Underground pipeline internal combination positioning method based on multi-sensor cooperation

Abstract

The invention discloses an underground pipeline internal integrated positioning method based on multi-sensor cooperation, and belongs to the technical field of navigation positioning. The method comprises the following steps: correcting a yaw angle based on a magnetometer, performing attitude compensation on a Z axis through the magnetometer, and effectively eliminating an integral error caused by performing attitude calculation only depending on a gyroscope; on the basis of displacement estimation of multi-redundancy odometers, four wheels at the bottom of the robot are each provided with a motor encoder, the four odometers can complement one another, and position estimation of the IMU is effectively corrected through more reliable data; based on data fusion of bidirectional unscented Kalman filtering, non-linear errors are avoided through unscented Kalman filtering, and a smooth trajectory with higher precision can be obtained in cooperation with bidirectional filtering. According to the invention, the underground pipeline track positioning precision in a satellite signal rejection environment can be effectively improved.

Description

Technical Field

[0001] The present invention relates to a method for combined positioning inside an underground pipeline based on multi-sensor collaboration, belonging to the technical field of navigation and positioning. Background Art

[0002] As an important infrastructure in the industrialization process, the safe operation of underground pipelines is crucial for energy transportation, municipal services, and public safety. The research on the three-dimensional spatial distribution of underground pipelines is a key step in the three-dimensional information perception and mapping of underground pipelines. Due to the concealment of the pipeline burial position, the original underground position distribution information of the pipeline is inaccurate or even missing, which may lead to the problem that the location of anomalies inside the pipeline cannot be determined and that other engineering construction excavations are extremely likely to damage normal underground pipelines. Different from outdoor navigation and positioning, in an underground scenario, a pipeline robot cannot receive satellite positioning signals, and many methods that use satellite positioning signals for assisted positioning are no longer effective.

[0003] Currently, in the field of pipeline navigation and positioning, some commonly used methods still have certain defects. Using the electromagnetic induction method to determine the pipeline position and burial depth is easily affected by the pipeline material. Using the ground penetrating radar method to infer the underground pipeline position is affected by underground media, and the data processing is complex, and these methods cannot obtain accurate information on the three-dimensional distribution of the pipeline. Using an inertial measurement unit for inertial navigation has the problem of rapid error accumulation, that is, the drift of the system will increase rapidly with time, so it is necessary to cooperate with other sensors or methods for error compensation and fusion. Due to space and instrument equipment limitations, some methods only use a high-precision IMU for the measurement of underground pipelines, but there are large error problems in the pure IMU navigation solution. For the case where the pipeline has sufficient lighting conditions, some studies have fused IMU with visual odometry or laser SLAM data for higher-precision trajectory reconstruction, but most pipeline scenarios have problems such as insufficient light, unclear pipeline features, and highly similar structures, which will cause laser or visual SLAM to fail. In addition, using lidar will also bring additional costs. In recent years, the inertial navigation technology that fuses multiple sensors has developed rapidly. Therefore, under the limitation of satellite signal rejection in underground pipelines, how to achieve accurate trajectory reconstruction has become a technical problem that needs to be studied. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method for combined positioning inside an underground pipeline based on multi-sensor collaboration, which solves the problem of large accuracy errors in the existing underground pipeline positioning trajectory.

[0005] A method for combined positioning inside an underground pipeline based on multi-sensor collaboration includes the following:

[0006] S1: Introduce a magnetometer into the inertial navigation devices of the accelerometer and gyroscope carried by the pipeline robot to perform attitude compensation on the Z-axis and eliminate the yaw angle integration error of attitude solution that only relies on the gyroscope.

[0007] S2: Install wheel odometers on the four wheels at the bottom of the pipeline robot, estimate the moving mileage through multi-redundant coded wheels, and correct the position estimation of the IMU.

[0008] S3: Collect data once in both the forward and reverse directions of the pipeline robot, and perform unscented Kalman filtering separately to obtain the forward filtering result and the reverse filtering result. Then fuse the forward and reverse filtering results to obtain a smoother trajectory with higher accuracy.

[0009] Specifically, S1 specifically includes the following sub-steps:

[0010] S1-1: Define the carrier coordinate system as the b-system and the navigation coordinate system as the n-system. When the carrier, that is, the pipeline robot, is stationary, the relationship between the gravity field measurement value of the accelerometer in the b-system and the gravity vector in the n-system is expressed as:

[0011]

[0012] Among them, f x b 、f y b and f z b respectively represent the acceleration values of the x, y, and z axes in the b-system, represents the attitude transformation matrix from the b-system to the n-system, and the involved Euler angles are the pitch angle θ and the roll angle γ, and g represents the gravitational acceleration;

[0013] S1-2: The pitch angle θ and the roll angle γ are first obtained from the accelerometer:

[0014]

[0015] S1-3: Using the attitude angles measured by the IMU, the relationship between the geomagnetic field vectors H b and H n in the b-system and the n-system is expressed as:

[0016]

[0017] Among them, and respectively represent the geomagnetic fields in the x, y, and z directions in the b-system; and respectively represent the geomagnetic fields in the x, y, and z directions in the n-system;

[0018] S1-4: The yaw angle ψ corrected using geomagnetic information is:

[0019]

[0020] Specifically, S2 specifically includes the following sub-steps:

[0021] S2-1: Collect the motor encoder data M of the wheels driving the pipeline robot enc , and calculate the displacement output value S of the odometer od :

[0022] S od = α enc × M enc (25)

[0023] Among them, α enc represents the calculated encoder coefficient, and the specific calculation is:

[0024] α enc = S enc ÷ R enc ÷ i enc × C wheel (26)

[0025] Among them, S enc represents the rotational displacement of the motor encoder, R enc represents the resolution of the encoder, i enc represents the transmission ratio of the speed reducer, and C wheel represents the circumference of the robot wheel;

[0026] S2-2: For the data of the four motor encoders, consistency checking and elimination or replacement are required to reduce the influence of abnormal outlier data. Assuming that a certain wheel slips, the data will deviate significantly from other data. The standard deviation method is used to detect abnormal data, and the mean μ od and the standard deviation σ od of the motor sensor displacement data at each sampling moment are calculated:

[0027]

[0028] Among them, represents the displacement data of the four motor sensors. To sensitively detect data fluctuations, 2 times the standard deviation σ od is set as the threshold. If a certain data is more than 2 standard deviations σ od away from the mean μ od , that is:

[0029]

[0030] Then will be determined as an outlier;

[0031] S2-3: The weighted average method is used to fuse the four groups of data. Weights are assigned according to the accuracy and reliability of the sensors. The detected abnormal data will be given a smaller weight. If the outlier deviates too much, the data will be completely ignored. Assuming the weights of the four odometers are w1, w2, w3, and w4 respectively, the fused displacement data is:

[0032]

[0033] Specifically, S3 specifically includes the following sub-steps:

[0034] S3-1: The unscented Kalman filter is divided into two parts: state prediction and observation update. Based on the IMU data including the pitch angle θ, roll angle γ, and the corrected yaw angle ψ, a state transition equation is constructed. Using the odometer data including the fused displacement data an observation equation is constructed;

[0035] S3-2: The unscented Kalman filter approximately represents the state distribution of the system through a set of sigma points. The generated sigma points are used to predict the state transition equation to obtain a new predicted state. For each sigma point, their weighted mean is calculated to obtain the predicted state estimate and the covariance matrix of the predicted state The observation equation is predicted, and similarly, the estimated value of the observation is calculated using the weight parameters

[0036] S3-3: Use the unscented Kalman gain for state update K k :

[0037]

[0038] where P kz and P zz respectively represent the predicted observation covariance and cross-covariance, k represents the t k moment. Subsequently, the updated state of the state estimate and the covariance matrix P k are calculated by the following formula:

[0039]

[0040] where Y k represents the deviation between the actual observation value and the predicted observation value, represents the transpose matrix of K k ;

[0041] S3-4: Considering the motion scenario of the pipeline robot inside the pipeline, collect data once for both the forward and backward directions of the pipeline robot, and perform unscented Kalman filtering separately to obtain the forward filtering result and the backward filtering result, thus obtaining two motion trajectories of the same pipeline. The forward filtering result is and P fk , and the backward filtering result is and P bk ;

[0042] S3-5: Obtain the state after fusing the forward filtering result and the backward filtering result through weighted averaging

[0043]

[0044] where w f and w b represent the weights of the forward and backward filtering results respectively, and the new covariance matrix P fu is expressed as:

[0045]

[0046] S3-6: To further smooth the fused trajectory, perform post-processing on the updated state and the covariance matrix P fu , and apply the low-pass filtering method of Gaussian smoothing to smooth the fused trajectory:

[0047]

[0048] where X smooth (t) represents the smoothed trajectory, M represents the size of the smoothing window, taking the value 1, represents the natural exponential function, σ represents the standard deviation of the Gaussian kernel, t represents the current time point, and t′ represents the relative time offset;

[0049] Thus far, the position calculation is performed using the sensor data, and the multi-sensor collaborative in-pipeline combined positioning based on two-way unscented Kalman filtering is realized to obtain the pipeline distribution trajectory.

[0050] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The present invention proposes a combined positioning method for the interior of underground pipelines based on multi-sensor collaboration. High-precision accelerometers, gyroscopes, and magnetometers are used for attitude calculation. The magnetometer is added to utilize geomagnetic information to assist in correcting Euler angles. By stably compensating the attitude of the Z-axis, the integration error of relying solely on the gyroscope for attitude calculation is effectively eliminated. Four odometers are installed on the bottom wheels of the pipeline robot to increase redundancy and robustness, and the position estimation of the IMU is effectively corrected through the more reliable data of the odometers. The multi-sensor data fusion positioning method based on the unscented Kalman filter can avoid non-linear errors, and a smoother trajectory with higher accuracy can be obtained by combining two-way filtering. This method can effectively complete the precise positioning and trajectory reconstruction of underground pipelines and has a wider range of applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 FIG. is a flowchart of a combined positioning method for the interior of underground pipelines based on multi-sensor collaboration proposed by the present invention;

[0052] Figure 2 FIG. is a schematic diagram of the carrier coordinate system of the pipeline robot of the present invention;

[0053] Figure 3 FIG. is a schematic diagram of the mobile mileage estimation of the multi-redundancy coded wheel of the present invention;

[0054] Figure 4 FIG. is a schematic diagram of the fusion algorithm based on the unscented Kalman filter of the present invention;

[0055] Figure 5 FIG. is a three-dimensional trajectory reconstruction diagram of a 6m pipeline of the present invention;

[0056] Figure 6 FIG. is a three-dimensional trajectory reconstruction diagram of an 8m pipeline of the present invention;

[0057] Figure 7 FIG. is a three-dimensional trajectory reconstruction diagram of a 10m pipeline of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] The technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0059] The present invention adopts the following technical solutions. In combination with Figure 1 , in order to complete the pipeline navigation and positioning task, a combined positioning method for the interior of underground pipelines based on multi-sensor collaboration proposed by the present invention includes the following:

[0060] S1: Introduce a magnetometer into the inertial navigation devices of the accelerometer and gyroscope carried by the pipeline robot to perform attitude compensation on the Z-axis and eliminate the yaw angle integration error of attitude solution relying solely on the gyroscope;

[0061] S2: Install wheel odometers on the four wheels at the bottom of the pipeline robot, estimate the moving mileage through multi-redundant coding wheels, and correct the position estimation of the IMU;

[0062] S3: Collect data once in each of the forward and backward directions of the pipeline robot, and perform unscented Kalman filtering separately to obtain the forward filtering result and the backward filtering result, and fuse the forward filtering result and the backward filtering result to obtain a smoother trajectory with higher accuracy.

[0063] Combined with Figure 2 , S1 specifically includes the following sub-steps:

[0064] S1-1: Define the carrier coordinate system as the b-system and the navigation coordinate system as the n-system. When the carrier, that is, the pipeline robot, is stationary, the relationship between the gravity field measurement value of the accelerometer in the b-system and the gravity vector in the n-system is expressed as:

[0065]

[0066] Among them, f x b , f y b and f z b respectively represent the acceleration values of the x, y, and z axes in the b-system, represents the attitude transformation matrix from the b-system to the n-system, and the involved Euler angles are the pitch angle θ and the roll angle γ, and g represents the gravitational acceleration;

[0067] S1-2: The pitch angle θ and the roll angle γ are first obtained from the accelerometer:

[0068]

[0069] S1-3: Using the attitude angles measured by the IMU, the relationship between the geomagnetic field vectors H b and H n in the b-system and the n-system is expressed as:

[0070]

[0071] Among them, and respectively represent the geomagnetic fields in the x, y, and z directions in the b-system; and respectively represent the geomagnetic fields in the x, y, and z directions in the n-system;

[0072] S1-4: The yaw angle ψ corrected using geomagnetic information is:

[0073]

[0074] Combined with Figure 3 , S2 specifically includes the following sub-steps:

[0075] S2-1: Collect the motor encoder data M of the wheels driving the pipeline robot enc , and calculate the displacement output value S of the odometer od :

[0076] S od = α enc × M enc (41)

[0077] Where α enc represents the calculated encoder coefficient, and the specific calculation is:

[0078] α enc = S enc ÷ R enc ÷ i enc × C wheel (42)

[0079] Where S enc represents the rotational displacement of the motor encoder, R enc represents the resolution of the encoder, i enc represents the transmission ratio of the reducer, and C wheel represents the circumference of the robot wheel;

[0080] S2-2: For the data of the four motor encoders, consistency check and elimination or replacement are required to reduce the influence of abnormal outlier data. Assuming that a certain wheel slips, the data will deviate significantly from other data. The standard deviation method is used to detect abnormal data, and the mean μ od and standard deviation σ od of the motor sensor displacement data at each sampling moment are calculated:

[0081]

[0082] Where, represents the displacement data of the four motor sensors. To sensitively detect data fluctuations, 2 times the standard deviation σ od is set as the threshold. If a certain data is more than 2 standard deviations σ od away from the mean μ od , that is:

[0083]

[0084] That will be determined as an outlier;

[0085] S2-3: The weighted average method is used to fuse four groups of data. Weights are assigned according to the accuracy and reliability of the sensors. The detected abnormal data will be given a smaller weight. If the outlier deviates too much, the data will be completely ignored. Assuming the weights of the four odometers are w1, w2, w3, and w4 respectively, the fused displacement data is:

[0086]

[0087] Combined with Figure 4 , S3 specifically includes the following sub-steps:

[0088] S3-1: The unscented Kalman filter is divided into two parts: state prediction and observation update. Based on the IMU data including the pitch angle θ, roll angle γ, and the corrected yaw angle ψ, a state transition equation is constructed, and an observation equation is constructed using the odometer data including the fused displacement data ;

[0089] S3-2: The unscented Kalman filter approximately represents the state distribution of the system through a set of sigma points. The generated sigma points are used to predict the state transition equation to obtain a new predicted state. For each sigma point, their weighted mean is calculated to obtain the predicted state estimate and the covariance matrix of the predicted state The observation equation is predicted, and similarly, the estimated value of the observation is calculated using the weight parameters

[0090] S3-3: Use the unscented Kalman gain to perform state update K k :

[0091]

[0092] where P kz and P zz represent the predicted observation covariance and cross-covariance respectively, k represents the t k moment, and then the updated state of the state estimate and the covariance matrix P k are calculated by the following formula:

[0093]

[0094] where Y k represents the deviation between the actual observation value and the predicted observation value, represents the K k transpose matrix;

[0095] S3-4: Considering the motion scenario of the pipeline robot inside the pipeline, data is collected once in both the forward and backward directions of the pipeline robot, and unscented Kalman filtering is performed separately to obtain the forward filtering result and the backward filtering result, resulting in two motion trajectories of the same pipeline. The forward filtering result is and P fk , and the backward filtering result is and P bk ;

[0096] S3-5: The state after fusing the forward filtering result and the backward filtering result is obtained through weighted averaging

[0097]

[0098] where w f and w b represent the weights of the forward and backward filtering results respectively, and the new covariance matrix P fu is expressed as:

[0099]

[0100] S3-6: To further smooth the fused trajectory, post-processing is performed on the updated state and the covariance matrix P fu , and the Gaussian smoothing low-pass filtering method is applied to smooth the fused trajectory:

[0101]

[0102] where X smooth (t) represents the smoothed trajectory, M represents the size of the smoothing window, and M is taken as 1 in this embodiment, represents the natural exponential function, σ represents the standard deviation of the Gaussian kernel, t represents the current time point, and t′ represents the relative time offset;

[0103] Thus, the position is calculated using the sensor data, and multi-sensor collaborative in-pipeline integrated positioning based on two-way unscented Kalman filtering is achieved to obtain the pipeline distribution trajectory.

[0104] To verify the navigation and positioning effect of the proposed in-pipeline integrated positioning method based on multi-sensor data fusion inside the pipeline, experiments are carried out using the self-designed and developed underground pipeline robot system and the pipeline. By splicing different numbers of pipelines, pipeline scenarios of various lengths can be realized. That is, the pipeline robot can be placed in the pipeline, and the robot can be controlled to move forward and backward through the remote control, and then data such as the collected IMU and odometer can be obtained from the computer terminal for subsequent method processing.

[0105] The experiment is designed with three parts. The pipeline robot is controlled to travel back and forth in straight pipelines of 6m, 8m, and 10m respectively to record data, so as to verify the effectiveness and accuracy of the proposed method for in-pipeline navigation and positioning. Due to the length of the pipeline robot itself, the actual moving distance of the robot in the pipeline is less than the pipeline length. After actual measurement, the actual moving distances in the three pipelines are 5.7m, 7.7m, and 9.7m respectively. To comprehensively evaluate the accuracy of the navigation trajectory, the Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Standard Deviation (STD) are used as evaluation tools to calculate the error between the trajectory reconstruction result and the actual trajectory. RMSE can intuitively measure the gap between the estimated trajectory and the actual true trajectory, and is more sensitive to large errors. MAE calculates the average value of the absolute value of the Euclidean distance error between the estimated trajectory and the true trajectory, which is an easy-to-understand and more intuitive indicator. STD can represent the degree of dispersion of the point errors between the two trajectories, and can reflect the stability of the method in different scenarios.

[0106] Combined with Figure 5 , the trajectory results are calculated with the starting point of the robot as (0, 0, 0). In the first group of pipeline experiments with a length of 6m, the coordinates of the end point of the robot are (0.0094, 5.6984, 0.0114), the error of the X-axis is 0.0094m, the error of the Y-axis is 0.0016m, and the error of the Z-axis is 0.0114m. From the analysis of the index results, the values of RMSE, MAE, and STD are 0.06365, 0.06166, and 0.01578 respectively. This indicates that the trajectory accuracy is relatively high, there are not many abnormal points in the trajectory processed by the method, and the overall average error level has been effectively controlled.

[0107] Combined with Figure 6 , in the second group of pipeline experiments with a length of 8m, the coordinates of the end point of the robot are (0.0195, 7.6774, 0.0130), the error of the X-axis is 0.0195m, the error of the Y-axis is 0.0226m, and the error of the Z-axis is 0.0130m. From the analysis of the index results, the values of RMSE, MAE, and STD are 0.09288, 0.08229, and 0.04309 respectively. All the index values are still lower than 0.1. The reconstructed trajectory errors are concentrated, with small fluctuations and relatively stable output.

[0108] Combined with Figure 7, in the 10m pipeline experiment of the third group, the coordinates of the robot's end point are (-0.0110, 9.7293, 0.0188), the error of the X-axis is 0.0110m, the error of the Y-axis is 0.0293m, and the error of the Z-axis is 0.0188m. From the analysis of the index results, the values of RMSE, MAE, and STD are 0.19148, 0.15094, and 0.11785 respectively. In the third group of experiments, due to the lengthening of the experimental pipeline, the errors all increase, but a relatively high-precision reconstructed trajectory can still be obtained.

[0109] From the analysis of the results of the three groups of experiments, it can be seen that the UKF and two-way filtering are introduced in this method, which can avoid linearization errors and improve the robustness of the fusion. Therefore, the obtained trajectory is close to the true value, and the overall error is controlled within a small range.

[0110] The above are only embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the scope of the claims of the present invention pending approval.

Claims

1. A combined positioning method for the interior of underground pipelines based on multi-sensor collaboration, characterized in that The method includes the following steps: S1: Introduce a magnetometer into the inertial navigation devices of the accelerometer and gyroscope carried by the pipeline robot to perform attitude compensation on the Z-axis and eliminate the yaw angle integration error that only relies on the gyroscope for attitude solution; S2: Install wheel odometers on the four wheels at the bottom of the pipeline robot, estimate the moving mileage through multi-redundant coded wheels, and correct the position estimation of the IMU; S3: Collect data once in each of the forward and backward directions of the pipeline robot, and perform unscented Kalman filtering respectively to obtain the forward filtering result and the backward filtering result, and fuse the forward filtering result and the backward filtering result to obtain a smoother trajectory with higher accuracy.

2. The combined positioning method inside an underground pipeline based on multi-sensor collaboration according to claim 1, characterized in that, S1 specifically includes the following sub-steps: S1-1: Define the carrier coordinate system as the b system and the navigation coordinate system as the n system. When the carrier, that is, the pipeline robot is stationary, the relationship between the gravity field measurement value of the accelerometer in the b system and the gravity vector in the n system is expressed as: Among them, and respectively represent the x, y, and z-axis acceleration values in the b coordinate system, represents the attitude transformation matrix from the b coordinate system to the n coordinate system. The involved Euler angles are the pitch angle θ and the roll angle γ, and g represents the gravitational acceleration; S1-2: The pitch angle θ and the roll angle γ are first obtained from the accelerometer: S1-3: Using the attitude angles measured by the IMU, the geomagnetic field vectors H in the b-frame and the n-frame b and H n The relationship between them is expressed as: Among them, and respectively represent the geomagnetic fields in the x, y, and z directions under the b system; and respectively represent the geomagnetic fields in the x, y, and z directions under the n system; S1-4: The yaw angle ψ corrected using geomagnetic information is:

3. A method for internal combined positioning of underground pipelines based on multi-sensor collaboration according to claim 1 or 2, characterized in that S2 specifically includes the following sub-steps: S2-1: Collect the motor encoder data M of the wheels of the drive pipeline robot, and calculate the displacement output value S of the odometer enc , and calculate the displacement output value S of the odometer od : S od = α enc × M enc (7) where α enc represents the calculated encoder coefficient, and the specific calculation is as follows: α enc = S enc ÷ R enc ÷ i enc × C wheel (8) Among them, S enc represents the rotational displacement of the motor encoder, R enc represents the resolution of the encoder, i enc represents the transmission ratio of the reducer, C wheel represents the circumference of the robot wheel; S2-2: For the data of the four motor encoders, consistency check and elimination or replacement are required to reduce the influence of abnormal outlier data. Assuming that a certain wheel slips, the data will deviate significantly from other data. The standard deviation method is used to detect abnormal data, and the mean μ of the motor sensor displacement data at each sampling moment is calculated. od and the standard deviation σ od : Among them, represents the displacement data of four motor sensors. Set the threshold of the displacement data. If a certain data is at a distance from the mean value μ od exceeds the threshold, then it will be determined as an outlier; S2-3: The weighted average method is used to fuse the four groups of data. Assuming that the weights of the four odometers are w1, w2, w3, and w4 respectively, the fused displacement data is:

4. A method for internal combined positioning of underground pipelines based on multi-sensor collaboration according to claim 3, characterized in that, The setting of the displacement data threshold described in step S2-2 is specifically to set 2 times the standard deviation σ od as the threshold, that is, the displacement data of the four motor sensors from the mean value μ od exceeds 2 times the standard deviation σ od , then it will be determined as an outlier, as specifically shown in formula (12):

5. A combined positioning method for the interior of underground pipelines based on multi-sensor collaboration according to claim 1, characterized in that, S3 specifically includes the following sub-steps: S3-1: The unscented Kalman filter is divided into two parts: state prediction and observation update. Based on the IMU data including the pitch angle θ, roll angle γ, and the corrected yaw angle ψ, a state transition equation is constructed, and the odometer data including the fused displacement data is used to construct an observation equation; S3-2: The unscented Kalman filter approximates the state distribution of the system through a set of sigma points, uses the generated sigma points to predict the state transition equation to obtain a new predicted state, calculates their weighted mean for each sigma point, and obtains the predicted state estimate. and the covariance matrix of the predicted state Predict the observation equation, and similarly calculate the estimated value of the observation using the weight parameters. S3-3: Update the state K using the unscented Kalman gain k : where P kz and P zz represent the predicted observation covariance and the cross covariance respectively, k represents the k time instant, and the updated state and the covariance matrix P k are calculated by the following equations: where Y k represents the deviation between the actual observed value and the predicted observed value, represents K k transpose matrix; S3-4: Considering the motion scenario of the pipeline robot inside the pipeline, collect data once in both the forward and backward directions of the pipeline robot, and perform unscented Kalman filtering separately to obtain the forward filtering result and the backward filtering result, obtaining two motion trajectories of the same pipeline. The forward filtering result is and P fk , and the backward filtering result is and P bk ; S3-5: Obtain the state after fusing the forward filtering result and the reverse filtering result through weighted averaging where, w f and w b represent the weights of the forward and reverse filtering results respectively, and the new covariance matrix P fu is expressed as:

6. The internal combined positioning method for underground pipelines based on multi-sensor collaboration according to claim 5, characterized in that, The method further includes post-processing on the updated state and covariance matrix P fu to further smooth the fused trajectory, and applying a low-pass filtering method of Gaussian smoothing to smooth the fused trajectory: where X smooth (t) represents the smoothed trajectory, M represents the smoothing window size, denotes the natural exponential function, σ represents the standard deviation of the Gaussian kernel, t represents the current time point, and t′ represents the relative time offset; Thus, the position is solved using sensor data, and multi-sensor collaborative in-pipe integrated positioning based on two-way unscented Kalman filtering is achieved to obtain the pipeline distribution trajectory.

7. A method for internal combined positioning of underground pipelines based on multi-sensor collaboration according to claim 6, characterized in that, The value of the smoothing window size M is 1.

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