Installation error correction method for mine pose sensing system

By using components such as gyro total stations in the mining position perception system to measure and adjust the placement angle of the navigation system box, the problem of large installation errors in the downhole environment is solved, high-precision navigation and position perception are achieved, and mining efficiency and safety are improved.

CN119779241AActive Publication Date: 2025-04-08TAIYUAN INST OF CHINA COAL TECH & ENG GROUP +1
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Patent Information

Application Number
CN202411926207.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-25
Publication Date
2025-04-08
Estimated Expiration
2044-12-25

AI Technical Summary

Technical Problem

The existing mining position perception system has large installation errors in the underground environment, resulting in low measurement accuracy and cannot meet the needs of remote intelligent mining.

Method used

The navigation system box consisting of a gyroscope total station, prism, reflector, gyroscope, main controller, display, and RTK base station is used to measure the spatial vector direction and reflected light angle data of the reflector and prism, calculate the absolute heading of the excavation equipment, and adjust the placement angle of the navigation system box to compensate the heading information of the gyroscope to ensure accurate positioning.

Benefits of technology

It realizes precise positioning and navigation of the navigation system, optimizes path planning, enhances system stability, extends service life, improves mining efficiency and safety, and improves intelligence level.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention belongs to the technical field of mining intelligent sensing and control, and provides an installation error correction method for a mining pose sensing system in order to solve the problem that the pose measurement stability of remote intelligent mining cannot be met at present. A high-precision gyroscopic total station in a precisely designed navigation system box body is matched with a gyroscope, and one side of the gyroscope and the corresponding side of the box body are strictly kept in a parallel state in the structural design process of the box body, so that error angles and installation error angles between the navigation system box body and tunneling equipment are reduced and eliminated from the design of a hardware foundation; and finally, compensating, correcting and optimizing an installation error by using a Kalman filtering algorithm.
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Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent perception and control for mining, and in particular relates to a method for correcting installation errors of a mining posture perception system. Background Art

[0002] The key technical difficulty in achieving the goal of intelligent mining and unmanned operation in coal mines lies in the positioning and attitude determination of tunneling equipment. Since there is no GPS signal underground, it is impossible to output the heading and positioning information in real time through satellite positioning, which brings many uncertainties to the remote mining process of coal mines. The current technologies that assist mining equipment in achieving the guidance function include laser pointers, combined inertial navigation, visual recognition and laser targets. From the perspective of measurement accuracy, anti-interference and portability, the combined inertial navigation system is a technology with a high degree of matching among the current market application technologies.

[0003] In the process of station setting and relocation, in order to ensure that the infrared laser beam of the laser pointer can be consistent with the preset heading angle of tunnel mining, the coal mine survey team needs to determine the station location and direction in advance through relevant measuring instruments (such as gyro total station, line-laying instrument, etc.), first install the laser pointer below the vertical line of the preset station location and fix it, and keep the origin of the infrared beam overlapping with the measurement azimuth circle of the survey team, that is, the station setting and relocation are completed. The installation of this equipment is simple and portable, and there are many human intervention factors. The entire installation process is basically based on the human eye. Considering the measurement accuracy, it cannot be expressed by quantitative indicators, so the specific situation of the installation accuracy cannot be confirmed. As a guiding auxiliary device for realizing intelligent mining of tunneling equipment, it cannot meet its application requirements.

[0004] Existing posture sensing and measurement equipment are all installed based on the airborne mode, in which the visual recognition and laser target measurement methods realize the change of relative posture based on specific markers in the tunnel. Therefore, in this measurement process, it is only necessary to ensure the absolute position of the characteristic markers in the tunnel. The markers in the tunnel need to be parallel to the horizontal section of the tunnel and vertical to the longitudinal plane of the tunnel mining direction. The posture measurement device has high perception accuracy, but weak environmental interference resistance. In a dusty environment, its measurement accuracy cannot be guaranteed. Therefore, for the posture auxiliary measurement device for realizing remote intelligent mining, it cannot meet the application requirements of achieving real-time stable output. Summary of the invention

[0005] In order to solve at least one of the above-mentioned technical problems existing in the prior art, the present invention provides a method for correcting installation errors of a mining posture perception system.

[0006] The present invention is implemented by the following technical scheme: a method for correcting installation errors of a mining posture perception system, which is applied to a navigation system box composed of a gyro total station, a prism, a reflector, a gyroscope, a main controller, a display, and an RTK base station. The bottom surface of the navigation system box is provided with a support surface, and the gyroscope is positioned in the box based on the support surface and the positioning hole. The box is installed on the tunneling equipment, and a perspective window is installed on one side of the box and is equipped with a prism, a first reflector, and a second reflector. The prism is located on the preset central axis of the tunneling equipment, and comprises the following steps:

[0007] Establishing an absolute coordinate system relative to the earth based on the gyro total station;

[0008] Measuring the spatial vector directions of two points represented by the first reflector and the second reflector in the absolute coordinate system based on the gyro total station;

[0009] Measuring the reflected light angle data of the prism based on the gyro total station, and calculating the absolute heading of the parking position of the tunneling equipment based on the reflected light angle data;

[0010] Based on the spatial vector directions of the first reflector and the second reflector and the absolute heading of the parking position of the tunneling equipment, adjusting the placement angle of the navigation system box until the placement angle of the navigation system box is consistent with the absolute heading of the parking position of the tunneling equipment;

[0011] The currently measured attitude and heading information of the gyroscope are extracted, and based on the absolute heading of the parking position of the tunneling equipment, the currently measured heading information of the gyroscope is compensated so that the currently measured heading information of the gyroscope is consistent with the absolute heading of the parking position of the tunneling equipment.

[0012] Preferably, the establishing of an absolute coordinate system relative to the earth based on the gyro total station comprises:

[0013] Determine the position of the navigation system box. When the navigation system box is on the ground, first obtain at least two control points through the RTK base station, and then the gyro total station uses the station setting method to establish an absolute coordinate system relative to the earth based on the control points; when the navigation system box is underground, first obtain at least two control points, and then the gyro total station uses the station setting method to establish an absolute coordinate system relative to the earth based on the control points.

[0014] Preferably, the measuring the spatial vector directions of two points represented by the first reflector and the second reflector in the absolute coordinate system based on the gyro total station includes:

[0015] Respectively obtaining a first space vector and a second space vector of the first reflector and the second reflector in an absolute coordinate system;

[0016] The spatial vector directions of the two points represented by the first reflector and the second reflector in the absolute coordinate system are determined based on the first spatial vector and the second spatial vector.

[0017] Preferably, it also includes:

[0018] Determining an angle between corresponding space vectors based on the first space vector and the second space vector;

[0019] The relative direction of the first space vector and the second space vector is determined according to the angle.

[0020] Preferably, calculating the absolute heading of the tunneling equipment when it stops running includes:

[0021] The first space vector and the second space vector are projected onto a preset plane, and the quadrant where the projection is located is determined according to the angle between the first space vector and the second space vector, and the absolute heading of the tunneling equipment when it stops running is calculated.

[0022] Preferably, adjusting the heading information of the gyroscope based on the space vector direction and the absolute heading includes:

[0023] Based on the space vector direction and the absolute heading, the heading information of the gyroscope is adjusted through a Kalman filter algorithm.

[0024] Preferably, it also includes:

[0025] Process noise is introduced and a state equation is constructed according to the angular velocity of the gyroscope.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] Precise positioning and navigation: The installation of an accurate navigation system can ensure that mining equipment mines according to the predetermined path and depth during underground operations, reduce over-excavation or under-excavation caused by positioning errors, and thus improve mining accuracy; Optimize path planning: Accurate navigation information helps mining equipment select the optimal path in complex mine tunnels, avoid unnecessary detours and repeated operations, and improve mining efficiency.

[0028] Enhance system stability: The underground mine environment is usually accompanied by high-intensity vibration and shock. Precise box installation can more effectively resist these external interferences and maintain the stability and reliability of the navigation system; Extend service life: Reducing mechanical stress concentration caused by improper installation can reduce the risk of wear and damage to the navigation system and its components, thereby extending the service life of the entire system.

[0029] Optimize operation process: Accurate navigation information helps mining equipment to achieve fast and accurate path planning in the mine, reduce unnecessary detours and waiting time, and optimize the entire mining operation process. By integrating with other control systems of mining equipment (such as automated control systems, remote monitoring systems, etc.), the navigation system can achieve comprehensive control and optimization of mining equipment and further improve mining efficiency.

[0030] Enhanced safety: The precise navigation system can monitor the distance between the mining equipment and the surrounding environment in real time, including mine walls, other equipment, personnel, etc., and issue obstacle avoidance instructions in time to prevent equipment collisions and accidents. Combined with sensor technology and data analysis algorithms, the navigation system can provide early warning of possible safety hazards, such as geological disasters, equipment failures, etc., and provide timely warning information for mining equipment to ensure operational safety.

[0031] Improve the level of intelligence: Combined with the remote control system, the precise navigation system can realize remote digital precise control of mining equipment. Operators can view the operating status and location information of mining equipment in real time through the remote monitoring system at the ground control center, and conduct remote control and command. This greatly improves the level of intelligence and automation of mining operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 It is a flow chart of a method for correcting installation errors of a mining posture perception system provided by an embodiment of the present invention;

[0034] Figure 2 It is a schematic diagram of a navigation box structure provided by an embodiment of the present invention;

[0035] Among them, 1-rest surface; 2-gyroscope; 3-gyroscope positioning hole; 4-navigation box positioning hole. DETAILED DESCRIPTION

[0036] In conjunction with the drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments 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 implementation methods obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention. It should be noted that in this specification, relational terms such as first and second are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0038] The core component of the combined inertial navigation system is the gyroscope, which is a precision instrument for high-precision measurement. The main operating mode of the instrument is to calculate its own attitude and heading information by sensing the rotation of the earth. It is a sensitive device for independent measurement. Therefore, if the installation error cannot be reduced and eliminated in time during the installation of the device, there will be many uncertainties in the output attitude and heading information, affecting the efficient operation of the tunneling equipment. Since the gyroscope is a non-explosion-proof product, two installation angle errors will be generated during the installation process. One is the installation angle error of the gyroscope placed in the flameproof box; the other is the installation angle error between the flameproof box and the tunneling equipment. Therefore, it is impossible to ensure that the high-precision heading and attitude information output by the navigation system is highly consistent with the tunneling equipment, which ultimately affects the output of the measurement results and cannot provide a reference benchmark for accurate heading and attitude information.

[0039] In order to solve the above problems, the present invention provides a method for correcting installation errors of a mining posture perception system, which aims to eliminate and reduce the arm error and inherent installation error of the navigation system in the airborne mode.

[0040] like Figure 1 As shown, the present invention provides a schematic diagram of a method for correcting installation errors of a mining posture perception system, which is applied to Figure 2 The navigation system box shown is composed of a gyro total station, a prism, a reflector, a gyroscope 2, a main controller, a display, and an RTK base station. The bottom surface of the navigation system box is provided with a support surface 1. The gyroscope 2 is positioned in the box based on the support surface 1 and the positioning hole. The box is installed on the tunneling equipment. A perspective window is installed on one side of the box and is equipped with a prism, a first reflector, and a second reflector. The prism is located on the preset central axis of the tunneling equipment, including the following steps:

[0041] S1: establishing an absolute coordinate system relative to the earth based on the gyro total station;

[0042] S2: measuring the spatial vector directions of two points represented by the first reflector and the second reflector in the absolute coordinate system based on the gyro total station;

[0043] S3: measuring the reflected light angle data of the prism based on the gyro total station, and calculating the absolute heading of the parking position of the tunneling equipment based on the reflected light angle data;

[0044] S4: adjusting the placement angle of the navigation system box based on the spatial vector directions of the first reflector and the second reflector and the absolute heading of the parking position of the tunneling equipment until the placement angle of the navigation system box is consistent with the absolute heading of the parking position of the tunneling equipment;

[0045] S5: Extract the currently measured attitude and heading information of the gyroscope 2, and compensate the currently measured heading information of the gyroscope 2 based on the absolute heading of the parking position of the tunneling equipment, so that the currently measured heading information of the gyroscope 2 is consistent with the absolute heading of the parking position of the tunneling equipment.

[0046] In this embodiment, the gyroscope 2 and the corresponding side surfaces in the navigation system box are kept highly parallel. The specific structure is as follows: Figure 2 As shown, during the initial processing of the navigation system case, a high degree of accuracy needs to be ensured, and the bottom position of the case, that is, the contact portion between the gyroscope 2 and the navigation case also needs to be processed with high accuracy; the gyroscope positioning hole 3 is arranged at the center position of the navigation system case, and the accuracy of the opening needs to ensure that no sliding error of the screw is generated, and the gyroscope 2 is fixed through the gyroscope positioning hole 3, and the side of the gyroscope 2 is ensured to be close to the surface 1.

[0047] In this embodiment, during the installation of the navigation system box in the airborne mode, the central axis of the navigation system box and the Y-axis direction of the gyroscope 2 are kept consistent with the preset central axis of the tunneling equipment.

[0048] In a preferred embodiment, an absolute coordinate system relative to the earth is established based on the gyro total station, comprising: determining the position of the navigation system box, when the navigation system box is on the ground, first obtaining at least two control points through an RTK base station, and then the gyro total station establishes an absolute coordinate system relative to the earth based on the control points by using a station setting method; when the navigation system box is underground, first obtaining at least two control points, and then the gyro total station establishes an absolute coordinate system relative to the earth based on the control points by using a station setting method.

[0049] In this embodiment, if the installation error correction process of the mine posture perception system is carried out on the ground, first, two or more control points are pre-measured through the RTK base station, and the gyro total station uses the known control points to establish an absolute coordinate system relative to the earth by using the station setting method; if the installation error correction process of the mine posture perception system is carried out underground, more than two known control point information must be provided by the gyro total station or the mine to complete the station setting.

[0050] In a preferred embodiment, measuring the spatial vector directions of the two points represented by the first reflector and the second reflector in the absolute coordinate system based on the gyro total station includes: respectively acquiring the first spatial vector and the second spatial vector of the first reflector and the second reflector in the absolute coordinate system; and determining the spatial vector directions of the two points represented by the first reflector and the second reflector in the absolute coordinate system based on the first spatial vector and the second spatial vector.

[0051] In this embodiment, the vector coordinates corresponding to the first coordinate are set to The vector coordinates corresponding to the second coordinate are but arrive The space vector direction of for:

[0052]

[0053] Then normalize the space vector:

[0054]

[0055] In the formula, represent The model, represent The value of the modulus, Represents the normalized space vector direction

[0056] The spatial vector directions of the two points represented by the first reflector and the second reflector in the absolute coordinate system are determined according to the normalization result.

[0057] In a preferred embodiment, it also includes: determining the angle between corresponding space vectors based on the first space vector and the second space vector; and judging the relative direction between the first space vector and the second space vector according to the angle.

[0058] In this embodiment, the angle calculation formula is:

[0059]

[0060] In the formula, and They are The modulus and The mold length.

[0061] In this embodiment, the sign of the dot product is used to determine the relative direction of two vectors:

[0062] if but and The angle between them is acute, indicating that they point in roughly the same direction;

[0063] if but and Direction vertical;

[0064] if but and The angle between them is an obtuse angle, indicating that they point in opposite directions.

[0065] In a preferred embodiment, the absolute heading of the tunneling equipment when it stops operating is calculated, including: projecting the first space vector and the second space vector onto a preset plane, and determining the quadrant in which the projection is located based on the angle between the first space vector and the second space vector, and calculating the absolute heading of the tunneling equipment when it stops operating.

[0066] In this embodiment, the reflected light angle between the prism, the first reflector and the second reflector installed on the preset central axis of the tunneling equipment is measured by a gyro total station, and the measurement data is recorded. In actual application, the central axis of the tunneling equipment is calibrated and designed before leaving the factory, and the position pointed by the central axis represents the forward heading of the tunneling equipment.

[0067] In this embodiment, the calculation formula is:

[0068]

[0069] θ=arctan2(y1-y,x1-x)

[0070] In the formula, express exist The length in the direction, θ represents between The angle between y and x is determined by arctan2, which indicates the quadrant in which the angle is returned.

[0071] In this embodiment, the absolute heading is used as a reference, and the spatial vector directions of the two points represented by the first reflector and the second reflector in the navigation system box are repeatedly measured by a gyro total station as a reference to manually fine-tune the placement angle of the navigation box on the excavation equipment to be consistent with the reference data.

[0072] In a preferred embodiment, adjusting the heading information of the gyroscope 2 based on the space vector direction and the absolute heading includes: adjusting the heading information of the gyroscope 2 based on the space vector direction and the absolute heading through a Kalman filter algorithm.

[0073] In a preferred embodiment, the method further includes: introducing process noise and constructing a state equation according to the angular velocity of the gyroscope 2 .

[0074] In this embodiment, the main controller extracts the attitude and heading information currently measured by the gyroscope 2, and uses the absolute heading as a reference to perform data compensation through the Kalman filter algorithm to ensure that the heading angles of the three headings remain consistent.

[0075] In this embodiment, it is assumed that the angular velocity (in radians per second) measured by the gyroscope 2 is ω t , then after the time interval Δt, the state equation of the angle change can be approximated as:

[0076] θ t+1 =θ t +ω t Δt

[0077] However, considering the noise and drift of gyroscope 2, a process noise ω is introduced g , so the state equation for the change in angle becomes:

[0078] θ t+1 =θ t +ω t Δt+ω g

[0079] Where, process noise ω g is a Gaussian noise with mean 0 and covariance Q.

[0080] In this embodiment, the angle measurement value z is calculated by the reflected light data measured by the gyro total station. t The angle θ calculated by gyroscope 2 t The relationship between can be expressed as:

[0081] z t =θ t +v t

[0082] In the formula, v t represents measurement noise with mean 0 and covariance R.

[0083] In this embodiment, during the optimization process of the Kalman filter algorithm, the prediction mode is:

[0084]

[0085] P t+1t =P tt +Q

[0086] In the formula, is the state equation estimate at time t (a posteriori estimate), is the angle prediction (prior estimate) at time t+1, P t∣t and P t+1∣t is the corresponding estimated covariance, Q is ω g The covariance in .

[0087] The optimization modes are:

[0088] K t =P t+1t (P t+1t +R) -1

[0089]

[0090] P t+1t+1 =(1-K t ) t+1t

[0091] In the formula, R represents v t The covariance in K t is the Kalman gain.

[0092] The correction of installation error angles must be strictly controlled in many links of the mining inertial navigation system during assembly and mounting. For example, the assembly of gyroscope 2 requires the correction of installation error angles of gyroscope and accelerometer; the assembly of navigation system box requires the correction of installation error angles between gyroscope 2 and box; and the installation of navigation system box requires the correction of installation error angles between box and tunneling equipment.

[0093] At present, the assembly of gyroscopes is strictly implemented in accordance with military standards, and the technology is relatively mature. There are many patents involved in eliminating installation errors. Before leaving the factory, the products are tested by high-precision three-axis turntable instruments to meet product application requirements. However, during the assembly of the navigation system box, the installation error between the gyroscope and the box itself is usually not considered. During the installation process, it is only fixed according to the hole positions designed in the drawings, which will cause the first-order error in the installation process of the navigation system. Therefore, in the structural design process of the box, it is necessary to focus on one side of the gyroscope and the corresponding side of the box to strictly maintain a parallel state, and reduce and eliminate the generation of the first-order error angle from the hardware basic design. The second-order error of the navigation system installation is generated by the installation error between the navigation box and the tunneling equipment. The present invention uses a high-precision gyro total station to cooperate with the gyroscope to perform multi-data fusion processing, and finally reduces and eliminates the installation error from the hardware structure, and corrects and optimizes the installation error from the algorithm compensation.

[0094] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for correcting installation errors of a mining posture perception system, applied to a navigation system box composed of a gyro total station, a prism, a reflector, a gyroscope (2), a main controller, a display, and an RTK base station, wherein the bottom surface of the navigation system box is provided with a support surface (1), the gyroscope (2) is positioned in the box based on the support surface (1) and a positioning hole, the box is installed on a tunneling equipment, a perspective window is installed on one side of the box and a prism, a first reflector, and a second reflector are mounted, the prism is located on a preset central axis of the tunneling equipment, and is characterized in that: The steps include: Establishing an absolute coordinate system relative to the earth based on the gyro total station; Measuring the spatial vector directions of two points represented by the first reflector and the second reflector in the absolute coordinate system based on the gyro total station; Measuring the reflected light angle data of the prism based on the gyro total station, and calculating the absolute heading of the parking position of the tunneling equipment based on the reflected light angle data; Based on the spatial vector directions of the first reflector and the second reflector and the absolute heading of the parking position of the tunneling equipment, adjusting the placement angle of the navigation system box until the placement angle of the navigation system box is consistent with the absolute heading of the parking position of the tunneling equipment; The currently measured attitude and heading information of the gyroscope (2) is extracted, and based on the absolute heading of the parking position of the tunneling equipment, the currently measured heading information of the gyroscope (2) is compensated so that the currently measured heading information of the gyroscope (2) is consistent with the absolute heading of the parking position of the tunneling equipment.

2. The method for correcting installation errors of a mining posture perception system according to claim 1, characterized in that: The step of establishing an absolute coordinate system relative to the earth based on the gyro total station comprises: Determine the position of the navigation system box. When the navigation system box is on the ground, first obtain at least two control points through the RTK base station, and then the gyro total station uses the station setting method to establish an absolute coordinate system relative to the earth based on the control points; when the navigation system box is underground, first obtain at least two control points, and then the gyro total station uses the station setting method to establish an absolute coordinate system relative to the earth based on the control points.

3. The installation error correction method of the mining posture perception system according to claim 1 is characterized in that: The measuring, based on the gyro total station, the spatial vector directions of two points represented by the first reflector and the second reflector in the absolute coordinate system comprises: Respectively obtaining a first space vector and a second space vector of the first reflector and the second reflector in an absolute coordinate system; The spatial vector directions of the two points represented by the first reflector and the second reflector in the absolute coordinate system are determined based on the first spatial vector and the second spatial vector.

4. The method for correcting installation errors of a mining posture perception system according to claim 3 is characterized in that: Also includes: Determining an angle between corresponding space vectors based on the first space vector and the second space vector; The relative direction of the first space vector and the second space vector is determined according to the angle.

5. The method for correcting installation errors of a mining posture perception system according to claim 3 is characterized in that: The calculating the absolute heading of the tunneling equipment when it stops running comprises: The first space vector and the second space vector are projected onto a preset plane, and the quadrant where the projection is located is determined according to the angle between the first space vector and the second space vector, and the absolute heading of the tunneling equipment when it stops running is calculated.

6. The method for correcting installation errors of a mining posture perception system according to claim 1, characterized in that: The adjusting the heading information of the gyroscope (2) based on the space vector direction and the absolute heading comprises: Based on the space vector direction and the absolute heading, the heading information of the gyroscope (2) is adjusted through a Kalman filter algorithm.

7. The method for correcting installation errors of a mining posture perception system according to claim 6, characterized in that: Also includes: Process noise is introduced and a state equation is constructed according to the angular velocity of the gyroscope (2).

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