processing, and insufficient stability under conditions of limited information distribution.

[0004] L1-norm-based optimization methods possess inherent robustness to anomalous measurements and have theoretical advantages. However, directly applying them to drilling attitude calculations for rotary steerable systems still presents two challenges. First, traditional optimization algorithms involve numerous matrix inversions and high-dimensional iterative operations, resulting in extremely high computational complexity, making them difficult to run in real-time on downhole embedded microprocessors with strictly limited power consumption and computing power. Second, iterative optimization algorithms often struggle to determine when the global optimum is reached, lacking strict and computationally inefficient stopping criteria.

[0005] Given the aforementioned technical challenges of rotary steering systems, there is an urgent need for a gravity acceleration estimation method that can effectively address Gaussian-Laplace mixed noise, possesses robustness, low computational complexity, and deterministic real-time convergence characteristics, in order to meet the high-precision attitude measurement requirements of rotary steering systems under highly dynamic and harsh operating conditions. Summary of the Invention

[0006] This invention proposes a gravity acceleration path estimation method for Rotary Steerable Systems (RSS) in directional drilling based on L1 norm optimization and iteratively reweighted least squares (IRLS) with sliding window, which is used to achieve high-precision gravity vector extraction and attitude calculation in downhole environments with strong vibration and severe impact.

[0007] See Figure 1As shown, the present invention proposes a gravity acceleration estimation method for a rotary steerable system based on L1 norm optimization and sliding window iterative weighted least squares (IRLS). This method is installed in the ground monitoring system of the rotary steerable system (RSS) and aims to solve the technical problem of low accuracy and poor robustness of gravity acceleration estimation caused by strong vibration and severe impact under high dynamic drilling conditions.

[0008] The core idea of ​​this invention is to employ a two-stage frequency-time domain decoupled processing chain to match the mixed statistical characteristics of noise: In the first stage, a low-pass FIR filter is used to suppress rotationally correlated broadband noise and Gaussian white noise in the frequency domain, which is the optimal linear processing under the L2 norm; in the second stage, the heavy-tailed Laplace impulse residue remaining after the low-pass FIR filter is robustly estimated within a sliding window in the time domain using L1 norm optimization, which is the statistically optimal estimate under Laplace noise. By complementing the frequency domain and statistical distribution dimensions, dual robustness against mixed noise is achieved. To meet the real-time calculation requirements of drilling downhole, this invention decouples the three-dimensional gravity vector estimation into three independent scalar optimization subproblems and designs an efficient solution algorithm based on IRLS. Furthermore, a dual nonoptimality convergence criterion based on duality theory is introduced to provide a theoretical upper bound for the iterative process, ensuring deterministic convergence to the global optimum within a finite time. This invention improves the online estimation accuracy of gravity acceleration in rotary steering systems.

[0009] This invention proposes a method for estimating the gravitational acceleration of a rotary steering system based on the L1 norm and the sliding window IRLS. It utilizes the correspondence between the gravity vector and the geomagnetic vector in the drill coordinate system and the navigation coordinate system to perform dual-vector attitude estimation; the method comprises the following steps:

[0010] Step 1: Simultaneously acquire measurement data from the triaxial accelerometer, triaxial magnetometer, and gyroscope of the rotary steering system, and complete multi-sensor time alignment to construct a synchronous measurement dataset in the drill coordinate system;

[0011] Step 2: Perform data preprocessing on the triaxial accelerometer measurement data, including outlier detection, linear interpolation repair and spectrum analysis. Select an appropriate cutoff frequency based on the spectrum characteristics and design a low-pass filter to pre-filter the measurement data to suppress high-frequency random white noise.

[0012] Step 3: Based on L1 norm optimization and sliding window iterative weighted least squares algorithm, and in the process of iterative weighted least squares solution, a dual convergence criterion based on duality principle is introduced to set the iteration stopping condition, and robust gravity estimation is performed on the pre-filtered triaxial gravity accelerometer data to obtain the triaxial gravity acceleration component estimation results in the drill coordinate system.

[0013] Step 4: Using the dual-vector attitude calculation method, the direction cosine matrix is ​​constructed by utilizing the correspondence between the gravity vector and the geomagnetic vector in the drill coordinate system and the navigation coordinate system. The roll angle, pitch angle and yaw angle are extracted to complete the attitude estimation of the rotary steering system.

[0014] Step 5: Output the gravity acceleration estimation results and attitude angle sequence. If the gravity acceleration estimation and attitude estimation results of the rotary guidance system do not meet the preset accuracy requirements, return to step 2 and iteratively adjust the data preprocessing parameters and robust estimation parameters until the output gravity acceleration estimation results and attitude angle sequence that meet the accuracy requirements are obtained.

[0015] The measurement data in step one are obtained by synchronously collecting triaxial accelerometer measurement sequences, triaxial magnetometer measurement sequences, and gyroscope measurement sequences at a fixed sampling frequency during actual drilling operations.

[0016] The outlier detection and linear interpolation in step two are to preprocess the measurement sequence of the triaxial accelerometer; (A) calculate the local mean and standard deviation within the sampling time sliding window, and construct a statistical discrimination criterion based on this; when the deviation between the measured value and the local mean at a certain moment exceeds a preset threshold, the data point is identified as an outlier and removed; (B) the removed position is reconstructed using the linear interpolation method to restore the sampling continuity and integrity; (C) the outlier determination condition is: the absolute value of the difference between the current measured value and the corresponding local mean is greater than 3 times the standard deviation.

[0017] The objective function designed in step three is: , This represents the entire measurement sequence acquired within the sampling time, after passing through a low-pass filter. This represents the estimated value of gravity. This indicates taking the L1 norm.

[0018] The navigation coordinate system reference matrix constructed in step four is: ,in, This indicates the magnetic field strength northward in the navigation coordinate system. This indicates the magnetic field strength westward in the navigation coordinate system. The magnetic field strength in the celestial direction of the navigation system is represented by the geomagnetic vector of the navigation coordinate system, which can be expressed as: In the navigation coordinate system, the gravity vector is analytically expressed as: Geomagnetic vector From the total geomagnetic intensity Magnetic declination and magnetic inclination Sure.

[0019] The measurement matrix constructed in the drill coordinate system in step four is as follows: , This is an estimated value of gravity in the drill string coordinate system. This is the estimated geomagnetic value in the drill coordinate system after the magnetometer has been calibrated.

[0020] In step four, the attitudes are respectively the roll angle. Pitch angle and yaw angle Then the attitude estimation of the rotary steering system is as follows: .

[0021] Compared with the prior art, the method of the present invention has at least the following beneficial effects:

[0022] (1) The two-stage frequency domain-time domain decoupling processing chain (FIR+L1-IRLS) proposed in this invention performs optimal suppression of Gaussian and Laplace noise components respectively, and achieves dual robustness against complex downhole mixed noise from both frequency domain and statistical distribution dimensions, effectively overcoming the defect of traditional L2 norm method being sensitive to heavy-tailed pulse impact.

[0023] (2) This invention proposes a scalar decoupled IRLS algorithm, which decouples the original optimization problem of three-dimensional gravity vector estimation into three independent scalar optimization subproblems, and degenerates the high-dimensional matrix inversion into scalar weighted average, which greatly reduces the computational overhead of downhole microprocessors and solves the problem that traditional multidimensional optimization algorithms have a large computational load and are difficult to solve in real time in microprocessors.

[0024] (3) The present invention introduces a dual convergence criterion based on the duality principle, which provides a strict, computable and low-cost stopping condition for IRLS iteration, avoids the problem of convergence uncertainty of traditional iterative algorithms, and ensures the reliability and real-time performance of the algorithm in resource-constrained embedded environments. Attached Figure Description

[0025] Figure 1 This is a flowchart of the gravity acceleration estimation method for a rotating guidance system based on L1 norm and sliding window IRLS according to the present invention.

[0026] Figure 2 This is a schematic diagram of the navigation coordinate system, drilling tool coordinate system, and attitude angles designed in this invention.

[0027] Figure 3 This is a diagram showing the triaxial acceleration reconstruction result of dataset 1 according to an embodiment of the present invention.

[0028] Figure 4 This is a diagram showing the triaxial acceleration reconstruction result of dataset 2 according to an embodiment of the present invention.

[0029] Figure 5 This is a magnified view of the X-axis gravitational acceleration reconstruction result of dataset 1 according to an embodiment of the present invention.

[0030] Figure 6 This is a magnified view of the X-axis gravitational acceleration reconstruction result of dataset 2 according to an embodiment of the present invention.

[0031] Figure 7 This is a magnified view of the well inclination angle estimation results of dataset 1 according to an embodiment of the present invention.

[0032] Figure 8 This is a magnified view of the well inclination angle estimation results of dataset 2 according to an embodiment of the present invention. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. The examples of the parameters listed are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

[0034] See Figure 1 As shown, the present invention proposes a gravity acceleration estimation method for a rotary steerable system based on L1 norm optimization and sliding window iterative weighted least squares (IRLS). This method is installed in the ground monitoring system of the rotary steerable system (RSS) and aims to solve the technical problem of low accuracy and poor robustness of gravity acceleration estimation caused by strong vibration and severe impact under high dynamic drilling conditions.

[0035] Rotary Steerable Systems (RSS) utilize directional sensors (triaxial accelerometers, triaxial magnetometers, gyroscopes, etc.) to acquire real-time drilling information during directional drilling measurements. This real-time drilling information comprises: accelerometer data collected by the triaxial accelerometer, magnetometer data collected by the triaxial magnetometer, and gyroscope data such as magnetic declination, magnetic inclination, and total geomagnetic intensity collected by the gyroscope based on a geomagnetic reference model. The present invention employs a five-step process for processing the acquired real-time drilling information using a rotary steerable system gravity acceleration estimation method based on L1 norm optimization and sliding window iterative weighted least squares.

[0036] Rotary steering systems typically involve geodetic coordinate systems, body coordinate systems, and navigation coordinate systems during directional drilling measurements. In this invention, the navigation coordinate system is selected as the reference coordinate system used to determine the position, velocity, and attitude parameters of the measurement-while-drilling instrument (or drill string). The navigation coordinate system designed in this invention is a north-western geographic coordinate system (abbreviated as n-system, denoted by the superscript n in the various physical quantities of this invention), with its origin located at the current position of the drill string. The axis points to the geographical north. The axis points to the geographical west. The axes point upwards in the opposite direction of gravity, and the three axes conform to the right-hand rule. (See below) Figure 2 As shown. This coordinate system is fixed to the Earth, and its spatial orientation is considered constant during short-term measurements.

[0037] exist Figure 2 The drill string coordinate system is a front-left-top-right-hand coordinate system (abbreviated as b-system, denoted by the superscript b in the various physical quantities of this invention), with the origin located at the mounting center of the inertial measurement unit (IMU). Pointing towards the front of the drill bit along the axis of the drill string. The shaft points to the left radially along the drill string. The axis points radially towards the high side of the drill string, and the three axes satisfy the right-hand rule.

[0038] See Figure 1 As shown, the method of this invention requires the acquisition of measurement data from the triaxial accelerometer, magnetometer, and gyroscope of the rotary steering system. After preprocessing the measurement data, a two-stage frequency-time domain decoupling strategy is used to complete robust gravity acceleration estimation, and finally, attitude calculation is achieved through the dual-vector method. This method has the characteristics of high computational efficiency, strong real-time performance, and good robustness. It can effectively solve the problem of interference of strong vibration and large impact on gravity acceleration estimation in high-dynamic drilling environments, laying the foundation for accurate attitude estimation of the rotary steering system. In detail, the robust gravity acceleration estimation method for a rotary steering system based on L1 norm optimization and sliding window IRLS of this invention includes the following steps:

[0039] Step 1: Simultaneously acquire measurement data from the triaxial accelerometer, triaxial magnetometer, and gyroscope;

[0040] In actual drilling operations using a rotary steering system, this invention synchronously acquires measurement sequences from a triaxial accelerometer, a triaxial magnetometer, and a gyroscope at a fixed sampling frequency. For ease of explanation, the measurement sequence from the triaxial accelerometer is denoted as... The measurement sequence of the triaxial magnetometer is denoted as... The measurement sequence of the gyroscope is denoted as The three measurement sequences mentioned above record synchronously acquired information in the drill coordinate system, namely the drill system-measurement vector.

[0041] Record the nominal gravity value during real-time drilling information acquisition. Total geomagnetic intensity Magnetic declination and magnetic inclination This serves as the reference vector parameter for the navigation coordinate system of the drill bit acquisition location, i.e., the navigation reference vector. The navigation reference vector is used to construct the reference vector for subsequent attitude calculations.

[0042] During rotary drilling, the triaxial accelerometer installed near the drill bit on the drill collar is subjected to an extremely complex dynamic environment. Its output signal typically contains multiple components: the gravitational acceleration component to be extracted, the centrifugal acceleration generated by the drill string rotation, the broadband vibration caused by friction between the drill string and the wellbore and rock breaking by the drill bit, and sudden impact disturbances. Among these, the centrifugal acceleration is essentially caused by rotational motion and can be compensated for by combining angular velocity information measured by a gyroscope with an installation error model. To simplify the analysis, this invention ignores the influence of centrifugal acceleration; therefore, in this invention, the measurement sequence of the triaxial accelerometer... It includes: gravitational acceleration component Acceleration generated by the high-speed rotation of the drill bit Strong vibration and impact and observation noise Information, upper left corner mark For the coordinate system marking of the drill string, subscript It is a measurement time marker. It exhibits sparsity and heavy-tailedness, and its statistical properties follow a Laplace distribution. It follows a zero-mean Gaussian distribution. Since the measurement noise of a triaxial accelerometer is composed of the superposition of Gaussian and Laplace components, under the Gaussian-Lappland mixture model, the L1 norm estimator is the maximum likelihood estimate of the Laplace component, thus ensuring the natural robustness to impulse disturbances. This is also the statistical basis for choosing the L1 optimization method in this invention.

[0043] In step one, the synchronous acquisition by multiple sensors can ensure the consistency and integrity of the measurement information from the accelerometer, magnetometer, and gyroscope, reduce the attitude calculation error caused by the sampling delay of different sensors, provide a reliable data foundation for the subsequent robust estimation of gravitational acceleration, and meet the data synchronization requirements of the online measurement of the rotary guidance system.

[0044] Step 2: Preprocessing of triaxial accelerometer measurement data;

[0045] Outlier detection and linear interpolation repair are performed on the synchronously acquired drill string measurement information, and spectrum analysis is conducted. A low-pass filter is designed with a suitable cutoff frequency to pre-filter the data and suppress high-frequency random white noise.

[0046] Step 21, outlier detection and linear interpolation;

[0047] Because the rotary steering system operates in a highly dynamic drilling environment, the drill string is affected by various complex factors during drilling, such as changes in drilling pressure, drill string vibration, wellbore impact, and formation impact. Inevitably, outliers such as amplitude anomalies, sudden spikes, and transient distortions will appear in the triaxial accelerometer measurement data. These outliers typically do not conform to the continuous variation of gravitational acceleration. If directly used in subsequent gravitational acceleration estimation, they will cause distortion of the residual distribution during L1 norm optimization, reducing the accuracy of triaxial gravitational acceleration component estimation and even affecting the stability of attitude calculation results. Therefore, before performing triaxial gravitational acceleration estimation, it is necessary to first detect and repair outliers in the accelerometer measurement data to improve the data quality and estimation reliability of subsequent algorithms. Therefore, this invention employs outlier detection and linear interpolation to correct outliers in the triaxial accelerometer measurement sequence. Preprocessing is performed. (A) The local mean and standard deviation within the sliding window of the sampling time are calculated, and a statistical discrimination criterion is constructed accordingly. When the deviation between the measured value and the local mean at a certain moment exceeds a preset threshold, the data point is identified as an outlier and removed. (B) The removed positions are reconstructed using linear interpolation to restore the continuity and integrity of the sampling. (C) The outlier determination condition is: the absolute value of the difference between the current measured value and the corresponding local mean is greater than 3 times the standard deviation. This multiple is a preset threshold coefficient used to control the sensitivity of outlier detection. Specifically, the local mean is denoted as... The standard deviation is denoted as The measured value at a certain moment is denoted as , to satisfy Data points are marked as outliers and removed. Linear interpolation is then performed on the marked outlier points to restore sampling integrity.

[0048] Step 22, low-pass pre-filtering;

[0049] Low-pass pre-filtering: Based on the data sampling frequency and the cutoff frequency obtained from spectral analysis, a low-pass FIR filter with an appropriate cutoff frequency and order is designed. This filter is then used to perform low-pass filtering on the triaxial accelerometer data after outlier repair, initially suppressing rotationally correlated broadband noise and high-frequency Gaussian white noise. The filtered accelerometer measurement sequence is denoted as the FIR-filtered sequence. This stage utilizes the optimal linear estimation characteristic of the low-pass FIR filter for Gaussian white noise and is the first stage of the two-stage processing chain. Finite Impulse Response (FIR) refers to a digital filter whose impulse response returns to zero after a finite time.

[0050] In step two, the low-pass pre-filtering method guided by spectrum analysis, which combines outlier detection and linear interpolation repair, is used to address the problem of data quality degradation caused by abnormal abrupt changes, signal discontinuities, and high-frequency noise interference in accelerometer measurement data under high dynamic environments downhole. This differs from traditional data preprocessing methods that only perform simple filtering or do not distinguish outliers. It achieves effective removal and reconstruction of outlier data and suppression of high-frequency random noise and rotation-related interference, thereby obtaining a continuous, smooth, and more physically consistent acceleration sequence, providing high-quality input data for subsequent L1 norm estimation.

[0051] Step 3: Use the L1 norm and sliding window IRLS algorithm to estimate the triaxial gravity components;

[0052] To address the challenges of extracting gravitational acceleration from accelerometers under conditions of strong vibration, high impact, and fluctuating rotational speed, where accelerometers are affected by vibration and impact disturbances, and where traditional filtering methods fail due to poor observability and impact sensitivity, this paper investigates an L1-norm optimization-based gravitational acceleration estimation method. The L1-norm optimization method breaks away from the traditional filtering framework that relies on the gravity propagation equation. It directly models the accelerometer based on an algebraic measurement model and introduces the L1-norm optimization framework. Leveraging the inherent robustness of L1-norm optimization to anomalous measurements, it separates gravitational acceleration from accelerometer measurements contaminated by strong vibration and impact, effectively overcoming the deficiency of traditional L2-norm optimization in averaging outlier energy into the estimation results under impact disturbances. Furthermore, this invention introduces a dual convergence criterion based on the duality principle into the L1-norm optimization algorithm, providing a strict, computable, and low-cost stopping condition for IRLS iteration. This avoids the convergence uncertainty problem of traditional iterative algorithms and ensures the reliability and real-time performance of the algorithm in resource-constrained embedded environments. Within a sliding window framework, mean estimation based on L1 norm optimization and the IRLS algorithm is performed on the triaxial accelerometer data (i.e., the FIR-filtered sequence) after low-pass FIR filtering. This is the second stage of the two-stage processing chain of this invention, a time-domain nonlinear robust processing. Its core is to decouple the triaxial coupling problem into three independent single-axis scalar optimization problems, thereby achieving the removal of the Laplace-type pulse residue remaining after FIR filtering with extremely low computational complexity.

[0053] This invention further combines the IRLS algorithm with a sliding window mechanism, utilizing the slow change in gravity components between adjacent windows. The estimation result of the previous window is used as the initial value of the current window. Furthermore, a dual convergence criterion based on duality theory is used to monitor and control the iteration process in real time. This reduces the number of iterations while maintaining estimation accuracy, improving the algorithm's convergence efficiency and reliability in engineering applications. This invention has a length of... Within the sliding window, the FIR-filtered sequence of any axis is denoted as... ,and subscript Indicates length is Different sampling points within the same window, For the uniaxial gravity component to be estimated, To mitigate residual uniaxial background noise, This is the single-axis background noise after FIR filtering.

[0054] In this invention, all measurement sequences acquired within the sampling time after low-pass FIR filtering are denoted as... ,and ,use The objective function chosen for constructing the L1 norm estimation problem is: , It is a defined estimate of gravity. The objective function, This indicates taking the L1 norm, and the superscript T indicates matrix transpose. The objective function... This objective function aims to find an optimal estimate of gravity within the entire sliding window that minimizes the sum of the absolute values ​​of all observed residuals. It concerns the estimated value of gravity. A convex function has the property that local optima are also global optima. Therefore, any local optimal solution is also a global optimal solution, ensuring the stability and uniqueness of the solution.

[0055] The present invention uses the L1 norm and sliding window IRLS algorithm to estimate triaxial gravity components, which includes the following steps:

[0056] Step 31, Initialize the sliding window;

[0057] Initialize the sliding window and select an appropriate window size according to the sampling frequency (i.e., the maximum is...). The sliding window is then processed as a non-overlapping sliding window based on its size. The current sliding window is denoted as c, and the window preceding c is denoted as the previous sliding window. The window that follows the current sliding window c is called the next sliding window. To accelerate convergence, the previous sliding window... Gravity estimation results The initial gravity value for the current sliding window c This invention utilizes the characteristic of the slow, gradual change of gravity components in adjacent windows to accelerate convergence, making the iteration starting point extremely close to the optimal solution, thus significantly reducing the number of iterations and the amount of computation.

[0058] Step 32, IRLS iterative solution;

[0059] Rotary steering systems operate in a highly dynamic drilling environment where downhole processors have limited computing and storage resources, placing high demands on the real-time performance and computational efficiency of the algorithm. The IRLS algorithm, however, involves only weight updates and weighted least squares calculations in each iteration, eliminating the need to solve complex nonlinear optimization problems or calculate higher-order derivatives or perform large-scale matrix operations. Therefore, it offers advantages such as low computational complexity, fast convergence, and ease of embedded implementation, meeting the real-time computational requirements for online gravity acceleration estimation and attitude calculation in rotary steering systems. In this invention, iteratively reweighted least squares (IRLS) is used to iteratively solve for each sampling point within each sliding window. The steps of the IRLS iterative solution are as follows:

[0060] (1) Calculate the residuals: , Represents the c-th iteration window. The residuals of each sampling point, i.e., the observed values Compared with the current gravity estimate The residual between the two estimates. This residual reflects the magnitude of the current estimation error.

[0061] (2) Update the weight matrix: The weight matrix is ​​updated using the regularized Weizfeld form. .

[0062] in, Represents the weight matrix The Middle Line number The weighted element of the column, the The weight of a data point is inversely proportional to the absolute value of the residual. The larger the residual, the smaller the corresponding weight, thus reducing the impact of outliers on the gravity estimation results. Data points with smaller residuals have larger weights, thus dominating the gravity estimation results. This is a regularization parameter to prevent the matrix from becoming ill-conditioned when the weights tend to infinity as the residuals approach zero. The weight update in this invention addresses the following problem: Since the L1 norm objective function is not differentiable at zero, it is difficult to solve directly using traditional gradient optimization methods. Using linear programming, interior-point methods, or other general convex optimization algorithms not only results in high computational complexity but also fails to meet the engineering requirements of real-time downhole calculations for rotary steering systems. Therefore, this invention employs an Iteratively Reweighted Least Squares (IRLS) algorithm to iteratively transform the L1 norm optimization problem into a series of weighted least squares problems. By continuously updating the sample weights, the weights corresponding to abnormal data adaptively decrease while the weights corresponding to normal data remain relatively large. This maintains L1 norm robustness while fully utilizing the advantages of low-squares solution—high efficiency, computational stability, and ease of implementation—to achieve fast and robust estimation of triaxial gravitational acceleration.

[0063] (3) Weighted least squares solution: In the IRLS framework, the L1 norm problem is transformed into a weighted L2 problem. Since the three-axis problem has been decoupled into a single-axis scalar problem, the weighted least squares solution degenerates into a weighted arithmetic mean form, that is, a weighted summation of all samples within the window according to their weights, without the need for matrix inversion, thus significantly reducing computational complexity and meeting the requirements of real-time downhole drilling computation.

[0064] Step 33: Convergence judgment and stopping;

[0065] Because rotary steerable systems operate in a highly dynamic drilling environment, measurement data are affected by strong vibrations, severe shocks, and non-Gaussian mixed noise, resulting in varying convergence speeds for the IRLS algorithm across different windows. Using a fixed number of iterations or a single convergence criterion as the stopping condition can easily lead to premature termination in some windows, insufficient estimation accuracy, or excessive iterations in some windows, wasting computational resources. Therefore, this invention constructs a dual convergence criterion based on duality theory, evaluating the convergence state of the current iterative solution from both the primal and dual optimization problems, and combining this with the maximum number of iterations to determine the iteration stopping condition. This method more accurately reflects the proximity between the current estimation result and the optimal solution, reducing invalid iterations while ensuring the accuracy of gravity acceleration estimation, improving algorithm convergence efficiency, reducing real-time downhole computational load, and enhancing the robustness and engineering applicability of this invention under complex drilling conditions.

[0066] Let the convergence criterion be denoted as... Let the second convergence criterion be denoted as .

[0067] Convergence judgment and stopping: Introducing a biconvergence criterion based on the duality principle. and This provides a theoretically optimal upper bound for iteration. .

[0068] in, This represents the gravity estimate in the c-th iteration window. The objective function, This is the transpose of the measurement sequence after FIR filtering in the current window. Let c be the sequence of dual variables for the c-th iteration window. Let represent the residual sequence at the c-th iteration window point. This represents the sum of the absolute values ​​of the elements in the residual sequence within the current window. The subscript 1 indicates the L1 norm. This indicates retrieving the maximum value of the elements in the dual variable sequence within the current window. Indicates retrieving from the current window Elements and The maximum value of the dot product of the elements.

[0069] In this invention, convergence criterion one Convergence Criterion 2 The degree of closeness between the current solution and the global optimal solution is characterized by the relative duality gap between the primal problem and the dual problem.

[0070] The dual variable of this invention The construction method is as follows The subscript Indicates the first One element, This indicates the index of the smallest residual element.

[0071] Iteration stops when any of the following conditions are met. Let the objective convergence value be denoted as... Stop condition one: or That is, either convergence criterion one or convergence criterion two is less than the target convergence value; stopping condition two: set the maximum number of iterations according to actual engineering needs. ,when When the maximum number of iterations is reached, the iteration stops to ensure the computational controllability of the algorithm in engineering applications.

[0072] In this invention, step three is performed on each of the three axes to obtain the triaxial gravity estimate of the gravity acceleration vector in the drill coordinate system. .

[0073] In step three, the decoupled estimation method based on L1 norm optimization and sliding window iterative weighted least squares (IRLS) is used to address the problem of large estimation deviations and insufficient robustness of gravity components caused by impact disturbances and heavy tail noise in highly dynamic drilling environments. This differs from traditional methods based on L2 norm or global triaxial coupling, enabling independent and robust estimation of triaxial gravity components, adaptive weight reduction processing of outlier data, and rapid convergence and real-time stable output under low computational complexity. Furthermore, by combining sliding window L1 norm optimization with IRLS iterative solution and introducing a dual convergence criterion based on duality theory, robust estimation and deterministic convergence of triaxial gravity acceleration are achieved. This significantly reduces computational complexity while maintaining estimation accuracy, improving the algorithm's real-time downhole execution capability and engineering application reliability in rotary steering systems.

[0074] Step 4: Dual-vector attitude calculation;

[0075] During drilling operations, rotary steering systems face high-speed rotation of the drill string, intense vibration, and impact loads. Attitude calculation requires not only high computational accuracy but also real-time performance and stability. Relying solely on gyroscope integration for attitude updates inevitably introduces zero-bias accumulation errors; relying solely on gravity vectors fails to provide complete three-dimensional attitude information. Therefore, this invention utilizes the correspondence between gravity and geomagnetic vectors in the drill string and navigation coordinate systems to calculate the direction cosine matrix and extract Euler angles, thus completing the attitude calculation for the rotary steering system. The basic principle is as follows: for the navigation and drill string coordinate systems in three-dimensional space, the attitude rotation matrix between the two coordinate systems is solved using the projected coordinates of two non-collinear reference vectors in both coordinate systems through coordinate transformation. This fully considers the high stability of the directions of gravity and geomagnetic vectors in space, and their typically non-collinearity, meeting the requirements for drill string attitude estimation.

[0076] Step 41, construct the reference matrix in the navigation coordinate system;

[0077] In the navigation coordinate system (northwest-sky coordinate system), the gravity vector is analytically expressed as: Geomagnetic vector From the total geomagnetic intensity Magnetic declination and magnetic inclination The constructed navigation coordinate system reference matrix is ​​confirmed to be... ,in, This indicates the magnetic field strength northward in the navigation coordinate system. This indicates the magnetic field strength westward in the navigation coordinate system. The magnetic field strength in the celestial direction of the navigation system is represented by the geomagnetic vector of the navigation coordinate system, which can be expressed as: .

[0078] The orthogonal basis constructed in the navigation coordinate system is: in, It is the first orthogonal basis. It is the second orthogonal basis. This forms the third orthogonal basis. Stacking the three basis vectors row-wise creates the navigation frame reference matrix. Its inverse matrix can be pre-computed offline, requiring only one matrix multiplication at each time step.

[0079] Step 42, construct the measurement matrix in the drill string coordinate system;

[0080] Using the gravity estimate in the drill string coordinate system obtained after optimization in step three Geomagnetic estimates in the drill string coordinate system after magnetometer calibration Construct a measurement matrix in the drill coordinate system ,and .

[0081] Step 43, calculate the direction cosine matrix;

[0082] In this invention, the direction cosine matrix is ​​obtained by the two-vector method. Euler angles are extracted from the direction cosine matrix, and the results are obtained. For roll angle, The pitch angle, This refers to the yaw angle. When calculating the roll, pitch, and yaw angles of the navigation coordinate system,... Represents the direction cosine matrix The element in the first row and first column of the data. Represents the direction cosine matrix The element in the 2nd row and 1st column, Represents the direction cosine matrix The element in the 3rd row and 1st column, Represents the direction cosine matrix The element in the 3rd row and 2nd column, Represents the direction cosine matrix The element in the 3rd row and 3rd column of the data has... .

[0083] In step four, this invention uses a dual-vector attitude calculation method based on gravity vector and geomagnetic vector to solve the problem of insufficient accuracy and poor stability caused by the reliance on a single information source for attitude calculation in rotary steering systems under complex working conditions. This is different from the traditional method of attitude estimation that relies only on accelerometers or a single reference vector. It can realize the rapid construction of the direction cosine matrix between the navigation system and the home system, as well as the accurate extraction of roll angle, pitch angle and yaw angle, thereby obtaining stable attitude calculation results with engineering applicability.

[0084] Step 5: Check the output and parameter adjustments;

[0085] Check the output and the convergence of the iteration, and adjust the parameters accordingly.

[0086] Step 51: Output the gravitational acceleration estimation results and attitude angle sequence;

[0087] Record the triaxial gravitational acceleration estimation results obtained by the L1-IRLS algorithm, and the attitude angle sequence at each moment obtained by the dual-vector attitude solution. Simultaneously, it records convergence statistics such as convergence rate and average number of iterations of the output attitude angle sequence and triaxial gravity acceleration data. The convergence rate and average number of iterations not only reflect the computational load of the algorithm, but also serve as indirect indicators of real-time vibration intensity, providing auxiliary information for drilling downhole condition diagnosis.

[0088] Step 52, parameter adjustment;

[0089] If the convergence rate is too low or the estimation result does not meet the accuracy requirements, return to step two and adjust the low-pass FIR filter cutoff frequency and window size. Regularization parameters The algorithm parameters are adjusted until the output of the gravity acceleration estimation result and attitude angle sequence that meet the accuracy requirements are obtained.

[0090] In step five of this invention, a closed-loop parameter feedback adjustment mechanism of estimation-evaluation-adjustment is established in the ground monitoring system of the Rotary Steerable System (RSS). This achieves adaptive optimization of the algorithm parameters, enabling the algorithm to automatically adjust the estimation strategy according to different drilling conditions. This solves the problem that the performance of the rotary steerable system algorithm may fluctuate and it is difficult to maintain the optimal state continuously under complex and variable drilling conditions. This improves the adaptability, robustness and engineering applicability of the method of this invention in unknown drilling downhole environments.

[0091] Example 1

[0092] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment:

[0093] This invention employs two sets of drilling data for verification. The data originates from IMU measurement sequences acquired by the Rotary Steering System (RSS) tool during actual drilling operations, including sampling data from triaxial accelerometers and triaxial magnetometers, with a sampling frequency of 200Hz. Dataset 1 contains 143,485 original data points, corresponding to an effective acquisition time of approximately 717 seconds; Dataset 2 contains 149,450 original data points, corresponding to an effective acquisition time of approximately 747 seconds. Both sets of data are drilling records without ground truth.

[0094] Non-overlapping sliding window processing was performed with a window size of N=100 points (0.5s). Dataset 1 generated a total of 1435 estimation windows, and Dataset 2 generated a total of 1495 estimation windows. All experiments were run in the MATLAB environment, with a maximum number of iterations set to 200. The comparison methods included: the method of performing only FIR low-pass filtering (cutoff frequency 10Hz, 64th order) (hereinafter referred to as the FIR method); the method of estimating using a Kalman filter after FIR low-pass filtering (hereinafter referred to as the KF method); the method of estimating using the L1-IRLS algorithm designed in this invention after FIR low-pass filtering (i.e., the L1 method); and the FIR+MA method of performing a 100-point moving average after FIR filtering (i.e., the FIR+MA method).

[0095] Adaptive outlier detection is performed on the acquired raw data, and linear interpolation is used to repair the marked outlier points. A 64th-order FIR low-pass filter with a cutoff frequency of 10Hz is used to pre-filter the triaxial accelerometer data.

[0096] The data after low-pass FIR filtering is processed by non-overlapping sliding window with a window size of N=100 points. IRLS iteration is performed on the data of each axis in each window. The convergence statistics of gravity acceleration estimation according to the embodiment of the present invention are shown in Table 1.

[0097] Table 1. Statistical results of convergence of gravity acceleration estimation

[0098]

[0099] Table 1 summarizes the convergence performance of gravity acceleration estimation for each axis in the two sets of drilling data. Overall, the L1-IRLS algorithm can meet the preset suboptimal convergence criterion threshold with fewer iterations in most windows. The average number of iterations for both datasets is less than 20, indicating that the recursive initialization strategy between windows effectively accelerates convergence, and the actual computational cost meets the requirements of use under the condition of limited downhole computing resources.

[0100] The convergence rate metric (the proportion of convergence windows to total windows) further validates the robustness of the algorithm. In both sets of data, the convergence rates for the Y and Z axes are both above 85%, while the X-axis convergence rate is approximately 74%, indicating that the algorithm can reliably find high-precision suboptimal solutions in the vast majority of windows. Although the X-axis convergence rate is relatively low, this does not necessarily mean that the algorithm is diverging or has failed in estimation. Further data analysis shows that the X-axis sections that did not trigger the stopping condition are mostly stable well sections with extremely low vibration. In these windows, the residual amplitude is close to the limits of background noise and numerical calculation accuracy, making it difficult to further reduce the relative duality gap below the stringent set threshold. In fact, the gravity component estimates output at this point already possess sufficient attitude solution accuracy.

[0101] Figure 3 and Figure 4 The results of triaxial acceleration signal reconstruction for two datasets are presented. Significant high-frequency oscillations and pulse spikes exist in the original measurement data, particularly along the transverse axes (Y and Z axes), caused by drill string vibration and impact interference. After FIR filtering, most of the high-frequency noise is attenuated; however, noticeable residual spikes remain, indicating that linear filtering alone is insufficient to suppress impulse interference. While the KF method offers some noise suppression through state prediction, its Gaussian noise assumption still introduces significant estimation bias when dealing with heavy-tailed distributions (Laplace-type impacts). In contrast, the proposed L1-IRLS method effectively eliminates these residual spikes while preserving the low-frequency gravity trend. This is particularly evident on the X-axis, where the signal becomes significantly smoother without introducing noticeable bias. Across all three axes, the L1-based reconstruction method demonstrates stronger robustness against impulse noise compared to FIR processing alone. Overall, both traditional FIR filtering and Kalman filtering (KF) methods can track the changing trends of the gravity component for most of the time, but they show significant shortcomings in the strong impact and severe vibration ranges. This phenomenon can be explained from the perspective of its optimization objective function: the L1 norm penalizes large residuals with linear growth, which, compared to the squared growth of the L2 norm, gives less weight to outliers, thus effectively suppressing the impact of impulse noise.

[0102] Figure 5 and Figure 6The diagram shows magnified views of the X-axis gravitational acceleration of two datasets over short time intervals to highlight their behavior under impulse perturbations. It can be seen that in the strong impulse range, the original signal exhibits significant impulse jumps. While FIR and KF partially smooth these perturbations, their limited ability to handle non-Gaussian noise leaves noticeable residual fluctuations. The L1 method of this invention effectively suppresses these spikes, producing a nearly piecewise smooth signal. This demonstrates the advantage of L1 optimization in handling high-amplitude perturbations, improving its time-domain robustness. Furthermore, the KF output exhibits a certain recovery lag after the impulse, while the L1 method, employing a sliding window local optimization and not relying on long-term state propagation, can quickly recover to the normal estimation level after the impulse, demonstrating better transient response characteristics.

[0103] In summary, the L1-IRLS method significantly outperforms traditional filtering methods in non-Gaussian, high-pulse measurement-while-drilling environments. The well inclination angle statistical results according to this embodiment (unit: As shown in Table 2.

[0104] Table 2 Comparison of Well Inclination Angle (Pitch Angle) Calculation Results of Four Methods

[0105]

[0106] Table 2 compares the method of this invention with the FIR method, the Kalman filter method, and the FIR+MA method. It can be seen that the average wellbore inclination angle (pitch angle) given by the four methods is consistent, with the maximum deviation not exceeding [a certain value]. This demonstrates that the L1-IRLS method of this invention does not introduce systematic bias. In dataset 1, the L1-IRLS method reduces the standard deviation of well inclination angle from that of the FIR method. Down to The reduction reached 79.7% in dataset 1 and 69.4% in dataset 2. In terms of range, the estimation range of the FIR and KF methods exceeded... The L1-IRLS method is only about This further illustrates that traditional methods suffer from severe instantaneous divergence under impact, while the L1 method can effectively constrain the estimated fluctuations. Compared with the FIR+MA method, the L1 method of this invention can evaluate the estimation reliability of each window in real time through a dual convergence criterion, effectively suppressing instantaneous deviations and obtaining a smooth angle estimation curve.

[0107] Figure 7 and Figure 8The results of wellbore inclination (pitch) estimation for two datasets under different processing methods are presented. The FIR method exhibits numerous spikes and fluctuations, showing significant high-frequency volatility, which leads to noise in the inclination estimation. The L1-IRLS method effectively suppresses these fluctuations. In addition, although the FIR+MA method is statistically close to the L1-IRLS method, it exhibits obvious residual jitter.

[0108] Based on the combined gravity estimation and attitude calculation results, the robust gravity acceleration estimation method for rotary steering systems provided in this invention, based on L1 norm optimization and sliding window IRLS, can efficiently and robustly estimate gravity acceleration in highly dynamic drilling environments. It is applicable to rotary steering systems under various complex operating conditions. The method features a clear algorithm structure, high computational efficiency, good real-time performance, strong robustness, and applicability to downhole environments, overcoming the shortcomings of traditional methods that rely on Gaussian noise assumptions and lack sufficient shock resistance in dynamic environments. This invention will effectively solve the problem of insufficient accuracy in gravity acceleration estimation in rotary steering systems, providing important technical support for future engineering applications that improve the positioning accuracy and reliability of rotary steering systems.

[0109] This invention relates to a method for estimating gravity acceleration in rotary steerable systems (RSS) for directional drilling. It addresses the technical problem of low accuracy and poor robustness in gravity acceleration estimation caused by Gaussian-Laplace mixed noise resulting from near-single-axis high-speed rotation, strong vibration, and severe impacts in highly dynamic drilling environments. This method is installed in the surface monitoring system of the RSS. Its core is a two-stage frequency-time domain decoupled processing chain using a low-pass FIR filter and L1-norm IRLS sliding window optimization. This decouples the complex multidimensional optimization problem into an independently solvable scalar problem. Combined with a dual-convergence criterion based on the duality principle, deterministic iteration is performed, thereby achieving real-time robust estimation of downhole gravity acceleration. This results in significantly improved estimation accuracy, computational efficiency, and shock resistance under extremely harsh operating conditions.

Claims

1. A method for estimating the gravitational acceleration of a rotary steering system based on L1 norm and sliding window IRLS, which utilizes the correspondence between the gravity vector and the geomagnetic vector in the drill coordinate system and the navigation coordinate system to perform dual-vector attitude estimation; characterized in that... The steps are as follows: Step 1: Simultaneously acquire measurement data from the triaxial accelerometer, triaxial magnetometer, and gyroscope of the rotary steering system, and complete multi-sensor time alignment to construct a synchronous measurement dataset in the drill coordinate system; Step 2: Perform data preprocessing on the triaxial accelerometer measurement data, including outlier detection, linear interpolation repair and spectrum analysis. Select an appropriate cutoff frequency based on the spectrum characteristics and design a low-pass filter to pre-filter the measurement data to suppress high-frequency random white noise. Step 3: Based on L1 norm optimization and sliding window iterative weighted least squares algorithm, and in the process of iterative weighted least squares solution, a dual convergence criterion based on duality principle is introduced to set the iteration stopping condition, and robust gravity estimation is performed on the pre-filtered triaxial gravity accelerometer data to obtain the triaxial gravity acceleration component estimation results in the drill coordinate system. Step 4: Using the dual-vector attitude calculation method, the direction cosine matrix is ​​constructed by utilizing the correspondence between the gravity vector and the geomagnetic vector in the drill coordinate system and the navigation coordinate system. The roll angle, pitch angle and yaw angle are extracted to complete the attitude estimation of the rotary steering system. Step 5: Output the gravity acceleration estimation results and attitude angle sequence. If the gravity acceleration estimation and attitude estimation results of the rotary guidance system do not meet the preset accuracy requirements, return to step 2 and iteratively adjust the data preprocessing parameters and robust estimation parameters until the output gravity acceleration estimation results and attitude angle sequence that meet the accuracy requirements are obtained.

2. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The measurement data in step one are obtained by synchronously collecting triaxial accelerometer measurement sequences, triaxial magnetometer measurement sequences, and gyroscope measurement sequences at a fixed sampling frequency during actual drilling operations.

3. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The outlier detection and linear interpolation in step two are to preprocess the measurement sequence of the triaxial accelerometer; (A) calculate the local mean and standard deviation within the sampling time sliding window, and construct a statistical discrimination criterion based on this; when the deviation between the measured value and the local mean at a certain moment exceeds a preset threshold, the data point is identified as an outlier and removed; (B) the removed position is reconstructed using the linear interpolation method to restore the sampling continuity and integrity; (C) the outlier determination condition is: the absolute value of the difference between the current measured value and the corresponding local mean is greater than 3 times the standard deviation.

4. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The low-pass filter structure in step two is an FIR filter.

5. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The objective function designed in step three is: , This represents the entire measurement sequence acquired within the sampling time, after passing through a low-pass filter. This represents the estimated value of gravity. This indicates taking the L1 norm.

6. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The navigation coordinate system reference matrix constructed in step four is: ,in, This indicates the magnetic field strength northward in the navigation coordinate system. This indicates the magnetic field strength westward in the navigation coordinate system. The magnetic field strength in the celestial direction of the navigation system is represented by the geomagnetic vector of the navigation coordinate system, which can be expressed as: In the navigation coordinate system, the gravity vector is analytically expressed as: Geomagnetic vector From the total geomagnetic intensity Magnetic declination and magnetic inclination Sure.

7. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: The measurement matrix constructed in the drill coordinate system in step four is as follows: , This is an estimated value of gravity in the drill string coordinate system. This is the estimated geomagnetic value in the drill coordinate system after the magnetometer has been calibrated.

8. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: In step four, the attitudes are respectively the roll angle. Pitch angle and yaw angle Then the attitude estimation of the rotary steering system is as follows: .

9. The method for estimating gravitational acceleration of a rotating guidance system based on L1 norm and sliding window IRLS according to claim 1, characterized in that: In step five, the convergence statistics of the output attitude angle sequence and triaxial gravity acceleration data, including the convergence rate and average number of iterations, are recorded.

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