All-source navigation method based on RTK and laser inertial navigation odometer fusion

Abstract

The invention discloses an all-source navigation method based on RTK and laser inertial navigation odometer fusion, and relates to the technical field of all-source navigation, and the method comprises the following steps: S1, carrying out data acquisition through a sensor, including RTK data, laser radar data and IMU data acquisition, establishing a sensor measurement model to process the acquired data, and the like. According to the method, a laser speedometer factor and an IMU pre-integration factor are constructed by using measurement data of a laser radar and an IMU, motion distortion of the laser point cloud is eliminated by using motion estimated by the IMU, the motion distortion is used as an initial value for matching the laser point cloud, and the initial value of the laser point cloud is calculated in a sliding window with a fixed number of key frames. According to the method, the IMU pre-integration factor and the laser odometer factor are jointly optimized by using the factor graph, so that the low-drift laser odometer is obtained, the IMU deviation is updated after the factor graph optimization is completed, the tight coupling of the laser radar and the IMU is realized, and the precision and the stability of the odometer are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of all-source navigation, and in particular to an all-source navigation method based on the fusion of RTK and laser inertial navigation odometer. Background Art

[0002] The exploration and development of navigation technology is a manifestation of human wisdom and innovative spirit, and its history is long. Since the invention of the compass in ancient China, navigation technology has begun its long evolution. As time goes by, navigation instruments such as magnetic compasses, speedometers, and odometers have been widely used in Europe, greatly promoting the development of navigation and aviation. In modern times, the emergence of inertial navigation and radio navigation technology marks that navigation technology has entered a new stage. In particular, the advent of the global satellite positioning system has not only completely changed people's travel methods, but also laid a solid foundation for the research and development of various new navigation systems.

[0003] Currently, common single navigation methods include inertial navigation and satellite navigation. However, in practical applications, a single navigation system often has limitations and is difficult to meet diverse and complex needs. In order to overcome the limitations of a single navigation system, a combined navigation system has emerged. This system integrates multiple different types of navigation technologies and uses their respective advantages to make up for each other's shortcomings, thereby improving the overall navigation performance.

[0004] However, in modern navigation technology, common combined navigation systems usually take the inertial navigation system (INS) as the core, combined with satellite navigation systems and other navigation technologies. However, the application of satellite navigation systems in certain specific environments is limited. For example, in complex environments such as indoors, canyons, urban high-rise buildings and underwater, satellite signals are easily blocked, making it difficult for satellite navigation systems to provide stable and reliable positioning services. In addition, the radio signal propagation between satellites and receivers is susceptible to interference and shielding, which further affects the performance and accuracy of the navigation system. Summary of the invention

[0005] The purpose of the present invention is to provide an all-source navigation method based on the fusion of RTK and laser inertial navigation odometer to solve the problems proposed in the above background technology that the application of satellite navigation systems in complex environments is limited, satellite signals are easily blocked, resulting in difficulty in the satellite navigation system to provide stable and reliable positioning services, and the radio signal propagation between the satellite and the receiver is susceptible to interference and shielding, which further affects the performance and accuracy of the navigation system.

[0006] To achieve the above object, the present invention provides the following technical solution: an all-source navigation method based on the fusion of RTK and laser inertial navigation odometer, comprising the following steps:

[0007] S1. Collect data through sensors, including RTK data, lidar data and IMU data, and establish a sensor measurement model to process the collected data;

[0008] S2. Using the original measurement data of inertial navigation and lidar, the IMU pre-integration factor and the laser odometer factor are constructed respectively. Using the factor graph model, the IMU pre-integration factor and the laser odometer factor are jointly optimized within the sliding window of the limited number of key frames to achieve high-precision tight coupling between the lidar and the inertial navigation system.

[0009] S3, using the close coupling of the two to finally output accurate laser odometer information and complete the calibration of the laser radar and IMU;

[0010] S4. Evaluate the availability of GNSS-RTK measurement. When the GNSS-RTK availability evaluation is reliable, provide relative motion constraints through the LiDAR factors constructed by scan matching, the IMU factors derived from pre-integration, and the GNSS factors, respectively, and construct residual equations to minimize the differences between the factors.

[0011] S5. The Levenberg-Marquardt algorithm is used to solve the nonlinear optimization problem. By iteratively updating the state in the window, the objective function, i.e. the sum of all residuals, is minimized to obtain the estimated state, thus realizing the data fusion of RTK and LIO.

[0012] Preferably, in step S1, the sensor measurement model includes an RTK measurement model, a lidar measurement model and an IMU measurement model;

[0013] The process of the RTK measurement model processing is as follows: the distance correlation value between the satellite and the receiver is calculated based on the observation equation of pseudorange and carrier phase, and the geodetic coordinate system information is converted into a local coordinate system;

[0014] The process of the laser radar measurement model processing is as follows: distance calculation is performed according to the triangulation or TOF ranging method, and point cloud distortion generated during the acquisition process is corrected;

[0015] The process of IMU measurement model processing is as follows: based on the IMU measurement principle, using the data collected by its core sensor, taking into account the existing systematic errors and random errors, an error model is constructed to describe the uncertainty in the measurement process.

[0016] Preferably, in step S2, the high-precision tight coupling between the laser radar and the inertial navigation system comprises the following steps:

[0017] S21. External parameter calibration of lidar and inertial navigation: The point cloud data obtained by the lidar scan is converted to the inertial navigation coordinate system using the preliminary estimated external parameter transformation matrix. The M-neighbor error of each point in the point cloud is calculated and used as the optimization target. The nonlinear optimization library NLopt is used for iterative solution to obtain the optimized external parameter transformation matrix. The high-precision laser odometer information is obtained through the lidar. At the same time, the posture constraint information of the same time period is calculated using the IMU pre-integration. The optimization equation is constructed based on the idea of ​​​​the overlap of the two sets of trajectories, and the external parameter estimation value is obtained by solving;

[0018] S22. Feature matching of laser odometer: A method based on spatial curvature is used to extract corner feature points and plane feature points from the point cloud scanned by the laser radar. The two frames of point cloud are accurately matched according to the spatial distance relationship between the feature points. For corner feature points, points with similar distances are searched in the two frames of point cloud and straight lines are constructed, and the distance from the point to the straight line is calculated. For plane feature points, points with similar distances are identified in the two frames of point cloud and planes are constructed. When calculating the distance from the point to the plane, the distance deviation is minimized, and the optimal posture transformation matrix is ​​solved to obtain the laser odometer.

[0019] S23, select key frames and perform sliding window optimization: using the distance reference method, when the travel exceeds a specific distance or the turning angle exceeds a preset threshold, the current laser frame is identified as a key frame, and the number of key frames in the sliding window is set. Whenever a new key frame is added, the oldest key frame in the window is removed;

[0020] S24. Factor graph model construction, and tight coupling of lidar and IMU is achieved through factor graph optimization.

[0021] Preferably, in step S22, the process of extracting corner feature points and plane feature points is: first, the point cloud is divided into point sets with different curvatures according to the curvature relationship, then points with significant features are selected in each part, and the corner feature points and plane feature points are filtered out according to the curvature threshold, and unstable feature points are eliminated.

[0022] Preferably, in step S24, the process of achieving tight coupling of the lidar and the IMU through factor graph optimization is: on a sliding window consisting of a fixed number of key frames, the laser odometer factor and the IMU pre-integration factor measured from the lidar and IMU are optimized using the factor graph, and after the factor graph optimization, the deviation of the IMU is further estimated, thereby achieving tight coupling of the lidar and the IMU.

[0023] Preferably, in step S4, the assessing the availability of the GNSS-RTK measurement comprises the following steps:

[0024] S41, after receiving the 3D point cloud and IMU self-motion measurement data, the LiDAR factor and the IMU factor are established by using scan matching and IMU pre-integration respectively, and are jointly optimized in a sliding tool based on the local FGO to gradually generate a global map;

[0025] S42, processing the GNSS raw data at the same time, calculating the average elevation mask based on the three-dimensional point cloud data to evaluate the availability of GNSS-RTK and remove unreliable data points;

[0026] S43, integrate reliable LiDAR factors, IMU factors and GNSS-RTK factors to achieve geo-referenced positioning;

[0027] S44, convert the GNSS-RTK data into ENU frame and extract the local map around it, removing points below 1m;

[0028] S45. Divide the area around the GNSS receiver into 36 sub-areas according to the azimuth angle, and evaluate its availability by calculating the average elevation angle of each sub-area as the average elevation angle mask for GNSS-RTK measurement.

[0029] Preferably, in step S42, the process of calculating the average elevation angle mask based on the three-dimensional point cloud data to evaluate the availability of GNSS-RTK and eliminate unreliable data points is as follows: first, after setting a predetermined threshold, data points with a larger average elevation angle mask indicate that there are factors such as high-rise buildings or tall trees around them that block the signal, and are considered unreliable and eliminated; while data points with a smaller average elevation angle mask indicate that they are in a relatively open environment and are therefore considered reliable.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] 1. In the present invention, laser odometer factors and IMU pre-integration factors are constructed by using the measurement data of laser radar and IMU, and the motion distortion of laser point cloud is eliminated by using the motion estimated by IMU, and it is used as the initial value of laser point cloud matching. In a sliding window with a fixed number of key frames, the IMU pre-integration factor and the laser odometer factor are jointly optimized by using factor graph, so as to obtain a low-drift laser odometer. At the same time, the IMU deviation is updated after the factor graph optimization is completed, so as to realize the close coupling of laser radar and IMU, so as to give full play to the advantages of the two sensors and improve the accuracy and stability of the odometer.

[0032] 2. In the present invention, by using the local map constructed by LIO and evaluating the unavailable GNSS through the average elevation mask, the RTK signal can be used more accurately, and the adaptability and reliability in different environments can be improved. By fusing RTK and LIO data, that is, by constructing a residual equation and using the Levenberg-Marquardt algorithm to solve the nonlinear optimization problem, the residual can be minimized, and the RTK and LIO data can be effectively fused to improve the positioning accuracy of the system.

[0033] 3. In the present invention, a sliding window is used to optimize and maintain a dynamic key frame time window. Whenever a new key frame is added, the oldest key frame in the window will be removed, thereby ensuring the constancy of the number of key frames during the optimization process, greatly reducing the calculation scale and the amount of data required to be processed, and effectively improving the real-time performance of the positioning system. In the calculation process of the laser inertial navigation odometer, the IMU pre-integration technology is used to provide more accurate motion information, reduce the accumulation of errors, and further improve the accuracy of the odometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The present invention is a flow chart of an all-source navigation method based on the fusion of RTK and laser inertial navigation odometer. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the implementation regulations described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] See also Figure 1 The present invention provides a technical solution: an all-source navigation method based on the fusion of RTK and laser inertial navigation odometer, comprising the following steps:

[0037] Step 1: Collect data through sensors, including RTK data, lidar data and IMU data, establish sensor measurement models to process the collected data, collect different types of data through multiple sensors, and establish corresponding measurement models for processing, providing an accurate and comprehensive data foundation for subsequent navigation calculations;

[0038] Among them, the sensor measurement model includes RTK measurement model, lidar measurement model and IMU measurement model;

[0039] The process of RTK measurement model processing is as follows: the distance correlation value between the satellite and the receiver is calculated based on the observation equation of pseudorange and carrier phase, and the geodetic coordinate system information is converted into the local coordinate system;

[0040] The process of laser radar measurement model processing is as follows: distance calculation is performed based on triangulation or TOF ranging methods, and point cloud distortion generated during the acquisition process is corrected;

[0041] The process of IMU measurement model processing is as follows: based on the IMU measurement principle, using the data collected by its core sensor, taking into account its existing systematic errors and random errors, and constructing an error model to describe the uncertainty in the measurement process;

[0042] Step 2: Use the original measurement data of inertial navigation and lidar to construct IMU pre-integration factors and laser odometer factors respectively. Use the factor graph model to jointly optimize the IMU pre-integration factors and laser odometer factors within a limited number of key frames in the sliding window to achieve high-precision tight coupling between the lidar and the inertial navigation system. By constructing and optimizing related factors, high-precision tight coupling between the lidar and the inertial navigation system is achieved, giving full play to the advantages of the two sensors and improving the accuracy and stability of the odometer.

[0043] The high-precision tight coupling between the lidar and the inertial navigation system includes the following steps:

[0044] 21) External parameter calibration of laser radar and inertial navigation: The point cloud data obtained by laser radar scanning is converted to the inertial navigation coordinate system using the preliminary estimated external parameter transformation matrix. The M-nearest error of each point in the point cloud is calculated and used as the optimization target. The nonlinear optimization library NLopt is used for iterative solution to obtain the optimized external parameter transformation matrix. High-precision laser odometer information is obtained through laser radar. At the same time, the posture constraint information of the same time period is calculated using IMU pre-integration. The optimization equation is constructed based on the idea of ​​​​overlapping two sets of trajectories, and the external parameter estimation value is obtained by solving;

[0045] 22) Feature matching of laser odometer: A method based on spatial curvature is used to extract corner feature points and plane feature points from the point cloud scanned by the laser radar. The two frames of point cloud are accurately matched according to the spatial distance relationship between the feature points. For corner feature points, points with similar distances are searched in the two frames of point cloud and straight lines are constructed, and the distance from the point to the straight line is calculated. For plane feature points, points with similar distances are identified in the two frames of point cloud and planes are constructed. When calculating the distance from the point to the plane, the distance deviation is minimized, and the optimal posture transformation matrix is ​​solved to obtain the laser odometer.

[0046] The process of extracting corner feature points and plane feature points is as follows: first, the point cloud is divided into point sets with different curvatures according to the curvature relationship, then points with significant features are selected in each part, and corner feature points and plane feature points are screened out according to the curvature threshold, while unstable feature points are removed;

[0047] 23) Select key frames and perform sliding window optimization: Use the distance reference method. When the travel exceeds a certain distance or the turning angle exceeds a preset threshold, the current laser frame is identified as a key frame. The number of key frames in the sliding window is set. Whenever a new key frame is added, the oldest key frame in the window is removed.

[0048] 24) Factor graph model construction, achieving tight coupling between lidar and IMU through factor graph optimization;

[0049] Among them, the process of achieving tight coupling of lidar and IMU through factor graph optimization is as follows: on a sliding window composed of a fixed number of key frames, the laser odometer factor and IMU pre-integration factor measured by lidar and IMU are optimized using factor graph. After factor graph optimization, the deviation of IMU is further estimated to achieve tight coupling of lidar and IMU.

[0050] Step 3: Use the close coupling of the two to finally output accurate laser odometer information and complete the calibration of the laser radar and IMU. Use the close coupling to output accurate laser odometer information and complete the calibration of the laser radar and IMU, which provides accurate odometer data for subsequent navigation and ensures the accuracy of the geometric relationship between the laser radar and IMU, thereby improving the accuracy and reliability of the entire navigation system.

[0051] Step 4: Evaluate the availability of GNSS-RTK measurement. When the GNSS-RTK availability evaluation is reliable, provide relative motion constraints through the LiDAR factors constructed by scanning matching, the IMU factors derived from pre-integration, and the GNSS factors, and construct residual equations to minimize the differences between the factors, so as to prepare for the fusion of RTK and laser inertial navigation odometer, and improve the adaptability and reliability of the system in different environments.

[0052] The evaluation of the availability of GNSS-RTK measurements includes the following steps:

[0053] 41) After receiving the 3D point cloud and IMU self-motion measurement data, the LiDAR factor and IMU factor are established by scan matching and IMU pre-integration respectively, and jointly optimized in the sliding tool based on the local FGO to gradually generate a global map;

[0054] 42) At the same time, the GNSS raw data is processed, and the average elevation mask is calculated based on the 3D point cloud data to evaluate the availability of GNSS-RTK and remove unreliable data points;

[0055] The process of evaluating the availability of GNSS-RTK and removing unreliable data points by calculating the average elevation mask based on the three-dimensional point cloud data is as follows: first, after setting a predetermined threshold, data points with a larger average elevation mask indicate that there are high-rise buildings or tall trees around them that block the signal, and are considered unreliable and removed; while data points with a smaller average elevation mask indicate that they are in a relatively open environment and are therefore considered reliable;

[0056] 43) Integrate reliable LiDAR factors, IMU factors and GNSS-RTK factors to achieve geo-referenced positioning;

[0057] 44) Convert GNSS-RTK data into ENU frame and extract the local map around it, removing points below 1m;

[0058] 45) The area around the GNSS receiver is divided into 36 sub-areas according to the azimuth angle, and the average elevation angle of each sub-area is calculated as the average elevation angle mask of GNSS-RTK measurement to evaluate its availability;

[0059] Step 5: Use the Levenberg-Marquardt algorithm to solve the nonlinear optimization problem. By iteratively updating the state in the window, the objective function, that is, the sum of all residuals, is minimized to obtain the estimated state, and the data fusion of RTK and LIO is realized. It can effectively fuse the data of different sensors, minimize the residuals, and improve the positioning accuracy and overall performance of the system.

[0060] In this method, laser odometer factors and IMU pre-integration factors are constructed by using the measurement data of laser radar and IMU. The motion estimated by IMU is used to eliminate the motion distortion of laser point cloud and use it as the initial value of laser point cloud matching. In a sliding window with a fixed number of key frames, the IMU pre-integration factor and laser odometer factor are jointly optimized by factor graph, so as to obtain a low-drift laser odometer. At the same time, the IMU deviation is updated after the factor graph optimization is completed, and the tight coupling of laser radar and IMU is realized. This tight coupling method can give full play to the advantages of the two sensors and improve the accuracy and stability of the odometer. By using the local map constructed by LIO and evaluating the unavailable GNSS by averaging the elevation mask, the RTK signal can be used more accurately, and the adaptability and reliability in different environments can be improved. By fusing RTK and LIO data, that is, by constructing the residual equation and using the Levenberg-Marquardt algorithm to solve the nonlinear optimization problem, the residual can be minimized. This data fusion method can effectively fuse RTK and LIO data and improve the positioning accuracy of the system.

[0061] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An all-source navigation method based on the fusion of RTK and laser inertial navigation odometer, characterized in that: The following steps are involved: S1. Collect data through sensors, including RTK data, lidar data and IMU data, and establish a sensor measurement model to process the collected data; S2. Using the original measurement data of inertial navigation and lidar, the IMU pre-integration factor and the laser odometer factor are constructed respectively. Using the factor graph model, the IMU pre-integration factor and the laser odometer factor are jointly optimized within the sliding window of the limited number of key frames to achieve high-precision tight coupling between the lidar and the inertial navigation system. S3, using the close coupling of the two to finally output accurate laser odometer information and complete the calibration of the laser radar and IMU; S4. Evaluate the availability of GNSS-RTK measurement. When the GNSS-RTK availability evaluation is reliable, provide relative motion constraints through the LiDAR factors constructed by scan matching, the IMU factors derived from pre-integration, and the GNSS factors, respectively, and construct residual equations to minimize the differences between the factors. S5. The Levenberg-Marquardt algorithm is used to solve the nonlinear optimization problem. By iteratively updating the state in the window, the objective function, i.e. the sum of all residuals, is minimized to obtain the estimated state, thus realizing the data fusion of RTK and LIO.

2. The all-source navigation method based on the fusion of RTK and laser inertial navigation odometer according to claim 1 is characterized in that: In step S1, the sensor measurement model includes an RTK measurement model, a lidar measurement model and an IMU measurement model; The process of the RTK measurement model processing is as follows: the distance correlation value between the satellite and the receiver is calculated based on the observation equation of pseudorange and carrier phase, and the geodetic coordinate system information is converted into a local coordinate system; The process of the laser radar measurement model processing is as follows: distance calculation is performed according to the triangulation or TOF ranging method, and point cloud distortion generated during the acquisition process is corrected; The process of IMU measurement model processing is as follows: based on the IMU measurement principle, using the data collected by its core sensor, taking into account the existing systematic errors and random errors, an error model is constructed to describe the uncertainty in the measurement process.

3. The all-source navigation method based on the fusion of RTK and laser inertial navigation odometer according to claim 1 is characterized in that: In step S2, the high-precision tight coupling between the laser radar and the inertial navigation system includes the following steps: S21. External parameter calibration of lidar and inertial navigation: The point cloud data obtained by the lidar scan is converted to the inertial navigation coordinate system using the preliminary estimated external parameter transformation matrix. The M-neighbor error of each point in the point cloud is calculated and used as the optimization target. The nonlinear optimization library NLopt is used for iterative solution to obtain the optimized external parameter transformation matrix. The high-precision laser odometer information is obtained through the lidar. At the same time, the posture constraint information of the same time period is calculated using the IMU pre-integration. The optimization equation is constructed based on the idea of ​​​​the overlap of the two sets of trajectories, and the external parameter estimation value is obtained by solving; S22. Feature matching of laser odometer: A method based on spatial curvature is used to extract corner feature points and plane feature points from the point cloud scanned by the laser radar. The two frames of point cloud are accurately matched according to the spatial distance relationship between the feature points. For corner feature points, points with similar distances are searched in the two frames of point cloud and straight lines are constructed, and the distance from the point to the straight line is calculated. For plane feature points, points with similar distances are identified in the two frames of point cloud and planes are constructed. When calculating the distance from the point to the plane, the distance deviation is minimized, and the optimal posture transformation matrix is ​​solved to obtain the laser odometer. S23, select key frames and perform sliding window optimization: using the distance reference method, when the travel exceeds a specific distance or the turning angle exceeds a preset threshold, the current laser frame is identified as a key frame, and the number of key frames in the sliding window is set. Whenever a new key frame is added, the oldest key frame in the window is removed; S24. Factor graph model construction, and tight coupling of lidar and IMU is achieved through factor graph optimization.

4. The all-source navigation method based on the fusion of RTK and laser inertial navigation odometer according to claim 3 is characterized in that: In step S22, the process of extracting corner feature points and plane feature points is: first, the point cloud is divided into point sets with different curvatures according to the curvature relationship, then points with significant features are selected in each part, and corner feature points and plane feature points are filtered out according to the curvature threshold, while unstable feature points are eliminated.

5. The all-source navigation method based on RTK and laser inertial navigation odometer fusion according to claim 3 is characterized in that: In step S24, the process of achieving tight coupling of the lidar and the IMU through factor graph optimization is as follows: on a sliding window consisting of a fixed number of key frames, the laser odometer factor and the IMU pre-integration factor measured from the lidar and IMU are optimized using the factor graph, and after the factor graph optimization, the IMU deviation is further estimated, thereby achieving tight coupling of the lidar and the IMU.

6. The all-source navigation method based on the fusion of RTK and laser inertial navigation odometer according to claim 1 is characterized in that: In step S4, the assessing the availability of the GNSS-RTK measurement comprises the following steps: S41, after receiving the 3D point cloud and IMU self-motion measurement data, the LiDAR factor and the IMU factor are established by using scan matching and IMU pre-integration respectively, and are jointly optimized in a sliding tool based on the local FGO to gradually generate a global map; S42, processing the GNSS raw data at the same time, calculating the average elevation mask based on the three-dimensional point cloud data to evaluate the availability of GNSS-RTK and remove unreliable data points; S43, integrate reliable LiDAR factors, IMU factors and GNSS-RTK factors to achieve geo-referenced positioning; S44, convert the GNSS-RTK data into ENU frame and extract the local map around it, removing points below 1m; S45. Divide the area around the GNSS receiver into 36 sub-areas according to the azimuth angle, and evaluate its availability by calculating the average elevation angle of each sub-area as the average elevation angle mask for GNSS-RTK measurement.

7. The all-source navigation method based on RTK and laser inertial navigation odometer fusion according to claim 6 is characterized in that: In step S42, the process of evaluating the availability of GNSS-RTK based on the three-dimensional point cloud data by calculating the average elevation mask and eliminating unreliable data points is as follows: first, after setting a predetermined threshold, data points with a larger average elevation mask indicate that there are factors such as high-rise buildings or tall trees around them that block the signal, and are considered unreliable and eliminated; while data points with a smaller average elevation mask indicate that they are in a relatively open environment and are therefore considered reliable.

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