Method and system for positioning a complex medium conveying pipeline inspection ball

Abstract

The present application aims at the problems of the existing positioning method in positioning the detection ball in the complex medium conveying pipeline, and provides a positioning method and system for the detection ball in the complex medium conveying pipeline, so as to improve the positioning accuracy of the detection ball in the complex medium conveying pipeline. The positioning method comprises the following steps: S1, continuously collecting the motion data of the detection ball in the pipeline, and obtaining the motion data sequence through processing; S2, using the motion data sequence data for the deep learning model of attitude prediction, obtaining the attitude increment vector for representing the rotation in the three-dimensional space, so as to obtain the corrected acceleration and angular velocity; S3, positioning the detection ball: solving the corrected current motion data to obtain the positioning result of the detection ball; the positioning result comprises the three-dimensional position, velocity and attitude result.

Description

Technical Field

[0001] This invention belongs to the field of pipeline inspection technology, and specifically relates to a method for locating an inspection ball inside a pipeline and an electronic device thereof. Background Technology

[0002] In existing pipeline internal inspection technologies, the inspection ball is a commonly used non-destructive testing device. It typically incorporates an inertial navigation system (INS) and a magnetic sensor. By fusing acceleration and angular velocity data output from the inertial measurement unit (IMU) and magnetometer data, combined with pipeline map information, and utilizing filtering algorithms, the position and attitude of the inspection ball within the pipeline are estimated, thereby accurately locating the pipeline leak or blockage. Currently, this technology is mostly applied in pipeline environments where the internal media are relatively clean and the fluid state is stable, such as urban water supply, oil transportation, and gas transportation. In these scenarios, the inspection ball is usually designed with counterweights to make its overall density slightly greater than the transported fluid, allowing it to roll stably along the bottom of the pipeline. This "bottom rolling" motion mode obtains relatively stable and low-noise acceleration and angular velocity signals, which are then used to calculate the location using traditional Kalman filtering algorithms or extended Kalman filtering algorithms, thus deducing the leak or blockage location. For example, patent number CN108415055B discloses a moving object positioning marker inside a liquid pipeline for detecting the inside of a slurry conveying pipeline, and patent number CN209511613U discloses an underwater intelligent ball retriever for deploying and retrieving positioning markers.

[0003] However, when the detection ball is applied to pipelines transporting complex media such as tailings slurry and mud, the internal liquid of these pipelines contains a high concentration of suspended solid particles, and a soft sediment layer easily forms at the bottom of the pipeline. If the detection ball continues to roll from the bottom, it is prone to getting stuck in the sediment or at structures such as the ore outlet, posing a high risk of "ball loss" and causing the detection task to fail. To avoid these problems, existing technologies typically adjust the counterweight of the detection ball to make it approximately floating or suspended in the pipeline. However, this change brings new technical problems: the motion of the detection ball changes from "rolling + a small amount of sliding" to "sliding + irregular floating," significantly increasing the signal fluctuations acquired by the inertial measurement unit and significantly enhancing the noise component in the acceleration and angular velocity data. This results in poor adaptability of the traditional Kalman filtering method to non-Gaussian noise environments and rapid error accumulation.

[0004] In addition, existing positioning algorithms are mostly based on conventional integral calculations of Euler angles or quaternions, without considering the geometric constraints of rotation. After long-term integration, they are prone to attitude divergence. At the same time, the algorithms fail to dynamically compensate for fluid disturbances in the floating state, and cannot accurately distinguish between the actual motion of the detected ball and the fluid disturbance components, resulting in a large deviation between the positioning results and the actual trajectory.

[0005] In summary, existing methods for locating detection spheres have the following shortcomings in complex fluid environments:

[0006] (1) The lack of robust modeling for unstable motion in floating state leads to large attitude estimation error;

[0007] (2) Traditional filtering algorithms are difficult to suppress non-Gaussian noise and are prone to cumulative drift;

[0008] (3) The rotation operation did not consider geometric consistency, resulting in long-term instability of the attitude results;

[0009] (4) The positioning and attitude calculation were not jointly optimized, resulting in a decrease in the accuracy of the leak point location.

[0010] Therefore, in order to avoid the detection ball producing large positioning errors that would prevent accurate location of pipeline leaks or blockages, it is necessary to further improve the positioning method of the detection ball. Summary of the Invention

[0011] The purpose of this invention is to address the problems existing in the positioning of detection balls in complex media transportation pipelines by proposing a positioning method and system for detection balls in complex media transportation pipelines, so as to improve the accuracy of positioning of detection balls in complex media transportation pipelines.

[0012] One of the technical solutions of the present invention is a method for locating a detection ball inside a complex medium transport pipeline, comprising the following steps:

[0013] S1, continuously collects motion data of the detection ball inside the pipe, and processes it to obtain a motion data sequence;

[0014] The specific steps are as follows:

[0015] S11, continuously collects motion data of the detection ball inside the pipeline;

[0016] The pipeline can be, but is not limited to, tailings slurry pipelines, as well as sewage pipelines, district heating pipelines, and pipelines for transporting complex or highly turbid media such as oil and gas; the motion data is collected by a multi-source inertial measurement unit (such as a three-axis gyroscope, accelerometer, and magnetometer) installed in the detection ball inside the pipeline, including but not limited to three-axis acceleration, three-axis angular velocity, and magnetic flux.

[0017] S12, Preprocess the motion data;

[0018] After denoising, normalizing and time-synchronizing the collected data, a continuous time series (i.e., motion data series) is generated according to a unified time step.

[0019] Among them, motion data sequences can be divided into one or more of the following: fixed time window (that is, continuous data stream is divided into non-overlapping segments according to a fixed time length), sliding window (the sliding window introduces the concept of overlap, and the window slides by a step size smaller than the window length each time, which can overcome the problem of fixed window segmentation of actions), and dynamic time (such as dividing the window based on the content of the data itself or external events, and the start and end points of the window are dynamically determined).

[0020] S2, the motion data sequence is used for a deep learning model for attitude prediction to obtain an attitude increment vector to represent rotation in three-dimensional space, thereby obtaining the corrected acceleration and angular velocity;

[0021] The specific steps are as follows:

[0022] S21, Establish a long short-term memory network model based on a three-dimensional rotated Lie group space;

[0023] The attitude increment vector is defined as follows:

[0024] Let the attitude increment vector in the Lie algebra space be:

[0025] (1)

[0026] in, Let represent the pose increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps. Indicates the rotation angle. It is represented as a unit rotation vector; x, y, and z represent the three dimensions.

[0027] The training method for Long Short-Term Memory (LSTM) network models is as follows:

[0028] 1) Input: Motion data sequence;

[0029] 2) Model: A deep learning model whose output layer is designed to output a 3-dimensional vector;

[0030] 3) Output: For each time step t, the model outputs a vector ω_t in the Lie algebra space;

[0031] S22, input the motion data sequence preprocessed in S1 into the established model to obtain the corresponding attitude increment vector;

[0032] S23, the vector is converted into a rotation matrix or a unit quaternion through an exponential mapping, and then the pose state of the detected ball is updated;

[0033] The exponential mapping implementation process specifically includes:

[0034] S231, Construct an antisymmetric matrix:

[0035] Antisymmetric matrices are used to represent the cross product of three-dimensional rotated vectors as matrix multiplication.

[0036] (2)

[0037] in, , , These represent the attitude increment vectors respectively. The three components correspond to the rotational differential components about the x, y, and z axes, respectively. This represents the attitude increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps; The attitude increment vector The antisymmetric matrix form is used to implement the vector cross product operation in matrix operations;

[0038] S232, Update the attitude state of the detected ball;

[0039] Using the Rodriguez rotation formula:

[0040] (3)

[0041] in, It is a three-dimensional rotation matrix used to describe the overall rotation of the detection ball from the previous pose to the current pose; Represents the attitude increment vector Exponential mapping operations in Lie algebra spaces; Let be the identity matrix, representing the initial state without rotation; This is the attitude increment vector; The attitude increment vector The antisymmetric matrix form is used to implement the vector cross product operation in matrix operations; Indicates the rotation angle; and Rotation angles The sine and cosine functions are used to calculate the nonlinear part of the rotation matrix; This is the square of the rotation angle, used for angle normalization. The squared terms of the antisymmetric matrix are used for calculating higher-order rotational components;

[0042] S24, perform gravity component separation to obtain the corrected acceleration and angular velocity;

[0043] S3, positioning of the detection ball;

[0044] The corrected current motion data is processed to obtain the positioning result of the detection ball; the positioning result includes three-dimensional position, velocity and attitude results.

[0045] Furthermore, in the above method, step S3 further includes:

[0046] S31, acquire external observations, which are physical quantities that do not rely on inertial sensors and can directly or indirectly provide constraints or absolute references for one or more of position, velocity, and attitude.

[0047] S32 employs a fractional-order Kalman filter algorithm based on the maximum correlation entropy criterion to adaptively fuse external observations and positioning results, thereby obtaining optimized positioning results.

[0048] Among them, the maximum correlation entropy criterion suppresses large error samples through the kernel function, and the fractional Kalman filter algorithm uses the state transition equation in fractional derivative form to model the inertial memory effect of floating motion;

[0049] Specifically, a fractional-order state estimation algorithm based on the maximum correlation entropy criterion is used to adaptively fuse external observations and positioning results. The implementation process may include:

[0050] 1) Initialization: Set the state vector, error covariance, fractional order, memory length L, and kernel width;

[0051] 2) Prediction (fractional model):

[0052] Predict the current state and error covariance using fractional-order state equations;

[0053] 3) Update (maximum correlation entropy criterion):

[0054] Receive external observations;

[0055] Calculate the residual, which is the difference between the external observed value and the predicted observed value;

[0056] The Gaussian kernel function value is calculated based on the residual, and the weight matrix is ​​constructed.

[0057] Calculate the maximum correlation entropy Kalman gain based on the weight matrix;

[0058] The state and covariance are updated based on the maximum correlation entropy Kalman gain, the current state, and the error covariance.

[0059] 4) Iteration: Repeat steps 2) and 3) to continuously output the optimized localization results.

[0060] Furthermore, in the above positioning method, step S32 also includes:

[0061] Based on the geometric conditions of the pipeline and the kinematic constraints of the detection ball, the feasible region is corrected for the optimized positioning results, so that the corrected positioning results are obtained.

[0062] The geometric conditions of the pipeline include one or more of the following: the pipeline's centerline trajectory, inner diameter, and curvature; the kinematic constraints include one or more of the following: the three-dimensional position of the detection ball is constrained within the pipeline's internal space; the deviation between the three-dimensional velocity direction of the detection ball and the local tangential direction of the pipeline is limited to a first preset range; and the deviation between the three-dimensional attitude of the detection ball and the local attitude of the pipeline is limited to a second preset range.

[0063] One or more of the following methods can be used to correct the feasible region of the optimized localization results:

[0064] Project the off-center three-dimensional location point onto the nearest centerline of the pipe, or onto the internal space boundary of the pipe;

[0065] The three-dimensional velocities and three-dimensional attitudes that do not conform to kinematic constraints are constrained to a third preset range through a filtering algorithm;

[0066] A state optimization problem is constructed with the positioning result as the observation and geometric and kinematic constraints as the constraints. The corrected positioning result is obtained by solving the problem.

[0067] The second technical solution of the present invention is a positioning system for a detection ball inside a complex medium transport pipeline, used to implement the above-mentioned positioning method for the detection ball inside a complex medium transport pipeline, comprising:

[0068] The data processing module is used to process the motion data collected by the detection ball to obtain a motion data sequence;

[0069] A deep learning model module for pose prediction, used to output pose increment vectors;

[0070] The positioning result calculation module is used to update the current posture and motion data of the detection ball to obtain the positioning result of the detection ball.

[0071] Compared with the prior art, the advantages of the present invention are:

[0072] 1. To address the problem of inertial navigation data distortion caused by irregular attitude changes and high signal noise when the detection ball is floating in complex fluid media such as tailings slurry, and to establish an attitude and position modeling method that can adapt to the floating motion characteristics.

[0073] 2. To address the problem that traditional Kalman filtering algorithms are not robust to anomaly observations and suffer from severe error accumulation in non-Gaussian noise environments, a fractional-order Kalman filtering fusion strategy based on the maximum correlation entropy criterion is proposed to achieve dynamic compensation for positioning errors in floating states.

[0074] 3. To address the issues of attitude drift and geometric distortion that easily occur in traditional Euler angle or quaternion calculations during long-term floating motion, a three-dimensional rotating Lie group and Lie algebra representation are introduced to maintain the geometric consistency of rotation operations and improve the stability and continuity of the detection ball's attitude calculation.

[0075] 4. Stable inertial navigation positioning can be achieved without relying on rolling attitude conditions. It has the advantages of strong consistency in modeling structure, excellent noise resistance and high attitude estimation accuracy, and can be widely used in the detection and monitoring of complex fluid transportation pipelines. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0077] Figure 2 This is a structural diagram of the system of the present invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments:

[0079] Example 1

[0080] A method for locating a detection ball inside a pipeline transporting complex media, such as... Figure 1 As shown, it includes the following steps:

[0081] S1, continuously collects motion data of the detection ball inside the pipe, and processes it to obtain a motion data sequence;

[0082] The specific steps are as follows:

[0083] S11, continuously collects motion data of the detection ball inside the pipeline;

[0084] The pipeline can be, but is not limited to, tailings slurry pipelines, as well as sewage pipelines, district heating pipelines, and pipelines for transporting oil and gas in complex or high-turbidity environments; the motion data is collected by a multi-source inertial measurement unit (such as a three-axis gyroscope, accelerometer, and magnetometer) installed in the detection ball inside the pipeline, including but not limited to three-axis acceleration, three-axis angular velocity, and magnetic flux.

[0085] S12, Preprocess the motion data;

[0086] After denoising, normalizing and time-synchronizing the collected data, a continuous time series (i.e., motion data series) is generated according to a unified time step.

[0087] Among them, motion data sequences can be divided into one or more of the following: fixed time window (that is, continuous data stream is divided into non-overlapping segments according to a fixed time length), sliding window (the sliding window introduces the concept of overlap, and the window slides by a step size smaller than the window length each time, which can overcome the problem of fixed window segmentation of actions), and dynamic time (such as dividing the window based on the content of the data itself or external events, and the start and end points of the window are dynamically determined).

[0088] Different processing methods can be used to improve the adaptability of deep learning models used for attitude prediction under different flow velocities and fluid disturbance conditions.

[0089] S2, the motion data sequence is used for a deep learning model for attitude prediction to obtain an attitude increment vector to represent rotation in three-dimensional space, thereby obtaining the corrected acceleration and angular velocity;

[0090] The specific steps are as follows:

[0091] S21, Establish a long short-term memory network model based on a three-dimensional rotated Lie group space;

[0092] The attitude increment vector is defined as follows:

[0093] Let the attitude increment vector in the Lie algebra space be:

[0094]

[0095] in, Let represent the pose increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps. Indicates the rotation angle. It is represented as a unit rotation vector; x, y, and z represent the three dimensions.

[0096] The training method for Long Short-Term Memory (LSTM) network models is as follows:

[0097] 1) Input: Motion data sequence;

[0098] 2) Model: A deep learning model whose output layer is designed to output a 3-dimensional vector;

[0099] 3) Output: For each time step t, the model outputs a vector ω_t in the Lie algebra space;

[0100] In this invention, by introducing a three-dimensional rotating Lie group and Lie algebraic representation, the geometric consistency of rotation operations is maintained, and the stability and continuity of the detection ball attitude calculation are improved. This solves the problem of attitude drift and geometric distortion that easily occur in traditional Euler angle or quaternion solutions during long-term floating motion.

[0101] Based on the three-dimensional rotated Lie group space (SO(3)), attitude can also be expressed using quaternion space, direction cosine matrix (DCM), or unit rotation vector (URV). As long as the geometric consistency and orthogonality constraints of the rotation are maintained, equivalent modeling of attitude calculation can be achieved.

[0102] In addition to the Long Short-Term Memory network model used in this embodiment, other deep learning structures with temporal dependency modeling capabilities can also be used for pose prediction, such as Gated Recurrent Unit (GRU), Bidirectional Recurrent Neural Network (Bi-RNN), and Temporal Convolutional Network (TCN).

[0103] S22, input the motion data sequence preprocessed in S1 into the established network model to obtain the corresponding attitude increment vector;

[0104] S23, the vector is converted into a rotation matrix or a unit quaternion through an exponential mapping, and then the pose state of the detected ball is updated;

[0105] The exponential mapping implementation process specifically includes:

[0106] S231, Construct an antisymmetric matrix:

[0107] Antisymmetric matrices are used to represent the cross product of three-dimensional rotated vectors as matrix multiplication.

[0108]

[0109] in, , , These represent the attitude increment vectors respectively. The three components correspond to the rotational differential components about the x, y, and z axes, respectively. This represents the attitude increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps; The attitude increment vector The antisymmetric matrix form is used to implement the vector cross product operation in matrix operations;

[0110] S232, Update the attitude state of the detected ball.

[0111] Using the Rodriguez rotation formula:

[0112]

[0113] in, It is a three-dimensional rotation matrix used to describe the overall rotation of the detection ball from the previous pose to the current pose; Represents the attitude increment vector Exponential mapping operations in Lie algebra spaces; Let be the identity matrix, representing the initial state without rotation; This is the attitude increment vector; This is the antisymmetric matrix form of the attitude increment vector ξ, used to implement the vector cross product operation in matrix operations; Indicates the rotation angle; and respectively the angle of rotation The sine and cosine functions are used to calculate the nonlinear part of the rotation matrix; This is the square of the rotation angle, used for angle normalization. The squared terms of the antisymmetric matrix are used for calculating higher-order rotational components;

[0114] S24, perform gravity component separation to obtain the corrected acceleration and angular velocity;

[0115] S3, positioning of the detection ball.

[0116] S31, The corrected current motion data is processed to obtain the updated positioning result of the detection ball; the positioning result includes three-dimensional position, velocity and attitude results;

[0117] S32, acquire external observations, which are physical quantities that do not rely on inertial sensors and can directly or indirectly provide constraints or absolute references for one or more of position, velocity, and attitude.

[0118] For example, the absolute three-dimensional position obtained through magnetic map matching, the velocity scalar obtained through odometry, the gravity vector obtained through accelerometer, and the geomagnetic vector obtained through magnetometer;

[0119] S33 uses a fractional-order Kalman filter algorithm based on the maximum correlation entropy criterion to adaptively fuse external observations with updated positioning results to obtain optimized positioning results;

[0120] Among them, the maximum correlation entropy criterion suppresses large error samples through the kernel function, and the fractional Kalman filter algorithm uses the state transition equation in fractional derivative form to model the inertial memory effect of floating motion, effectively reducing the error accumulation caused by non-Gaussian noise and random disturbances.

[0121] Specifically, a fractional-order Kalman filter algorithm based on the maximum correlation entropy criterion is used to adaptively fuse external observations and positioning results. The implementation process may include:

[0122] 1) Initialization: Set the state vector, error covariance, fractional order, memory length L, and kernel width;

[0123] 2) Prediction (fractional model):

[0124] Predict the current state and error covariance using fractional-order state equations;

[0125] 3) Update (maximum correlation entropy criterion):

[0126] Receive external observations;

[0127] Calculate the residual, which is the difference between the external observed value and the predicted observed value;

[0128] The Gaussian kernel function value is calculated based on the residual, and the weight matrix is ​​constructed.

[0129] Calculate the maximum correlation entropy Kalman gain based on the weight matrix;

[0130] The state and covariance are updated based on the maximum correlation entropy Kalman gain, the current state, and the error covariance.

[0131] 4) Iteration: Repeat steps 2) and 3) to continuously output the optimized localization results.

[0132] An adaptive fusion strategy is adopted for external observations and updated positioning results to achieve dynamic compensation for positioning errors in floating states; this solves the problem that traditional Kalman filtering algorithms are not robust to abnormal observations and suffer from severe error accumulation in non-Gaussian noise environments.

[0133] Specifically, a fractional-order state estimation algorithm based on the maximum correlation entropy criterion is used to adaptively fuse external observations and positioning results. The implementation process may include:

[0134] 1) Initialization: Set the state vector, error covariance, fractional order, memory length L, and kernel width;

[0135] 2) Prediction (fractional model):

[0136] Predict the current state and error covariance using fractional-order state equations;

[0137] 3) Update (maximum correlation entropy criterion):

[0138] Receive external observations;

[0139] Calculate the residual, which is the difference between the external observed value and the predicted observed value;

[0140] The Gaussian kernel function value is calculated based on the residual, and the weight matrix is ​​constructed.

[0141] Calculate the maximum correlation entropy Kalman gain based on the weight matrix;

[0142] The state and covariance are updated based on the maximum correlation entropy Kalman gain, the current state, and the error covariance.

[0143] 4) Iteration: Repeat steps 2) and 3) to continuously output the optimized localization results;

[0144] S33, based on the geometric conditions of the pipeline and the kinematic constraints of the detection ball, the feasible region is corrected for the optimized positioning result, so that the corrected positioning result is...

[0145] The geometric conditions of the pipeline include one or more of the following: the pipeline's centerline trajectory, inner diameter, and curvature; the kinematic constraints include one or more of the following: the three-dimensional position of the detection ball is constrained within the pipeline's internal space; the deviation between the three-dimensional velocity direction of the detection ball and the local tangential direction of the pipeline is limited to a first preset range; and the deviation between the three-dimensional attitude of the detection ball and the local attitude of the pipeline is limited to a second preset range.

[0146] One or more of the following methods can be used to correct the feasible region of the location results:

[0147] Project the off-center three-dimensional location point onto the nearest centerline of the pipe, or onto the internal space boundary of the pipe;

[0148] The three-dimensional velocities and three-dimensional attitudes that do not conform to kinematic constraints are constrained to a third preset range through a filtering algorithm;

[0149] A state optimization problem is constructed with the positioning result as the observation and geometric and kinematic constraints as the constraints. The corrected positioning result is obtained by solving the problem.

[0150] Example 2

[0151] A positioning system for a detection ball inside a complex medium transport pipeline, used to implement the aforementioned positioning method for the detection ball inside a complex medium transport pipeline, such as... Figure 2 As shown, it includes:

[0152] The data processing module is used to process the motion data collected by the detection ball to obtain a motion data sequence;

[0153] A deep learning model module for pose prediction, used to output pose increment vectors;

[0154] The positioning result calculation module is used to update the current posture and motion data of the detection ball to obtain the positioning result of the detection ball.

Claims

1. A method for locating a detection ball inside a complex medium transport pipeline, characterized in that, Includes the following steps: S1, continuously collects motion data of the detection ball inside the pipe, and processes it to obtain a motion data sequence; The specific steps are as follows: S11, continuously collects motion data of the detection ball inside the pipeline; The pipeline is a transport pipeline for complex or highly turbid media; the motion data is collected by a multi-source inertial measurement unit installed on the detection ball inside the pipeline, including but not limited to triaxial acceleration, triaxial angular velocity and magnetic flux. S12, Preprocess the motion data; After denoising, normalizing, and time-synchronizing the collected data, a continuous time series, i.e., a motion data series, is generated according to a unified time step. Among them, the motion data sequence can adopt one or more of fixed time window, sliding window, and dynamic time; S2, the motion data sequence is used for a deep learning model for attitude prediction to obtain an attitude increment vector to represent rotation in three-dimensional space, thereby obtaining the corrected acceleration and angular velocity; The specific steps are as follows: S21, Establish a long short-term memory network model based on a three-dimensional rotated Lie group space; The attitude increment vector is defined as follows: Let the attitude increment vector in the Lie algebra space be: （1） in, Let represent the pose increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps. Indicates the rotation angle. It is represented as a unit rotation vector; x, y, and z represent the three dimensions. S22, input the motion data sequence preprocessed in S1 into the established model to obtain the corresponding attitude increment vector; S23, the vector is converted into a rotation matrix or a unit quaternion through an exponential mapping, and then the pose state of the detected ball is updated; The exponential mapping implementation process specifically includes: S231, Construct an antisymmetric matrix: Antisymmetric matrices are used to represent the cross product of three-dimensional rotated vectors as matrix multiplication. （2） in, , , These represent the attitude increment vectors respectively. The three components correspond to the rotational differential components about the x, y, and z axes, respectively. This represents the attitude increment vector in the Lie algebra space, used to describe the local rotational changes of the detection sphere between adjacent time steps; The attitude increment vector The antisymmetric matrix form is used to implement the vector cross product operation in matrix operations; S232, Update the attitude state of the detected ball; Using the Rodriguez rotation formula: （3） in, It is a three-dimensional rotation matrix used to describe the overall rotation of the detection ball from the previous pose to the current pose; Represents the attitude increment vector Exponential mapping operations in Lie algebra spaces; Let be the identity matrix, representing the initial state without rotation; This is the attitude increment vector; The attitude increment vector The antisymmetric matrix form is used to implement the vector cross product operation in matrix operations; Indicates the rotation angle; and Rotation angles The sine and cosine functions are used to calculate the nonlinear part of the rotation matrix; This is the square of the rotation angle, used for angle normalization. The squared terms of the antisymmetric matrix are used for calculating higher-order rotational components; S24, perform gravity component separation to obtain the corrected acceleration and angular velocity; S3, positioning of the detection ball; The corrected current motion data is processed to obtain the positioning result of the detection ball; the positioning result includes three-dimensional position, velocity and attitude results.

2. The method for positioning a detection ball inside a complex medium transport pipeline according to claim 1, characterized in that, S3 further includes: S31, acquire external observations, which are physical quantities that do not rely on inertial sensors and can directly or indirectly provide constraints or absolute references for one or more of position, velocity, and attitude. S32 employs a fractional-order Kalman filter algorithm based on the maximum correlation entropy criterion to adaptively fuse external observations and positioning results, thereby obtaining optimized positioning results.

3. The method for positioning a detection ball inside a complex medium transport pipeline according to claim 2, characterized in that, Step S32 also includes: Based on the geometric conditions of the pipeline and the kinematic constraints of the detection ball, the feasible region is corrected for the optimized positioning results, so that the corrected positioning results are obtained. The geometric conditions of the pipeline include one or more of the following: the pipeline's centerline trajectory, inner diameter, and curvature; the kinematic constraints include one or more of the following: the three-dimensional position of the detection ball is constrained within the pipeline's internal space; the deviation between the three-dimensional velocity direction of the detection ball and the local tangential direction of the pipeline is limited to a first preset range; and the deviation between the three-dimensional attitude of the detection ball and the local attitude of the pipeline is limited to a second preset range. One or more of the following methods can be used to correct the feasible region of the optimized localization results: Project the off-center 3D location point onto the nearest centerline of the pipe, or onto the internal space boundary of the pipe; The three-dimensional velocities and three-dimensional attitudes that do not conform to kinematic constraints are constrained to a third preset range through a filtering algorithm; A state optimization problem is constructed with the optimized positioning result as the observation and geometric and kinematic constraints as the constraints. The corrected positioning result is obtained by solving the problem.

4. The method for positioning a detection ball inside a complex medium transport pipeline according to claim 1, characterized in that, The training method for the Long Short-Term Memory (LSTM) network model is as follows: 1) Input: Motion data sequence; 2) Model: A deep learning model whose output layer is designed to output a 3-dimensional vector; 3) Output: For each time step t, the model outputs a vector ω_t in the Lie algebra space.

5. A positioning system for a detection ball inside a complex medium transport pipeline, used to implement the above-mentioned positioning method for the detection ball inside a complex medium transport pipeline, comprising: The data processing module is used to process the motion data collected by the detection ball to obtain a motion data sequence; A deep learning model module for pose prediction, used to output pose increment vectors; The positioning result calculation module is used to update the current posture and motion data of the detection ball to obtain the positioning result of the detection ball.

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