CN111323804B - Ship attitude measurement equipment and measurement method based on Beidou system - Google Patents

Ship attitude measurement equipment and measurement method based on Beidou system Download PDF

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Publication number
CN111323804B
CN111323804B CN202010324308.7A CN202010324308A CN111323804B CN 111323804 B CN111323804 B CN 111323804B CN 202010324308 A CN202010324308 A CN 202010324308A CN 111323804 B CN111323804 B CN 111323804B
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antenna
beidou
ship
finding
measurement
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CN111323804A (en
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陈扬
吴海乐
侯利朋
陈云锋
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Cathay Nebula Science & Technology Co ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/53Determining attitude
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/40Correcting position, velocity or attitude
    • G01S19/41Differential correction, e.g. DGPS [differential GPS]
    • 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
    • Y02ATECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/30Assessment of water resources

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses ship attitude measurement equipment and a measurement method based on a Beidou system. Compared with the prior art, the invention has the following positive effects: the invention utilizes the existing Beidou dual-antenna direction-finding receiver board card to measure, and can accurately calculate the relative base line length and direction between two antennas by utilizing the mutual differential technology of the board card, thereby eliminating the dependence on differential reference stations. The two Beidou dual-antenna direction-finding receiver board cards are utilized to jointly measure a common Beidou satellite navigation antenna, so that the mutual connection and the measurement coordinate value unification of the two Beidou dual-antenna direction-finding receiver board cards are established, and the data fusion of the two Beidou dual-antenna direction-finding receiver board cards is realized.

Description

Ship attitude measurement equipment and measurement method based on Beidou system
Technical Field
The invention relates to a ship attitude measurement device and a measurement method based on a Beidou system.
Background
The traditional ship attitude measurement relies on an inertial navigation system consisting of a high-precision gyroscope and a high-precision accelerometer, but the measurement mode has the defect that navigation errors are accumulated along with time, and the price of the measurement mode is relatively high. Meanwhile, the inertial navigation system needs to be accurately installed and calibrated. Due to objective factors such as price, complicated installation and calibration, the popularity of the inertial navigation system in the aspect of ship measurement is limited.
Along with the establishment and the application of the Beidou No. three satellite navigation system in China, satellite application related to satellite positioning, navigation and time service is certainly and rapidly popularized in China. Compared with inertial navigation, the Beidou system can provide all-day and all-weather positioning functions, is relatively low in price and can ensure higher measurement accuracy. Therefore, in certain aspects, the ship attitude measurement method based on the Beidou multi-antenna has certain advantages over inertial navigation attitude measurement.
The Beidou attitude measurement equipment commonly used at present is a double-antenna direction-finding receiver, and can only accurately measure two attitude angles, but cannot meet the accurate measurement of three-dimensional attitude angles. And the heading, rolling and pitching information of the ship are mutually coupled and cannot be independently measured by a plurality of double-antenna direction-finding receivers.
The RTK accurate positioning technology is adopted, the positions of all the points can be measured by using a plurality of Beidou receivers, and then the ship body posture is calculated by a data post-processing method. However, this solution has the disadvantage that real-time measurements cannot be achieved and reference station equipment must be provided, which is costly and the range of application is limited by the reference station location.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides ship attitude measurement equipment and a measurement method based on a Beidou system, which are combined by utilizing two commercial dual-antenna direction-finding receiver boards, and according to the characteristics of high baseline and direction measurement precision and relatively poor absolute positioning precision of the dual-antenna direction-finding receiver, the measurement is creatively performed by using a common antenna, the deviation of the positioning of the two dual-antenna direction-finding receiver boards is eliminated, and then the accurate three-dimensional attitude information of a ship is calculated by a data fusion processing method.
The technical scheme adopted for solving the technical problems is as follows: the utility model provides a ship gesture measuring equipment based on beidou system, includes radio frequency interface module, two beidou dual antenna direction finding receivers, surveys appearance module, data storage module and communication interface module, wherein:
the radio frequency interface module comprises a satellite signal power divider which is used for transmitting radio frequency signals of three Beidou satellite navigation antennas A, B, C to two Beidou double-antenna direction-finding receivers, wherein the satellite signal power divider is used for dividing radio frequency signals of a public Beidou satellite navigation antenna B into two paths and transmitting the two paths of radio frequency signals to the two Beidou double-antenna direction-finding receivers respectively;
the two Beidou dual-antenna direction-finding receivers are respectively connected with two Beidou satellite navigation antennas through a radio frequency interface module, and are used for measuring the installation positions of the Beidou satellite navigation antennas and baseline and included angle information between the two antennas, and outputting positioning and gesture measurement information to a gesture measurement module;
the attitude measurement module outputs calibration parameters and real-time attitude measurement information of the ship to the data storage module through data synchronization, positioning data association and data fusion attitude measurement processing on the received positioning and attitude measurement information of the two Beidou dual-antenna direction-finding receivers, and meanwhile outputs the real-time attitude measurement information of the ship through the communication interface module.
The invention also provides a ship attitude measurement method based on the Beidou system, which comprises the following steps:
step one, converting positioning information and attitude measurement information acquired by two Beidou dual-antenna direction-finding receivers into local coordinates;
step two, according to the base line and the positioning position information, calculating the local coordinates of the antenna A and the antenna C;
calculating the attitude angle of the antenna plane by using coordinate values of 3 antennas;
and step four, calculating the attitude angle of the ship body according to the angle relation between the antenna plane and the transmission coordinate system.
Compared with the prior art, the invention has the following positive effects:
the invention utilizes the existing Beidou dual-antenna direction-finding receiver board card to measure, and can accurately calculate the relative base line length and direction between two antennas by utilizing the mutual differential technology of the board card, thereby eliminating the dependence on differential reference stations. The two Beidou dual-antenna direction-finding receiver board cards are utilized to jointly measure a common Beidou satellite navigation antenna, so that the mutual connection and the measurement coordinate value unification of the two Beidou dual-antenna direction-finding receiver board cards are established, and the data fusion of the two Beidou dual-antenna direction-finding receiver board cards is realized.
The invention combines the dual-antenna direction finding function and the data fusion algorithm to realize the three-axis attitude measurement function and measure the heading, rolling and pitching data of the ship in real time. Compared with the traditional ship attitude measurement equipment, the equipment is low in cost and convenient to install, measurement errors are not scattered with time based on the Beidou satellite positioning technology, and the equipment is a stable and reliable ship attitude measurement scheme.
Drawings
The invention will now be described by way of example and with reference to the accompanying drawings in which:
FIG. 1 is a block diagram of a Beidou system-based marine attitude measurement device;
fig. 2 is an installation schematic diagram of a beidou satellite navigation antenna, wherein: the antenna Ant-A is an antenna arranged on the front side of the ship, the antenna Ant-B is an antenna arranged on the rear side of the ship, the direction of a base line formed by the antenna Ant-A and the antenna Ant-B is consistent with the direction of the central axis of the ship, and the antenna Ant-C is an antenna arranged on the right chord (or left chord) of the ship;
FIG. 3 is a schematic view of a ship carrier coordinate system and an antenna plane coordinate system;
fig. 4 is an information flow diagram of a ship attitude measurement method based on a Beidou system;
fig. 5 is a flowchart of a ship attitude measurement method based on the beidou system.
Detailed Description
Ship attitude measurement equipment based on Beidou system, as shown in fig. 1, comprises: radio frequency interface module, two big dipper dual antenna direction finding receiver integrated circuit boards, survey appearance module, data storage module, communication interface module, power module etc. wherein the function of each module is as follows:
and the radio frequency interface module transmits radio frequency signals of the external Beidou satellite navigation antenna to the specified Beidou double-antenna direction-finding receiver board card. The radio frequency interface module comprises a satellite signal power divider, wherein the satellite signal power divider is responsible for dividing a public satellite antenna signal into two paths and respectively transmitting the two paths of public satellite antenna signals to the two double-antenna direction-finding board cards so as to realize the association of positioning data of the two double-antenna direction-finding board cards.
The Beidou dual-antenna direction-finding receiver board card is connected with two Beidou satellite navigation antennas through a radio frequency interface module, and the installation position of the Beidou satellite navigation antennas and baseline and included angle information between the two antennas are measured.
The gesture measuring module receives positioning and gesture measuring information of two Beidou dual-antenna direction-finding receiver board cards, and measures the real-time gesture of the carrier through data synchronization, positioning data association, data fusion gesture measuring and other processes. The module has two functions: a device calibration function and a carrier attitude measurement function. The equipment calibration function outputs the installation parameter information of the satellite antenna relative to the ship body and stores the installation parameter information into built-in calibration parameters; the carrier attitude measurement function measures the attitude of the plane of the satellite antenna, calculates the real-time attitude of the ship by combining with the built-in satellite antenna installation parameter information, stores the real-time attitude, and outputs the attitude information through the communication interface.
The data storage module is used for storing calibration parameters and real-time attitude measurement information.
The communication interface module is responsible for communicating with external devices.
The power module supplies power to the whole equipment and provides protection measures such as overvoltage.
The installation mode of the 3 Beidou antennas is shown in fig. 2. The 3 Beidou antennas are an antenna A, an antenna B and an antenna C respectively, wherein the antenna A and the antenna B are arranged front and back along the ship, the antenna A is close to the bow, the direction of an AB base line is consistent with the direction of the central axis of the ship, the antenna C is arranged on the side of the ship board, and ABC is guaranteed to be arranged in a triangle.
The connection of the 3 Beidou antennas and the measuring equipment is shown in fig. 1. The antenna B is divided into two paths by the power divider, one path of the antenna A and one path of the antenna B are commonly connected to the dual-antenna direction-finding receiver 1, and the other path of the antenna C and the other path of the antenna B are commonly connected to the dual-antenna direction-finding receiver 2. The antenna A and the antenna C are used as direction finding antennas, and the antenna B is used as a positioning antenna.
Through the above installation and connection, the dual antenna direction-finding receiver 1 can output the position of the antenna B and the heading of the baseline BA; the dual antenna direction-finding receiver 2 may output the position of the antenna B and the heading of the baseline BC.
The working principle of the dual-antenna direction-finding receiver determines that the direction-finding precision is high under the condition that a differential reference station is not provided, but the positioning precision is poor. And when measuring the same position, the fluctuation of measured values of different devices and different times of the same device is poor, so that the data of the dual-antenna direction-finding receiver needs to be corrected, thereby realizing the unification of the data of the two dual-antenna direction-finding receivers.
The pose detection module receives the positioning direction-finding data of the dual-antenna direction-finding receiver 1 and the dual-antenna direction-finding receiver 2, and due to the fact that the antenna B is the positioning antenna of the two dual-antenna direction-finding receivers, the difference (the generation reason is the same as the above) between the positioning data of the dual-antenna direction-finding receiver 1 and the positioning data of the dual-antenna direction-finding receiver 2 is the inconsistency of the position measurement of the two receivers. And by using the value to uniformly correct the measurement data of the double-antenna direction-finding receivers 2, the positioning and direction-finding data of the two double-antenna direction-finding receivers realize coordinate unification. At the moment, the ship attitude measurement can be realized by utilizing the positioning and direction-finding data of the two double-antenna direction-finding receivers and combining a least square algorithm.
The storage module stores two types of information. The information is configuration information of the equipment, such as antenna installation parameter information automatically formed after equipment calibration, equipment configuration information input by an external interface and the like; the information is measurement information stored in real time in the working process of the equipment, and can be read for post analysis.
The communication interface comprises a real-time information input/output interface and a post-processing data transmission interface. The real-time information input/output interface outputs the attitude measurement information and corresponding time information of the equipment in real time, and receives external configuration information, and can adaptively change the equipment working mode, data output rate, output data format and the like through the configuration information. The post data transmission interface can copy the measurement information stored by the storage module to mobile equipment such as a USB flash disk and the like for post analysis.
The invention also provides a ship attitude measurement method based on the Beidou system, which comprises the following steps:
definition of (one) coordinate System
The ship carrier coordinate system definition is shown in fig. 3. The center of the antenna B is a coordinate origin, and the Y axis horizontally points to the bow and is consistent with the direction of the central axis of the ship; the Z axis is vertically upward; the X axis points to the right chord of the ship and forms a right-hand rectangular coordinate system together with the YZ axis.
The antenna plane coordinate system is defined as shown in fig. 3. The center of the antenna B is the origin of coordinates, and the Y1 axis points to the antenna A from the antenna B; the Z1 axis is vertically upwards; x1, Y1 and Z1 axes together form a right-hand rectangular coordinate system.
3. Gesture measurement scheme
The scheme of (two) multi-antenna measurement requires approximately the following steps:
1. through Gaussian coordinate conversion, the positioning information (longitude and latitude) of the Beidou is converted into local coordinates;
2. calculating the local coordinates of the A, C antenna according to the base line and the positioning position information;
3. calculating the attitude angle of the antenna plane by using the coordinate values of the 3 antennas;
4. and calculating the attitude angle of the ship body according to the angular relation between the antenna plane and the transmission coordinate system.
The steps have the following key technical points:
(1) Two receiver coordinate unification
The dual antenna direction finding receiver can accurately measure the relative baseline between the two antennas. However, since the receiver 1 uses the antennas a and B to perform direction finding and the receiver 2 uses the antennas C and B to perform direction finding, there may be a difference in the combination of visible satellites used in locating the direction finding. In addition, the baseband noise level of each receiver objectively has a difference, so that the position measurement values of the two receivers on the antenna B are not identical, and two measurement results appear at the same position, which can influence the uniformity of the data of the two receivers, and further influence the final joint measurement accuracy. And therefore this error needs to be compensated for.
Assume that the local coordinates of the antenna A, B in the dual-antenna direction-finding receiver 1 are (X A ,Y A ,Z A )、(X B1 ,Y B1 ,Z B1 ) The local coordinates of the antenna B, C in the dual-antenna direction-finding receiver 2 are (X B2 ,Y B2 ,Z B2 )、(X C ,Y C ,Z C ). The two receivers measure the difference of the antenna B as (X B2 -X B1 ,Y B2 -Y B1 ,Z B2 -Z B1 )。
After error compensation, the local coordinate value of the antenna A, B, C is (X A ,Y A ,Z A )、(X B1 ,Y B1 ,Z B1 ),(X C -X B2 +X B1 ,Y C -Y B2 +Y B1 ,Z C -Z B2 +Z B1 )。
(2) Antenna measurement plane attitude measurement method
The local coordinate system is defined as n system, and the antenna plane coordinate system is defined as m system. The coordinate transformation matrix from n system to m system is as followsCoordinate transformation matrix from m system to n system is +.>Let the component of a certain base line vector under n series be X n The component under the m system is X m
If the actual azimuth, elevation and roll angles of the antenna plane are (ψ, θ, γ) respectively,can be expressed as:
x is converted according to the coordinate system m And X n The conversion relation of (2) can be expressed as:
from the above equation, each independent baseline vector may form an equation, and N independent baselines may form N equations.
Can form matrix M m ,/>Can form a matrixM n ,M m And M n Are all 3 xn matrices.
Therefore, when the number of independent baselines is more than or equal to 3, the least square principle is utilized to calculate the values of each element of the gesture matrix:
from the matrix, according to equations 1 and 4Calculating attitude information of an antenna plane:
in this application, three Beidou antennas can construct two independent baselines (BA and BC), so that a third virtual baseline is calculated by constructing virtual points, and the calculation of formula 4 is realized.
(3) Device installation angle calibration
Since the heights of the 3 antennas in the ship carrier coordinate system cannot be guaranteed to be consistent when the antennas are installed, an installation angle error exists between a measurement plane formed by the 3 antennas and the ship carrier. And because the direction of the base line AB is consistent with the direction of the central axis of the ship, only a horizontal included angle exists between the measurement plane and the ship carrier.
And (3) stopping the ship in a static water area, so that the ship is in a static state, and the horizontal attitude angle of the ship is 0. Through collecting Beidou positioning direction-finding data for a period of time (such as 20 min), the included angle error (0, theta, gamma) can be calculated by using the formulas 1-5, and the conversion matrix from the antenna measurement plane (m system) to the ship carrier coordinate system can be calculated by substituting the formula 1
(4) Ship attitude calculation
In accordance with the above analysis of the present invention,the conversion relation from the local coordinate system to the antenna plane coordinate system is thatThe antenna measurement value and the conversion matrix calculation formula can be calculated; the conversion relation from the antenna plane coordinate system to the ship carrier coordinate system is +.>Can be obtained through calibration, and the real-time conversion matrix from the local coordinate system to the ship carrier coordinate system is +.>The calculation method comprises the following steps:
according to the formula 5, the real-time attitude angle of the ship can be calculated.
(III) data processing flow
The information flow diagram of the ship attitude measurement method based on the Beidou system is shown in fig. 4.
According to the ship attitude measurement method based on the Beidou system, an attitude measurement algorithm is implemented in an attitude measurement module, and the algorithm flow is shown in fig. 5.

Claims (6)

1. A measuring method of ship attitude measuring equipment based on a Beidou system is characterized by comprising the following steps of: the method comprises the following steps:
step one, converting positioning information and attitude measurement information acquired by two Beidou dual-antenna direction-finding receivers into local coordinates;
step two, according to the base line and the positioning position information, calculating the local coordinates of the antenna A and the antenna C;
calculating the attitude angle of the antenna plane by using the coordinate values of 3 antennas:
(1) Defining a local coordinate system as an n-system and an antenna plane coordinate system as an m-system; the coordinate transformation matrix from n system to m system is as followsCoordinate transformation matrix from m system to n system is +.>Let the component of a certain base line vector under n series be X n The component under the m system is X m The method comprises the steps of carrying out a first treatment on the surface of the If the actual azimuth, elevation and roll angles of the antenna plane are (ψ, θ, γ), respectively, then we get:
(2) According to the coordinate system conversion relation, the following X is obtained m And X n Is a conversion relation of:
(3) The following N equations are constructed using N independent baseline vectors:
order theComposition matrix M m Let->Composition matrix M n ,M m And M n All are 3 XN matrixes;
(4) When N is more than or equal to 3, the least square principle is utilized to calculateIs defined by the respective element values of:
(5) Real-time transformation matrix from local coordinate system to ship carrier coordinate system according to formula 1 and formula 4Calculating the attitude angle of the antenna plane:
the saidThe calculation method of (1) is as follows:
1) Calculating a conversion matrix from m system to ship carrier coordinate system
The ship is stopped in a static water area, so that the ship is in a static state, and the horizontal attitude angle of the ship is 0; collecting Beidou positioning direction-finding data for a period of time, calculating an included angle error of (0, theta, gamma) by using formulas 1 to 5, and substituting the included angle error into the formula 1 to calculate
2) Calculated according to the following formula
Step four, calculating the attitude angle of the ship body according to the angle relation between the antenna plane and the transmission coordinate system;
the ship attitude measurement equipment comprises a radio frequency interface module, two Beidou dual-antenna direction-finding receivers, an attitude measurement module, a data storage module and a communication interface module, wherein:
the radio frequency interface module comprises a satellite signal power divider which is used for transmitting radio frequency signals of three Beidou satellite navigation antennas A, B, C to two Beidou double-antenna direction-finding receivers, wherein the satellite signal power divider is used for dividing radio frequency signals of a public Beidou satellite navigation antenna B into two paths and transmitting the two paths of radio frequency signals to the two Beidou double-antenna direction-finding receivers respectively;
the two Beidou dual-antenna direction-finding receivers are respectively connected with two Beidou satellite navigation antennas through a radio frequency interface module, and are used for measuring the installation positions of the Beidou satellite navigation antennas and baseline and included angle information between the two antennas, and outputting positioning and gesture measurement information to a gesture measurement module;
the attitude measurement module outputs calibration parameters and real-time attitude measurement information of the ship to the data storage module through data synchronization, positioning data association and data fusion attitude measurement processing on the received positioning and attitude measurement information of the two Beidou dual-antenna direction-finding receivers, and meanwhile outputs the real-time attitude measurement information of the ship through the communication interface module.
2. The measurement method of the ship attitude measurement equipment based on the Beidou system according to claim 1, wherein the measurement method comprises the following steps of: the antenna A is arranged on the front side of the ship, the antenna B is arranged on the rear side of the ship, the direction of a base line AB formed by the antenna A and the antenna B is consistent with the direction of the central axis of the ship, and the antenna C is arranged on the side of the ship board and ensures that ABC is arranged in a triangle.
3. The measurement method of the ship attitude measurement equipment based on the Beidou system according to claim 2, wherein the measurement method comprises the following steps of: one path of the antenna B and the antenna A are commonly connected to one Beidou double-antenna direction-finding receiver, the other path of the antenna B and the antenna C are commonly connected to the other Beidou double-antenna direction-finding receiver, the antenna A and the antenna C serve as direction-finding antennas, and the antenna B serves as a positioning antenna.
4. A measurement method of a ship attitude measurement device based on a beidou system according to claim 3, wherein: one Beidou dual-antenna direction-finding receiver outputs the position of the antenna B and the heading of the base line AB, and the other Beidou dual-antenna direction-finding receiver outputs the position of the antenna B and the heading of the base line BC.
5. The measurement method of the ship attitude measurement equipment based on the Beidou system according to claim 1, wherein the measurement method comprises the following steps of: the communication interface module comprises a real-time information input/output interface and a post-processing data transmission interface.
6. The measurement method of the ship attitude measurement equipment based on the Beidou system according to claim 1, wherein the measurement method comprises the following steps of: the method for determining the local coordinate value of the antenna A, B, C is as follows:
(1) The local coordinates of the antenna A, B in the Beidou double-antenna direction-finding receiver are set as (X) A ,Y A ,Z A )、(X B1 ,Y B1 ,Z B1 ) The local coordinates of the antenna B, C in the other Beidou dual-antenna direction-finding receiver are (X B2 ,Y B2 ,Z B2 )、(X C ,Y C ,Z C );
(2) Calculating the measurement difference of the two Beidou double-antenna direction-finding receivers to the antenna B to obtain (X) B2 -X B1 ,Y B2 -Y B1 ,Z B2 -Z B1 );
(3) Error compensation is performed by using the measured difference values to obtain local coordinate values of the antenna A, B, C respectively as (X) A ,Y A ,Z A )、(X B1 ,Y B1 ,Z B1 ),(X C -X B2 +X B1 ,Y C -Y B2 +Y B1 ,Z C -Z B2 +Z B1 )。
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