CN112526454A - Underwater control point positioning method considering surface layer sound velocity and coordinate prior information - Google Patents

Underwater control point positioning method considering surface layer sound velocity and coordinate prior information Download PDF

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CN112526454A
CN112526454A CN202011137076.0A CN202011137076A CN112526454A CN 112526454 A CN112526454 A CN 112526454A CN 202011137076 A CN202011137076 A CN 202011137076A CN 112526454 A CN112526454 A CN 112526454A
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coordinate
control point
sound velocity
error
underwater
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CN112526454B (en
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李治远
豆虎林
胡俊
张海泉
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First Institute of Oceanography MNR
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/26—Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C13/00—Surveying specially adapted to open water, e.g. sea, lake, river or canal
    • G01C13/008—Surveying specially adapted to open water, e.g. sea, lake, river or canal measuring depth of open water
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H5/00—Measuring propagation velocity of ultrasonic, sonic or infrasonic waves, e.g. of pressure waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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Abstract

The invention provides an underwater control point positioning method considering surface layer sound velocity and coordinate prior information, and belongs to the technical field of underwater positioning. The method considers surface sound velocity and coordinate prior information, obtains the sound velocity error of a circular navigation method and the control point plane coordinate prior information by analyzing the sound velocity error of the circular navigation method, takes the water depth value measured by the control point coordinate and the pressure sensor as random quantity, gives the water depth observation value prior variance to be 0.1% of the water depth according to experience, and finally solves the control point coordinate by adopting the generalized least square principle. The simulation of 50m and 1500m water depth positioning experiments proves that under the condition of not using a sound velocity profile, a higher-precision positioning result can be obtained by only considering surface sound velocity and coordinate prior information, so that the time of a ship can be effectively saved, and the operation efficiency is improved. The method has strong practicability, steady and reliable result and high efficiency, and is mainly used for transmitting the absolute coordinate reference of the underwater control network.

Description

Underwater control point positioning method considering surface layer sound velocity and coordinate prior information
Technical Field
The invention belongs to the field of underwater positioning, and particularly relates to an underwater control point positioning method considering surface layer sound velocity and coordinate prior information.
Background
The seabed control net is the foundation for carrying out ocean geodetic survey and has important significance for detecting and monitoring the motion of ocean plates and the deformation of the crust. In the process of calibrating the absolute position of the control point, the conventional method is to determine the coordinate of the submarine control point by using a shipborne GPS and underwater distance measuring equipment in a rendezvous manner. But has the following disadvantages: the distance measurement precision is greatly influenced by the sound velocity error, the positioning precision is greatly reduced due to the small sound velocity error, and particularly, the positioning error caused by the sound velocity error is not negligible during deep sea positioning. In order to weaken the influence caused by the sound velocity error and improve the positioning precision and the operation efficiency, a scholars provides a circular walking method.
The accuracy of the control point vertical solution depends on accurate distance determination, and an accurate sound velocity profile is the key for accurate ranging, however, the sound velocity profile is related to water temperature, salinity and pressure, and varies irregularly with time and space, so that it is difficult and time-consuming to obtain an accurate sound velocity profile.
In order to solve the problems and obtain a high-precision and stable three-dimensional absolute coordinate of a seabed control point, the invention provides an underwater control network point positioning method considering surface sound velocity and depth information.
Disclosure of Invention
The method aims to solve the defects of the prior art, is high in practicability, high in universality, time-saving and labor-saving, and can achieve the purpose of high-precision positioning of the underwater control point without sound velocity profile data.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention provides a precise positioning method for an underwater control point considering surface acoustic velocity and coordinate prior information, which takes the coordinates of the control point and a water depth value measured by a pressure sensor as random quantity, gives the prior variance of the water depth value measured by the pressure sensor to be 0.1% of the water depth according to an empirical value, and solves the problem by adopting a generalized least square principle. The method comprises the following specific steps:
the method comprises the steps of firstly considering the symmetry of circular navigation to obtain the influence of sound velocity errors on the coordinate precision of an underwater control point, then establishing a model for solving the plane coordinate of the underwater control point by using the surface sound velocity on the basis of the influence, and finally obtaining the underwater control mesh point precision positioning method only needing the surface sound velocity and depth information.
Optionally, the specific steps include the following:
(1) laying of underwater control points
Arranging a beacon with a built-in pressure sensor at a water bottom control point;
(2) round navigation observation
The ship sails for a circle at a constant speed along a circle with a control point as a center and a radius of water depth 1/2;
starting the shipborne transducer, measuring the distance between the transducer and the transponder at equal intervals, and recording the surface sound velocity of the transducer by using a surface sound velocity meter;
(3) circular navigation method sound velocity error analysis
Establishing underwater control points and shipborne transducer coordinates xoAnd xiThe observation equation of (1);
ρoi＝f(xo,xi)+δSoi+δρoi+εoi：
ρoias the observed distance between the underwater transponder and the transducer, f (x)o,xi) Is the geometric distance between the transponder and the transducer, δ SoiFor systematic errors due to transponder delay, δ ρoiIs a systematic error, ε, caused by an error in the speed of soundoiIs an accidental error;
(4) control point plane coordinate prior value acquisition
The one-way travel time of the sound ray between two points is tiSurface acoustic velocity vsThen observe the distance SiIs approximately equal to vstiEstablishing an observation equation:
Si＝f(Xo,Xi)+δSo+δSv+ε：
Xo(xo,yo,zo) As coordinates of underwater control points, Xi(xi,yi,zi) For the on-board transducer coordinates at the i-th observation,
Figure BDA0002737037140000021
for spatial skew between control point and transducer, δ SvIs the sound velocity error, δ SoFor transponder delays, ε is the occasional error;
solving the plane coordinates of the control points and neglecting delta SvCan establish corresponding error equations at each track point
Figure BDA0002737037140000031
Obtaining n error equations in a matrix form of V ═ BX-L;
according to the least squares criterion, the coordinates of the underwater control points can be found by the following formula:
Xo＝(BTPB)-1BTPL：
and P is an observation value weight array, and the posterior unit weight variance estimation value and the coordinate precision of the control point are as follows:
Figure BDA0002737037140000032
and
Figure BDA0002737037140000033
(5) precision positioning based on coordinate prior information
Establishing a survey vessel at tiPosition X of timeiWith underwater control points XoThe observation equation of (a):
ρi＝f(Xo,Xi)+δSoi+δSvi+εi
δSoiis tiTime of day transponder delay, epsiloniIs tiOccasional error in time, δ SvAs error of sound velocity, tiThe time delay of the sound ray from the transducer to the submarine transponder is measured at a moment of time as tauiUsing the surface acoustic velocity vsMultiplying by the time delay yields the approximate distance ρi；
After linearizing the observation equation, the following form is obtained:
Figure BDA0002737037140000034
Figure BDA0002737037140000035
is XoA priori value of, BiIs based on
Figure BDA0002737037140000036
XiCalculated f (X)o,Xi) With respect to XoThe first partial derivative of (a);
the observed water depth is regarded as random quantity, the prior variance of the observed water depth is 0.1% of the water depth, the control point coordinate is regarded as random quantity, and the generalized least square principle is adopted for solving.
Optionally, in step (3), δ ρ is calculated according to the least squares principleoiThe influence on the positioning result is as follows: dx ═ (B)TPB)- 1BTP delta rho, the weight matrix P is a unit weight matrix, and dx is [ 00 delta rho sec theta ]]TIt can be seen that the sound speed error has no influence on the plane coordinate, but only on the vertical coordinate.
Optionally, in step (5), the generalized least square principle is used for solving, and the error equation is as follows:
Vx＝x-μx
Vy＝y-μy
Vz＝z-μz
V＝BX-L
in the formula, mux,μy,μzSetting prior variance D of three-dimensional coordinates of control points for prior expectation of the three-dimensional coordinates of the control pointsx,Dy,DzThe variance matrix of the observed value is DΔThen μx,μy,μzThe variance matrix of L is:
Figure BDA0002737037140000041
x, y, z and L are independent, the variance matrix is a diagonal matrix, a virtual observation value is introduced, the three-dimensional coordinates of the control points are regarded as random quantity, the solution is carried out by adopting a classical least square method, and the three-dimensional coordinates of the control points can be obtained by the following formula
Figure BDA0002737037140000042
Figure BDA0002737037140000043
The method comprises the steps of expanding an error equation coefficient matrix, an observed value variance matrix and an error equation constant term after virtual observed values are introduced.
Optionally, in step (1), the underwater acoustic communication beacon with the built-in pressure sensor is arranged on the subsea control point by a fixed support or an anchoring system.
Compared with the prior art, the underwater control point positioning method considering surface layer sound velocity and coordinate prior information has the following beneficial effects:
through simulating 50m and 1500m water depth positioning experiments, positioning results with the same precision as a three-dimensional constraint adjustment method utilizing a sound velocity profile are obtained, and the method shows that in the underwater control point positioning process, under the condition of not using the sound velocity profile, only surface layer sound velocity and coordinate prior information are considered, a higher-precision positioning result can be obtained, the time of a ship can be effectively saved, and the operation efficiency is improved.
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FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a track chart and experimental zone sound velocity profile of the present invention.
Detailed Description
The invention is further described below with reference to fig. 1-2.
The traditional absolute positioning method of the underwater control network points determines the absolute coordinates of the underwater control points based on space distance intersection, determines the plane coordinates of the control points by adopting three-dimensional space distance intersection and a double triangular pyramid method, and determines the vertical coordinates of the control points by adopting a three-leaf method or a four-leaf method. This has a high requirement for the distance measurement accuracy, and is therefore greatly affected by the sound velocity error, and the coordinate solution in the depth direction is unstable.
In order to solve the problems, an underwater control point precise positioning method considering surface sound velocity and coordinate prior information is provided, coordinates of a control point and a water depth value measured by a pressure sensor are regarded as random quantities, a prior variance of the water depth value measured by the pressure sensor is given to be 0.1% of the water depth according to an empirical value, and a generalized least square principle is adopted for solving. Through simulating 50m and 1500m water depth positioning experiments, positioning results with the same precision as a three-dimensional constraint adjustment method utilizing a sound velocity profile are obtained, and the method shows that in the underwater control point positioning process, under the condition of not using the sound velocity profile, only surface layer sound velocity and coordinate prior information are considered, a higher-precision positioning result can be obtained, the time of a ship can be effectively saved, and the operation efficiency is improved.
The technical solution of the invention is mainly divided into the following 5 parts:
(1) laying of underwater control points
The underwater acoustic communication beacon with the built-in pressure sensor is arranged on a seabed control point in a fixed support or anchoring mode.
(2) Observation by round navigation
The vessel loaded with the transducer was used to travel a full turn around a circle centered at the control point and having a radius of water depth 1/2. And simultaneously starting the shipborne transducer, measuring the distance between the transducer and the transponder at equal intervals in an acoustic communication mode, and recording the surface sound velocity of the transducer by using a surface sound velocity meter in the measurement process.
(3) Circular navigation method sound velocity error analysis
According to the fact that the incident angle of the sound ray at each track point on the circular track is approximately equal, and the distance measurement errors at all the track points are also approximately equal, the coordinates x of the underwater control point and the shipborne transducer can be establishedoAnd xiThe observation equation of (1);
ρoi＝f(xo,xi)+δSoi+δρoi+εoi：
ρoias the observed distance between the underwater transponder and the transducer, f (x)o,xi) Is the geometric distance between the transponder and the transducer, δ SoiFor systematic errors due to transponder delay, δ ρoiIs a systematic error, ε, caused by an error in the speed of soundoiIs an accidental error;
obtaining delta rho according to the least square principleoiThe influence on the positioning result is as follows:
dx＝(BTPB)-1BTPδρ；
under the circular navigation mode, the distance measurement precision at each track point is basically equal, and the weight array P can be taken as a unit array, then:
Figure BDA0002737037140000061
it can be seen that the sound speed error has no influence on the plane coordinates of the control points, and only has influence on the vertical coordinates.
(4) Control point prior planar coordinate acquisition
According to the one-way travel time t of the sound ray between two pointsiSurface acoustic velocity vsThen observe the distance SiIs approximately equal to vstiEstablishing an observation equation as follows:
Si＝f(Xo,Xi)+δSo+δSv+ε，
Xo(xo,yo,zo) As coordinates of underwater control points, Xi(xi,yi,zi) For the on-board transducer coordinates at the i-th observation,
Figure BDA0002737037140000062
for spatial skew between control point and transducer, δ SvIs the sound velocity error, δ SoFor transponder delays, ε is the occasional error;
according to the circular navigation mode, the sound velocity error only affects the precision of the vertical solution of the control point, only the plane coordinate of the control point is focused here, and the delta S is ignoredvEstablishing a corresponding error equation:
Figure BDA0002737037140000063
the error equations can be established at each track point to obtain n error equations, and the matrix form of the n error equations is as follows: v ═ BX-L;
according to the least square criterion, the coordinates of the underwater control points are obtained by the following formula: xo＝(BTPB)-1BTPL, where P is the observation weight matrix, the posterior unit weight variance estimation and control point coordinate precision are:
Figure BDA0002737037140000071
and
Figure BDA0002737037140000072
at this point, the prior value (x) of the horizontal coordinate of the control point can be obtainedo,yo) And its prior variance Dx,Dy。
(5) Precision positioning based on coordinate prior information
Establishing a survey vessel at tiPosition X of timeiWith underwater control points XoObservation equation of (1), tiThe time delay of the sound ray from the transducer to the submarine transponder is measured at a moment of time as tauiUsing the surface acoustic velocity vsMultiplying by the time delay yields the approximate distance ρiThe equation is as follows: rhoi＝f(Xo,Xi)+δSoi+δSvi+εi，δSoiIs tiTime of day transponder delay, epsiloniIs tiOccasional error in time, δ SvIs the sound speed error;
after linearizing the observation equation, the following form is obtained:
Figure BDA0002737037140000073
in the formula (I), the compound is shown in the specification,
Figure BDA0002737037140000074
is XoA priori value of, BiIs based on
Figure BDA0002737037140000075
XiCalculated f (X)o,Xi) With respect to XoThe first partial derivative of (a);
the observed water depth is regarded as random quantity, the prior variance of the observed water depth is given according to an empirical value, 0.1% of the water depth is taken, the control point coordinate is regarded as the random quantity, the generalized least square principle is adopted for solving, and an error equation is as follows:
Vx＝x-μx
Vy＝y-μy
Vz＝z-μz
V＝BX-L
μx,μy,μzis a priori expectation of the three-dimensional coordinates of the control points.
Setting prior variance of three-dimensional coordinates of control points to be Dx,Dy,DzThe variance matrix of the observed value is DΔThen μxμ,yμ,zThe variance matrix of L is:
Figure BDA0002737037140000076
x, y, z and L are independent, the variance matrix is a diagonal matrix, a virtual observation value is introduced, and the three-dimensional coordinates of the control points are obtainedAnd (3) as a non-machine quantity, solving by adopting a classical least square method, and obtaining the three-dimensional coordinates of the control points by the following formula:
Figure BDA0002737037140000081
in the formula (I), the compound is shown in the specification,
Figure BDA0002737037140000082
the method comprises the steps of expanding an error equation coefficient matrix, an observed value variance matrix and an error equation constant term after virtual observed values are introduced.
Test of Experimental Effect
In order to verify the effectiveness of the method, experiments of 50m water depth and 1500m water depth are simulated respectively, and the control point coordinates are determined by using an underwater transponder as a circle center to perform a circular navigation method. In the experimental process, coordinate conversion between the GNSS receiver antenna and the transducer is ignored, a circular track of the transducer with the underwater transponder as the center of a circle and the radius as the water depth value 1/2 is directly given, and the circular track is shown as 2 a. The sound velocity profile adopts the measured data of two sea areas, sound velocity profile of 50m and 1500m water depth are respectively shown in fig. 2b and 2c, and the surface sound velocity takes the sound velocity profile value of 4m water depth in consideration of the draught of the transducer.
According to time delay between the transducer and the transponder obtained by circular navigation measurement, transducer coordinates provided by shipborne GNSS, and control point water depth and transducer surface sound velocity data measured by a built-in pressure sensor of the transponder, the following 3 data processing methods are adopted to calculate the three-dimensional coordinates of the underwater control point.
1) A precision positioning method based on sound ray tracking (A): and obtaining a relatively accurate observation distance by adopting sound ray tracking, and solving an optimal solution of the coordinates of the control points by utilizing a distance intersection positioning principle and combining with the water depth information adjustment provided by the transponder.
2) A three-dimensional positioning method based on surface sound velocity (B): and only multiplying the sound ray propagation time by the surface sound velocity to obtain the geometric distance between the transducer and the hydrophone, solving the absolute coordinates of the underwater control point by using the intersection positioning principle and the adjustment, and evaluating the accuracy of the calculation result.
3) A precision positioning method (C) taking water depth information and control point coordinate prior information into consideration: the geometric distance between the transducer and the hydrophone is obtained by multiplying the sound ray propagation time by the surface sound velocity, the prior plane coordinate of the control point and the water depth information provided by the depth sensor are introduced as the prior information of the coordinate of the control point, the three-dimensional coordinate of the control point is solved by adopting the generalized least square principle, and the precision of the three-dimensional coordinate is evaluated.
TABLE 1 transponder coordinate outside coincidence accuracy under different positioning methods
Figure BDA0002737037140000083
Figure BDA0002737037140000091
The results of the three data processing methods are compared with the absolute coordinates of the control points by taking the absolute coordinates of the control points as reference, so that the out-of-coordinate coincidence precision of the control points (see table 1) can be obtained, and the accuracy of the data processing results can be reflected more truly. It can be seen that:
1) the three methods have higher plane positioning precision, wherein the depth of 50m is basically 0.05m, and the depth of 1500m is basically 0.5 m. Note that in the method B, the observation distance is obtained by directly multiplying the surface acoustic velocity by the acoustic ray propagation time, and it can be proved that, in the circular navigation mode, the influence of the acoustic velocity error on the plane position of the control point is substantially negligible and is consistent with the theory.
2) The control point vertical coordinate precision of the method A and the method C is obviously higher than that of the method B. When the water depth is 50m, the precision of the former is centimeter level, and the latter reaches decimeter level; when the water depth is 1500m, the precision of the former is in sub-meter level, and the latter reaches meter level. By comparing the accuracy of the vertical coordinate of the control point of the method A and the accuracy of the control point of the method B, it can be seen that the accuracy of the method B is far lower than that of the method A, which shows that in the circular navigation mode measurement, although the sound velocity error does not affect the plane accuracy of the coordinate of the control point, a huge error is brought to the accuracy of the vertical coordinate. Compared with the method A and the method B, the precision of the plane coordinate and the vertical coordinate of the control point obtained by the method C is higher, and the method C does not adopt acoustic ray tracking to calculate the geometric distance between the transducer and the responder, so that the acquisition of an acoustic velocity profile is not needed, the operation flow is simplified, and the underwater control point precision positioning method considering the depth information and the plane coordinate prior information is effective.

Claims (5)

1. A method for positioning an underwater control point by considering surface layer sound velocity and coordinate prior information is characterized in that firstly, the symmetry of circular navigation is considered, the influence of sound velocity errors on the coordinate precision of the underwater control point is obtained, then a model for solving the plane coordinate of the underwater control point by using the surface layer sound velocity is established on the basis, and finally, the underwater control mesh point precision positioning method only needing the surface layer sound velocity and depth information is obtained.
2. The underwater control point positioning method considering surface sound velocity and coordinate prior information is characterized by comprising the following steps of:
(1) laying of underwater control points
Arranging a beacon with a built-in pressure sensor at a water bottom control point;
(2) round navigation observation
The ship sails for a circle at a constant speed along a circle with a control point as a center and a radius of water depth 1/2;
starting the shipborne transducer, measuring the distance between the transducer and the transponder at equal intervals, and recording the surface sound velocity of the transducer by using a surface sound velocity meter;
(3) circular navigation method sound velocity error analysis
Establishing underwater control points and shipborne transducer coordinates xoAnd xiThe observation equation of (1);
ρoi＝f(xo,xi)+δSoi+δρoi+εoi：
ρoias the observed distance between the underwater transponder and the transducer, f (x)o,xi) Is the geometric distance between the transponder and the transducer, δ SoiFor systematic errors due to transponder delay, δ ρoiIs a systematic error, ε, caused by an error in the speed of soundoiIs an accidental error;
(4) control point plane coordinate prior value acquisition
The one-way travel time of the sound ray between two points is tiSurface acoustic velocity vsThen observe the distance SiIs approximately equal to vstiEstablishing an observation equation:
Si＝f(Xo,Xi)+δSo+δSv+ε：
Xo(xo,yo,zo) As coordinates of underwater control points, Xi(xi,yi,zi) For the on-board transducer coordinates at the i-th observation,
Figure FDA0002737037130000011
for spatial skew between control point and transducer, δ SvIs the sound velocity error, δ SoFor transponder delays, ε is the occasional error;
solving the plane coordinates of the control points and neglecting delta SvCan establish corresponding error equations at each track point
Figure FDA0002737037130000021
Obtaining n error equations in a matrix form of V ═ BX-L;
according to the least squares criterion, the coordinates of the underwater control points can be found by the following formula:
Xo＝(BTPB)-1BTPL：
and P is an observation value weight array, and the posterior unit weight variance estimation value and the coordinate precision of the control point are as follows:
Figure FDA0002737037130000022
and
Figure FDA0002737037130000023
(5) precision positioning based on coordinate prior information
Establishing a survey vessel at tiPosition X of timeiWith underwater control points XoThe observation equation of (a):
ρi＝f(Xo,Xi)+δSoi+δSvi+εi
δSoiis tiTime of day transponder delay, epsiloniIs tiOccasional error in time, δ SvAs error of sound velocity, tiThe time delay of the sound ray from the transducer to the submarine transponder is measured at a moment of time as tauiUsing the surface acoustic velocity vsMultiplying by the time delay yields the approximate distance ρi；
After linearizing the observation equation, the following form is obtained:
Figure FDA0002737037130000024
Figure FDA0002737037130000025
is XoA priori value of, BiIs based on
Figure FDA0002737037130000026
XiCalculated f (X)o,Xi) With respect to XoThe first partial derivative of (a);
the observed water depth is regarded as random quantity, the prior variance of the observed water depth is 0.1% of the water depth, the control point coordinate is regarded as random quantity, and the generalized least square principle is adopted for solving.
3. The underwater control point positioning method considering surface sound velocity and coordinate priori information according to claim 1, wherein in the step (3), the δ ρ is determined according to the principle of least squaresoiThe influence on the positioning result is as follows: dx ═ (B)TPB)-1BTP delta rho, the weight matrix P is a unit weight matrix, and dx is [ 00 delta rho sec theta ]]TIt can be seen that the sound speed error has no influence on the plane coordinate, but only on the vertical coordinate.
4. The underwater control point positioning method considering surface sound velocity and coordinate priori information according to claim 1, characterized in that in the step (5), a generalized least square principle is adopted for solving, and an error equation is as follows:
Vx＝x-μx
Vy＝y-μy
Vz＝z-μz
V＝BX-L
in the formula, mux,μy,μzSetting prior variance D of three-dimensional coordinates of control points for prior expectation of the three-dimensional coordinates of the control pointsx,Dy,DzThe variance matrix of the observed value is DΔThen μx,μy,μzThe variance matrix of L is:
Figure FDA0002737037130000031
x, y, z and L are independent, the variance matrix is a diagonal matrix, a virtual observation value is introduced, the three-dimensional coordinates of the control points are regarded as random quantity, the solution is carried out by adopting a classical least square method, and the three-dimensional coordinates of the control points can be obtained by the following formula
Figure FDA0002737037130000032
Figure FDA0002737037130000033
The method comprises the steps of expanding an error equation coefficient matrix, an observed value variance matrix and an error equation constant term after virtual observed values are introduced.
5. The method for positioning the underwater control point considering the surface acoustic velocity and the coordinate priori information according to claim 1, wherein in the step (1), the underwater acoustic communication beacon with the built-in pressure sensor is arranged on the submarine control point in a fixed support or an anchoring system mode.
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