CN116202516A - Track three-dimensional reconstruction method for track BIM multidimensional parameter auxiliary IMU - Google Patents

Track three-dimensional reconstruction method for track BIM multidimensional parameter auxiliary IMU Download PDF

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CN116202516A
CN116202516A CN202211660578.0A CN202211660578A CN116202516A CN 116202516 A CN116202516 A CN 116202516A CN 202211660578 A CN202211660578 A CN 202211660578A CN 116202516 A CN116202516 A CN 116202516A
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mileage
bim
odometer
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CN116202516B (en
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齐春雨
房博乐
谭兆
杨云洋
杨双旗
安然
王少林
黄大中
张云龙
王娇
梁永
石德斌
胡锦民
何义磊
周文明
张宇
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China Railway Design Corp
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/16Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20Instruments for performing navigational calculations
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10Complex mathematical operations
    • G06F17/11Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00Road transport of goods or passengers
    • Y02T10/10Internal combustion engine [ICE] based vehicles
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Abstract

The invention discloses a track three-dimensional reconstruction method of a track BIM multidimensional parameter auxiliary IMU, which comprises the following steps: s1, performing time synchronization on mileage data of an odometer and IMU measurement data; s2, inertial navigation calculation is carried out through IMU mechanical arrangement, and navigation positioning information comprising three-dimensional positions, speeds and postures is obtained; s3, calibrating the odometer according to the actual mileage marked by the site position, and estimating the scale factor and the constant deviation of the odometer by adopting a least square method parameter estimation method; s4, searching and calculating three-dimensional coordinates of the track in the plane and longitudinal surface track engineering information of the BIM library according to the mileage after the calibration in the S3; s5, performing rough difference detection on track coordinates searched and calculated in the BIM library by adopting innovation filtering; and S6, performing three-dimensional reconstruction of the track, and updating the information of the flat longitudinal section track of the BIM database. The method realizes high-precision three-dimensional reconstruction of the track and can be used for updating the track horizontal and vertical section model.

Description

Track three-dimensional reconstruction method for track BIM multidimensional parameter auxiliary IMU
Technical Field
The invention relates to the field of precise measurement of rail transit rails, in particular to a rail three-dimensional reconstruction method of a rail BIM multidimensional parameter auxiliary IMU.
Background
In recent years, rail transit rapidly develops, the common speed railway is opened to operate for approximately 11 kilometers, the high speed railway is opened for 4 kilometers, the problem of rail operation and maintenance is continuously emerging, during the operation period of the rail transit, the rail is deformed due to foundation settlement, load and the like, in order to keep the relative smoothness of a railway line, the actual geometric parameters of the horizontal and vertical section of the rail are greatly changed after long-term track adjustment, the actual geometric parameters are greatly different from the existing line data, the information such as a standing account and the like, and many lines even completely lose the line data. For three-dimensional reconstruction and restoration of the alignment of the track, accurate measurements of the track plane and elevation coordinates are required.
In the commonly adopted GNSS measurement method, under the environments of tunnels, high buildings and the like, the problems of multipath effect, signal shielding and the like can seriously reduce the measurement precision, and even the coordinates cannot be obtained. The GNSS/INS integrated navigation positioning method can improve the measurement accuracy of the GNSS signals with poor quality to a certain extent, but has the characteristics of high short-term accuracy and large long-term accumulated error of inertial navigation, and still cannot solve the positioning problem under long-term signal shielding of long tunnels, mountainous areas and the like. The method is a great technical problem in fully mining big data information for assisting inertial navigation and maintaining long-term high-precision positioning.
The BIM technology is based on a three-dimensional digital technology, is rapidly developed and applied to collaborative decision-making and management of life cycles of planning, designing, construction and the like of rail transit, a great deal of researches are also carried out on a three-dimensional digital rail engineering design model based on the BIM technology, and the rapid extraction of rail engineering information such as planes, longitudinal planes and the like in the model is also realized. However, the technology is less applied in the line operation period, the ledger management line is adopted at present, the peripheral accessories of the line cannot be seen, each department forms an information island, the geometric parameters of the flat longitudinal section of the track cannot be fully utilized, and precious data information which can be used for assisting the inertial navigation system to restrain the divergence of the inertial navigation system is greatly wasted for the integrated navigation system.
Disclosure of Invention
Aiming at the problems of three-dimensional reconstruction and linear recovery of the track traffic track, the invention provides a track three-dimensional reconstruction method of a track BIM multidimensional parameter auxiliary IMU (inertial measurement unit).
The invention adopts the following technical scheme:
a track BIM multidimensional parameter auxiliary IMU track three-dimensional reconstruction method comprises the following steps:
s1, performing time synchronization on mileage data of an odometer and measurement data of an IMU, and realizing high-precision time synchronization by marking the IMU and the odometer with time labels of the same crystal oscillator;
s2, inertial navigation calculation is carried out through IMU mechanical arrangement, and navigation positioning information comprising three-dimensional positions, speeds and postures is obtained;
s3, calibrating the odometer according to the actual mileage marked by the site position, and estimating the scale factor and the constant deviation of the odometer by adopting a least square method parameter estimation method;
s4, searching and calculating three-dimensional coordinates of the track in the plane and longitudinal surface track engineering information of the BIM library according to the mileage after the calibration in the S3;
s5, based on Kalman filtering, the multi-dimensional parameters of the track BIM assist the IMU to carry out solution calculation, and the information filtering is adopted to carry out rough difference detection on track coordinates searched and calculated in the BIM library;
s6, carrying out three-dimensional reconstruction of the track, and updating the information of the flat longitudinal section track of the BIM database: and (3) equidistant interval sampling is carried out on the track three-dimensional coordinates and the three-dimensional gestures obtained by combined navigation calculation along the track mileage advancing direction, and meanwhile, reversing data are automatically identified and removed to obtain accurate coordinates after the track three-dimensional reconstruction.
Wherein, step S3 comprises the following sub-steps:
s31, when a clear mileage mark exists on the site, aligning the positions of the mileage meter and the mileage mark, comparing the output values of the site mileage meter and the mileage meter, and if the difference is large, automatically deleting the site mileage mark to prevent the error mileage mark from interfering with the mileage meter calibration; if the difference is not large, recording, thereby obtaining a series of on-site mileage values;
s32, estimating the proportion factor and the constant deviation of the odometer by adopting a least square method parameter estimation method:
Figure BDA0004013687390000021
wherein b (i) represents the ith in-situ recorded mileage, b 0 Represents a home mileage start value, d (i) represents an odometer output value when aligned with an ith home mileage, d 0 Indicating the output starting value of the odometer, x 1 Represents the drift factor of the odometer as mileage increases, x 2 Represents a constant deviation amount irrelevant to mileage, and delta is a random error; b (i) -b 0 Is denoted as Z, [ d (i) -d 0 ,1] T Is marked as H, [ x ] 1 ,x 2 ] T Marked as X;
solving parameter estimation according to a weighted least square criterion, wherein W is a weight matrix, and the solution meeting the least square criterion is taken as a least square solution
Figure BDA0004013687390000022
Figure BDA0004013687390000023
And calculates an updated mileage d' from these two parameters:
Figure BDA0004013687390000024
wherein d is an odometer output value;
step S4 comprises the following sub-steps:
s41, judging the intersection point section and the specific line element type according to the calibrated mileage d' obtained in the step S3 and the plane line shape information in the BIM; the specific line element type is a straight line, a moderation curve or a circular curve;
s42, calculating the parameters of the unified model curve element to obtain the plane coordinate values (x, y) of the orbit;
s43, obtaining the calibrated mileage d' and the longitudinal section linear information in the BIM through S3, and obtaining an elevation h through a vertical curve elevation rigorous calculation model;
the step S5 comprises the following sub-steps:
s51, forming an observation equation according to the three-dimensional coordinates (x, y, h) obtained in the S4 and the lever arm:
Figure BDA0004013687390000031
the position coordinates which should be obtained by the track at the wheel can be calculated according to the position obtained by inertial navigation in S2 and recorded as
Figure BDA0004013687390000032
Rail seat flag calculated by BIM library search in S4 is +.>
Figure BDA0004013687390000033
It has a certain error with the true position of the track, which is marked as e r ;/>
Figure BDA0004013687390000034
The vector of the position of the IMU center to the odometer wheel in the b-train, i.e. the lever arm. />
Figure BDA0004013687390000035
For a cosine matrix of the sensor coordinate system b-system transformed into the navigation coordinate system n-system +.>
Figure BDA0004013687390000036
And ψ represent the position error and the attitude error vector, respectively.
S52, carrying out fusion calculation on the coordinates extracted from the BIM and the IMU mechanical arrangement coordinates based on Kalman filtering;
s53, robust detection:
when the track coordinates searched and calculated in the BIM library have larger error abnormality, the adopted rough difference detection mode is to process by utilizing innovation filtering, the innovation of the Kalman filter can reflect whether the state estimation value is consistent with the observed quantity, the variance array is compared with the corresponding innovation, and the observed quantity exceeding a threshold value is removed:
Figure BDA0004013687390000037
wherein ,
Figure BDA0004013687390000038
representing the innovation of Kalman filter, C k Representing a new variance matrix, wherein R values represent different confidence degrees when the R values are different; when the above formula is not established, the track coordinate result obtained by searching and calculating in the BIM library is unreliable, and the track coordinate result is removed.
The invention assists inertial navigation through information such as flat vertical section, ultrahigh and the like in the track BIM, and suppresses the divergence of an inertial navigation system. Meanwhile, in the place where the track is seriously deformed, the track BIM flat longitudinal section information is a harmful auxiliary signal for an inertial navigation system, the accuracy of the multi-dimensional parameter information in the BIM is judged by adopting an robust detection method, the harmful BIM multi-dimensional parameter information is abandoned, the beneficial information is fully utilized to assist the inertial navigation, the high-precision three-dimensional reconstruction of the track is finally realized, and the track multi-dimensional parameter of the BIM can be updated.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the high-precision track three-dimensional position coordinates can be obtained under the condition of long-time signal shielding in long tunnels and mountainous areas without depending on GNSS positioning;
2. the BIM technology is used for three-dimensional reconstruction and operation maintenance of the track, the method has the advantages of visualization and synergy, the track information after three-dimensional reconstruction can be visually presented, the information of the appendages around the railway can be inquired, and the track data information is comprehensively mined;
3. the invention can negatively feed back and update the track information of the track horizontal and vertical sections in the BIM database, and correct the track information with larger deformation in time;
drawings
FIG. 1 is a flow chart of a method of three-dimensional reconstruction of a track according to the present invention;
FIG. 2 is a schematic diagram of flat profile track information in a BIM database;
FIG. 3 is a flow chart of combined navigation solution and negative feedback for an orbital BIM multidimensional parameter assisted IMU.
Detailed Description
The method of the present invention will be described in detail with reference to the accompanying drawings.
The track three-dimensional reconstruction method of the track BIM multidimensional parameter auxiliary IMU is based on Kalman filtering, and the track three-dimensional coordinate auxiliary IMU extracted from the track information of the flat longitudinal section of the BIM database is subjected to integrated navigation calculation to obtain high-precision track coordinates, so that the track is subjected to three-dimensional reconstruction and the track BIM database can be updated. As shown in fig. 1, the method specifically comprises the following steps:
s1, time synchronization is carried out on mileage data of an odometer and IMU measurement data: the IMU (inertial measurement unit) comprises a triaxial gyroscope and a triaxial accelerometer, is used for measuring the three-dimensional angular velocity and the three-dimensional acceleration of the carrier, and realizes high-precision time synchronization by marking the IMU and the odometer with time labels of the same crystal oscillator;
s2, inertial navigation calculation is carried out through IMU mechanical arrangement, and navigation positioning information comprising three-dimensional positions, speeds and postures is obtained;
s3, calibrating the odometer according to the actual mileage marked by the site position, wherein the method comprises the following steps of:
s31, when a clear mileage mark exists on the site, aligning the positions of the mileage meter and the mileage mark, comparing the output values of the site mileage meter and the mileage meter, and if the difference is large, automatically deleting the site mileage mark to prevent the error mileage mark from interfering with the mileage meter calibration; if the difference is not large, recording, thereby obtaining a series of on-site mileage values;
s32, estimating the proportion factor and the constant deviation of the odometer by adopting a least square method parameter estimation method:
Figure BDA0004013687390000041
wherein b (i) represents the ith in-situ recorded mileage, b 0 Representing a sceneMileage start value, d (i) represents the odometer output value when aligned with the ith on-site mileage, d 0 Indicating the output starting value of the odometer, x 1 Represents the drift factor of the odometer as mileage increases, x 2 Represents a constant deviation amount irrelevant to mileage, and delta is a random error; b (i) -b 0 Is denoted as Z, [ d (i) -d 0 ,1] T Is marked as H, [ x ] 1 ,x 2 ] T Denoted as X.
According to the weighted least square criterion, the parameter estimation can be solved, wherein W is called a weight matrix, and the solution meeting the least square criterion is the least square solution
Figure BDA0004013687390000051
Figure BDA0004013687390000052
And calculates updated mileage from the two parameters, namely mileage d' after calibration:
Figure BDA0004013687390000053
wherein d is an odometer output value;
and S4, searching and calculating the three-dimensional coordinates of the track in the plane and longitudinal track engineering information of the BIM database according to the calibrated mileage d' obtained in the S3, wherein the plane and longitudinal track information of the BIM database is shown in figure 2. The method comprises the following steps:
s41, judging the intersection point section and the specific line element type (straight line, relaxation curve and circular curve) according to the calibrated mileage d' obtained in the S3 and the plane linear information in the BIM;
s42, calculating the parameters of the unified model curve element to obtain the plane coordinate values (x, y) of the orbit;
s43, obtaining an elevation h by a vertical curve elevation rigorous calculation model according to the calibrated mileage d' obtained in the S3 and the linear information of the vertical section in the BIM;
s5, the multi-dimensional parameters of the track BIM assist the IMU to conduct integrated navigation for resolving. As shown in fig. 3, the method comprises the following sub-steps:
s51, forming an observation equation according to the three-dimensional coordinates (x, y, h) obtained in the S4 and the lever arm:
Figure BDA0004013687390000054
the position coordinates which should be obtained by the track at the wheel can be calculated according to the position obtained by inertial navigation in S2 and recorded as
Figure BDA0004013687390000055
Rail seat flag calculated by BIM library search in S4 is +.>
Figure BDA0004013687390000056
It has a certain error with the true position of the track, which is marked as e r ;/>
Figure BDA0004013687390000057
The vector of the position of the IMU center to the odometer wheel in the b-train, i.e. the lever arm. />
Figure BDA0004013687390000058
For a cosine matrix of the sensor coordinate system b-system transformed into the navigation coordinate system n-system +.>
Figure BDA0004013687390000059
And ψ represent the position error and the attitude error vector, respectively.
S52, carrying out fusion calculation on the coordinates extracted from the BIM and the IMU mechanical arrangement coordinates based on Kalman filtering;
s53, robust detection:
when the track coordinates searched and calculated in the BIM library have larger error abnormality, the adopted rough difference detection mode is to process by utilizing innovation filtering, the innovation of the Kalman filter can reflect whether the state estimation value is consistent with the observed quantity, the variance array is compared with the corresponding innovation, and the observed quantity exceeding a threshold value is removed:
Figure BDA0004013687390000061
wherein ,
Figure BDA0004013687390000062
representing the innovation of Kalman filter, C k Representing an innovation variance matrix; when the R values are different, the representative confidence is different. When the above formula is not established, the track coordinate result obtained by searching and calculating in the BIM library is unreliable, and the track coordinate result can be removed.
S6, performing three-dimensional reconstruction, and updating a BIM database: and (3) equidistant interval sampling is carried out on the track three-dimensional coordinates and the three-dimensional gestures obtained by combined navigation calculation along the track mileage advancing direction, and meanwhile, reversing data are automatically identified and removed to obtain accurate coordinates after the track three-dimensional reconstruction.
After the method is implemented, the track after three-dimensional reconstruction can be compared with the flat longitudinal section track information model in the BIM database, and if the track deformation is large, the BIM database is updated, so that the negative feedback update of the flat longitudinal section track information model of the BIM database is realized.

Claims (5)

1. A track BIM multidimensional parameter auxiliary IMU track three-dimensional reconstruction method comprises the following steps:
s1, performing time synchronization on mileage data of an odometer and measurement data of an IMU, and realizing high-precision time synchronization by marking the IMU and the odometer with time labels of the same crystal oscillator;
s2, inertial navigation calculation is carried out through IMU mechanical arrangement, and navigation positioning information comprising three-dimensional positions, speeds and postures is obtained;
s3, calibrating the odometer according to the actual mileage marked by the site position, and estimating the scale factor and the constant deviation of the odometer by adopting a least square method parameter estimation method;
s4, searching and calculating three-dimensional coordinates of the track in the plane and longitudinal surface track engineering information of the BIM library according to the mileage after the calibration in the S3;
s5, based on Kalman filtering, the multi-dimensional parameters of the track BIM assist the IMU to carry out solution calculation, and the information filtering is adopted to carry out rough difference detection on track coordinates searched and calculated in the BIM library;
s6, carrying out three-dimensional reconstruction of the track, and updating the information of the flat longitudinal section track of the BIM database: and (3) equidistant interval sampling is carried out on the track three-dimensional coordinates and the three-dimensional gestures obtained by combined navigation calculation along the track mileage advancing direction, and meanwhile, reversing data are automatically identified and removed to obtain accurate coordinates after the track three-dimensional reconstruction.
2. The method of three-dimensional reconstruction of a track according to claim 1, wherein step S3 comprises the sub-steps of:
s31, when a clear mileage mark exists on the site, aligning the positions of the mileage meter and the mileage mark, comparing the output values of the site mileage meter and the mileage meter, and if the difference is large, automatically deleting the site mileage mark to prevent the error mileage mark from interfering with the mileage meter calibration; if the difference is not large, recording, thereby obtaining a series of on-site mileage values;
s32, estimating the proportion factor and the constant deviation of the odometer by adopting a least square method parameter estimation method:
Figure FDA0004013687380000011
wherein b (i) represents the ith in-situ recorded mileage, b 0 Represents a home mileage start value, d (i) represents an odometer output value when aligned with an ith home mileage, d 0 Indicating the output starting value of the odometer, x 1 Represents the drift factor of the odometer as mileage increases, x 2 Represents a constant deviation amount irrelevant to mileage, and delta is a random error; b (i) -b 0 Is denoted as Z, [ d (i) -d 0 ,1] T Is marked as H, [ x ] 1 ,x 2 ] T Marked as X;
solving for parameter estimates based on a weighted least squares criterion, where W is a weight matrixA solution meeting the least square criterion is taken as a least square solution
Figure FDA0004013687380000012
Figure FDA0004013687380000013
And calculates an updated mileage d' from these two parameters:
Figure FDA0004013687380000014
wherein d is the odometer output value.
3. The method of three-dimensional reconstruction of a track according to claim 2, wherein step S4 comprises the sub-steps of:
s41, judging the intersection point section and the specific line element type according to the calibrated mileage d' obtained in the step S3 and the plane line shape information in the BIM;
s42, calculating the parameters of the unified model curve element to obtain the plane coordinate values (x, y) of the orbit;
s43, obtaining the calibrated mileage d' and the longitudinal section linear information in the BIM through S3, and obtaining the elevation h through a vertical curve elevation rigorous calculation model.
4. A method of three-dimensional reconstruction of a track according to claim 3, wherein: the specific line element type is a straight line, a mild curve or a circular curve.
5. The method of three-dimensional reconstruction of a track according to claim 1, wherein step S5 comprises the sub-steps of:
s51, forming an observation equation according to the three-dimensional coordinates (x, y, h) obtained in the S4 and the lever arm:
Figure FDA0004013687380000021
the position coordinates which should be obtained by the track at the wheel can be calculated according to the position obtained by inertial navigation in S2 and recorded as
Figure FDA0004013687380000022
Rail seat flag calculated by BIM library search in S4 is +.>
Figure FDA0004013687380000023
It has a certain error with the true position of the track, which is marked as e r ;/>
Figure FDA0004013687380000024
The position vector from the center of the IMU in the b system to the wheel of the odometer, namely a lever arm; />
Figure FDA0004013687380000025
For a cosine matrix of the sensor coordinate system b-system transformed into the navigation coordinate system n-system +.>
Figure FDA0004013687380000026
And ψ represent the position error and the attitude error vector, respectively;
s52, carrying out fusion calculation on the coordinates extracted from the BIM and the IMU mechanical arrangement coordinates based on Kalman filtering;
s53, robust detection:
when the track coordinates searched and calculated in the BIM library have larger error abnormality, the adopted rough difference detection mode is to process by utilizing innovation filtering, the innovation of the Kalman filter can reflect whether the state estimation value is consistent with the observed quantity, the variance array is compared with the corresponding innovation, and the observed quantity exceeding a threshold value is removed:
Figure FDA0004013687380000027
wherein ,
Figure FDA0004013687380000028
representing the innovation of Kalman filter, C k Representing a new variance matrix, wherein R values represent different confidence degrees when the R values are different; when the above formula is not established, the track coordinate result obtained by searching and calculating in the BIM library is unreliable, and the track coordinate result is removed. />
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CN109520492A (en) * 2018-08-30 2019-03-26 中铁上海工程局集团有限公司 Personnel's position data collecting method and system under BIM environment
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106060781A (en) * 2016-06-24 2016-10-26 李琦 Spatial location method based on fusion of BIM (Building Information Modeling) and Zigbee technology
CN107036609A (en) * 2016-10-18 2017-08-11 中建八局第建设有限公司 Virtual reality air navigation aid, server, terminal and system based on BIM
FR3068478A1 (en) * 2017-06-30 2019-01-04 Deutsches Zentrum Fur Luft- Und Raumfahrt E.V. METHOD FOR DETERMINING THE POSITION OF A RAILWAY VEHICLE IN A RAILWAY NETWORK
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