CN110109163B - Precise point positioning method with elevation constraint - Google Patents

Precise point positioning method with elevation constraint Download PDF

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CN110109163B
CN110109163B CN201910281682.0A CN201910281682A CN110109163B CN 110109163 B CN110109163 B CN 110109163B CN 201910281682 A CN201910281682 A CN 201910281682A CN 110109163 B CN110109163 B CN 110109163B
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elevation
model
constraint
satellite
receiver
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CN110109163A (en
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张安民
刘荣霞
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Tianjin University
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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
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • 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
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining 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
    • G01S19/42—Determining position

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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 relates to the fields of surveying and mapping science and technology, in particular to a precise point positioning method with elevation constraint, which comprises the following steps of firstly, calculating an elevation constraint condition equation formed by prior elevation information of a receiver; step two, constructing a PPP resolving model with elevation constraint: and (3) connecting an elevation constraint condition equation formed by the prior elevation information of the receiver with the linearized PPP conventional calculation model to obtain the PPP calculation model with elevation constraint. The precise single-point positioning method with the elevation constraint provides elevation constraint data with higher precision for the elevation direction with poor calculation precision, can theoretically enable the elevation calculation result to change near the constraint condition, and can improve the calculation precision in the elevation direction.

Description

Precise point positioning method with elevation constraint
Technical Field
The invention relates to the field of surveying and mapping science and technology, in particular to a precise point positioning method with elevation constraint.
Background
The problem that the plane positioning precision is obviously better than the positioning precision in the elevation direction exists in the dynamic calculation of the precise single-point positioning. The positioning accuracy in the elevation direction can only reach half of that of the plane positioning generally. The characteristic of precise single-point positioning obviously has a great disadvantage for the operation task with high requirement on the precision in the elevation direction.
Disclosure of Invention
In order to effectively solve the problems in the background art, the invention provides a precise point positioning method with elevation constraint, and the positioning precision in the elevation direction is improved.
A precise point positioning method with elevation constraint is characterized in that: the method comprises the following steps: step one, a coordinate system adopted by the GPS in the navigation positioning process is a 1984 world geodetic coordinate system (WGS-84), coordinates of a GPS satellite and a receiver are based on the WGS-84 coordinate system, and point position coordinates (X, Y and Z) on a WGS-84 reference ellipsoid satisfy the following conditions:
Figure BDA0002021870290000011
wherein, a and b areExcept for the long and short half axes of the WGS-84 reference ellipsoid. The height of the receiver erected on the to-be-positioned point relative to the reference ellipsoid is h. The distance between the GPS receiver and the reference ellipsoid is far less than the long half shaft and the short half shaft of the reference ellipsoid, so the position coordinate (X) of the GPS receiver isr,Yr,Zr) It is considered that the following formula is satisfied:
Figure BDA0002021870290000012
formula (2) is respectively paired with X at two sidesr,Yr,ZrCalculating the deviation, and finishing to obtain the following formula:
Figure BDA0002021870290000021
thus, it is possible to obtain:
Figure BDA0002021870290000022
equation (4) is an elevation constraint condition equation formed by the prior elevation information of the receiver;
step two, constructing a PPP resolving model with elevation constraint: and (3) connecting an elevation constraint condition equation formed by the prior elevation information of the receiver with the linearized PPP conventional calculation model to obtain the PPP calculation model with elevation constraint.
Preferably, the PPP calculation model with the elevation constraint in the second step is divided into an epoch-by-epoch model, a satellite-by-satellite model, and an observation-by-observation value model according to the difference of the added positions of the constraint conditions, the epoch-by-epoch model is obtained by adding an elevation constraint value to an observation epoch, when the satellite-by-satellite observation model is used for calculation, an elevation constraint value is added to an effective satellite observed in a certain epoch, and the observation-by-observation value model is obtained by adding the elevation constraint value to each effective carrier phase observation value and each effective pseudorange observation value.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
the precise single-point positioning method with the elevation constraint provides elevation constraint data with higher precision for the elevation direction with poor calculation precision, can theoretically enable the elevation calculation result to change near the constraint condition, and can improve the calculation precision in the elevation direction.
Detailed Description
In order to make the objects and technical solutions of the present invention more clear, the present invention is further described below.
The invention introduces a precision single-point positioning method accompanied with elevation constraint, wherein the elevation constraint is to add prior elevation information with certain precision in the conventional precision single-point positioning calculation process so as to achieve the purposes of constraining calculation results in the elevation direction and improving calculation precision in the elevation direction.
The invention relates to a precise point positioning method with elevation constraint, which consists of two main parts of an elevation constraint basic idea and a PPP calculation model with an elevation beam, and comprises the following specific processes:
step one, an elevation constraint basic idea, namely a PPP method with elevation constraint, which is a method for adding known elevation information of a receiver as a constraint condition and resolving the constraint condition together with an original observation equation. The elevation information as the constraint is data with a certain accuracy acquired by means other than PPP. The specific description is as follows:
the coordinate system adopted by the GPS in the navigation positioning process is a 1984 world geodetic coordinate system (WGS-84), the coordinates of a GPS satellite and a receiver are based on the WGS-84 coordinate system, and point position coordinates (X, Y, Z) on a WGS-84 reference ellipsoid satisfy that:
Figure BDA0002021870290000031
wherein, a and b are respectively the long half shaft and the short half shaft of the WGS-84 reference ellipsoid. The height of the receiver erected on the to-be-positioned point relative to the reference ellipsoid is h. The distance between the GPS receiver and the reference ellipsoid is far less than the long half shaft and the short half shaft of the reference ellipsoid, so the position coordinate (X) of the GPS receiver isr,Yr,Zr) It is considered that the following formula is satisfied:
Figure BDA0002021870290000032
formula (2) is respectively paired with X at two sidesr,Yr,ZrCalculating the deviation, and finishing to obtain the following formula:
Figure BDA0002021870290000033
thus, it is possible to obtain:
Figure BDA0002021870290000034
equation (4) is an elevation constraint equation formed by the elevation information a priori of the receiver.
Step two, constructing a PPP resolving model with elevation constraint: and (3) connecting an elevation constraint condition equation formed by the prior elevation information of the receiver with the linearized PPP conventional calculation model to obtain the PPP calculation model with elevation constraint.
The PPP conventional solution model is as follows:
Figure BDA0002021870290000035
Figure BDA0002021870290000036
wherein the content of the first and second substances,
Figure BDA0002021870290000037
which represents the geometric distance between the satellite s (s ═ 1,2,3, …, n) and the receiver r. r isr(tr) Indicating the moment t at which the receiver receives the signalrPosition vector of receiverAmount rr(tr)＝(Xr,Yr,Zr)；rs(ts) Representing the time t at which the satellite transmits a signalsPosition vector of satellite, rs(ts)＝(Xs,Ys,Zs)；ωeRepresenting the rotational angular velocity of the earth; c represents the speed of light; dtrRepresenting the receiver clock error; dTsRepresenting the satellite clock error;
Figure BDA0002021870290000041
means for representing pseudorange measurement errors caused by tropospheric delay;
Figure BDA0002021870290000042
representing Ionosphere-free Linear Combined (IF-LC) carrier-phase observed pseudoranges;
Figure BDA0002021870290000043
representing the IF-LC pseudoranges;
Figure BDA0002021870290000044
represents IF-LC carrier phase deviation, unit: m;
Figure BDA0002021870290000045
the specific calculation formula of the IF-LC carrier phase correction number including the antenna phase center correction, the solid tide correction, the phase winding correction and the relativistic effect correction of the satellite clock can be seen in an RTKLIB2.4.2 version of instruction manual. EpsilonφAnd εpRespectively representing carrier-phase pseudorange observation errors and pseudorange measurement errors due to other factors.
The formula (5) and the formula (6) are respectively subjected to linearization operation. The unknown parameters in equations (5) and (6) include: position parameters of three directions
Figure BDA0002021870290000046
Velocity parameters in three directions
Figure BDA0002021870290000047
Clock error parameter cdtrTotal delay parameter ZTD in tropospheric zenith directionrThe north component G of the tropospheric gradientN,rAnd east component GE,rAnd carrier phase deviation parameter of zero difference IF-LC
Figure BDA0002021870290000048
The parameters to be estimated are given by the equations (5) and (6)
Figure BDA0002021870290000049
And (3) carrying out linearization, and combining the obtained linear equation with the formula (4) to obtain a PPP linearization model with elevation constraint:
Figure BDA00020218702900000410
wherein the content of the first and second substances,
Figure BDA00020218702900000411
will be provided with
Figure BDA00020218702900000412
Referred to as the design matrix of the PPP linearized model with elevation constraints. Meanwhile, due to the addition of the observed quantity, the covariance matrix of the observed quantity used in the EKF calculation is written as:
R＝diag(RC,Rp,Rh)(9)
wherein R isCA covariance matrix representing errors of the linearly combined observations of the carrier phase; rPA covariance matrix representing a pseudo-range linear combination observed value error; rhA variance matrix representing a residual of the a priori elevation information.
The epoch-by-epoch model means that an elevation constraint value is added to an observation epoch in the resolving process. If the jth observation epoch observes n satellites and the n satellite observation values are all involved in the calculation, HPD,jCan be written as:
HPD，j＝(C1,P1,C2,P2,…,Cn,Pn,hj)T (10)
wherein:
Ci＝(-DE 0 1 DMT I)
Pi＝(-DE 0 1 DMT 0)
hj＝(dh/drr 0 0 0 0)
(i＝1,2,……,n)
meanwhile, the covariance matrix R of the observation model used in the EKF solution process should be written as:
Figure BDA0002021870290000051
wherein the content of the first and second substances,
Figure BDA0002021870290000052
a variance representing an i-th satellite carrier phase observation error;
Figure BDA0002021870290000053
representing the variance of the observed value error of the ith satellite pseudo range; varh,jRepresents the variance of the elevation constraint residual of the jth observation epoch.
When the satellite-by-satellite observation model is calculated, an elevation constraint value is added when an effective satellite is observed in a certain epoch. If n satellites are observed in the jth observation epoch and the observed values of the n satellites are all effective, adding an elevation constraint to each satellite, and HPD,jCan be written as:
HPD，j＝(C1，P1,hj,C2,P2,hj，…，Cn，Pn,hj)T (12)
the covariance matrix R of the observation model should be written as:
Figure BDA0002021870290000054
the observation-by-observation model is used for each effective carrier phase observation and effective pseudo range observationThe measurements are modeled with elevation constraints. If the jth observation epoch observes n satellites, 2n observation values are total, and if all the observation values are valid, HPD,jCan be written as:
HPD，j＝(C1,hj，P1,hj,C2,hj,P2,hj,…,Cn,hj,Pn,hj)T (14)
the covariance matrix R of the observation model should be written as:
Figure BDA0002021870290000061
the foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the invention.

Claims (2)

1. A precise point positioning method with elevation constraint is characterized in that: the method comprises the following steps: step one, a coordinate system adopted by the GPS in the navigation positioning process is a 1984 world geodetic coordinate system WGS-84, coordinates of a GPS satellite and a receiver are based on the WGS-84 coordinate system, and point position coordinates (X, Y and Z) on a WGS-84 reference ellipsoid satisfy the following conditions:
Figure FDA0003300850480000011
wherein a and b are respectively the long and short half axes of WGS-84 reference ellipsoid, the height of receiver erected at the point to be positioned relative to the reference ellipsoid is h, the distance between the GPS receiver and the reference ellipsoid is far less than the long and short half axes of the reference ellipsoid, so the position coordinate (X) of GPS receiver is obtainedr,Yr,Zr) It is considered that the following formula is satisfied:
Figure FDA0003300850480000012
formula (2) is respectively paired with X at two sidesr,Yr,ZrCalculating the deviation, and finishing to obtain the following formula:
Figure FDA0003300850480000013
thus, it is possible to obtain:
Figure FDA0003300850480000014
equation (4) is an elevation constraint condition equation formed by the prior elevation information of the receiver;
step two, constructing a PPP resolving model with elevation constraint: an elevation constraint condition equation formed by the prior elevation information of the receiver is connected with the linearized PPP conventional calculation model to obtain the PPP calculation model with elevation constraint;
the PPP conventional solution model is as follows:
Figure FDA0003300850480000015
Figure FDA0003300850480000016
wherein the content of the first and second substances,
Figure FDA0003300850480000017
denotes the geometric distance, r, between the satellite s (s ═ 1,2,3, …, n) and the receiver rr(tr) Indicating the moment t at which the receiver receives the signalrPosition vector of receiver, rr(tr)＝(Xr,Yr,Zr)；rs(ts) Representing the time t at which the satellite transmits a signalsPosition vector of satellite, rs(ts)＝(Xs,Ys,Zs)；ωeRepresenting the rotational angular velocity of the earth; c represents the speed of light; dtrRepresenting the receiver clock error; dTsRepresenting the satellite clock error;
Figure FDA0003300850480000021
means for representing pseudorange measurement errors caused by tropospheric delay;
Figure FDA0003300850480000022
representing Ionosphere-free Linear Combined (IF-LC) carrier-phase observed pseudoranges;
Figure FDA0003300850480000023
representing the IF-LC pseudoranges;
Figure FDA0003300850480000024
represents IF-LC carrier phase deviation, unit: m;
Figure FDA0003300850480000025
the specific calculation formula of the IF-LC carrier phase correction number including antenna phase center correction, solid tide correction, phase winding correction and relativistic effect correction of satellite clock can be seen in the instruction manual of RTKLIB2.4.2 versionφAnd εpRespectively representing a carrier phase pseudo-range observation error and a pseudo-range measurement error caused by other factors;
respectively carrying out linearization operation on the formula (5) and the formula (6), wherein unknown parameters in the formula (5) and the formula (6) comprise: three-directional position parameter rr TVelocity parameters in three directions
Figure FDA0003300850480000026
Clock error parameter cdtrTotal delay parameter ZTD in tropospheric zenith directionrConvection current ofNorth component G of the layer gradientN,rAnd east component GE,rAnd carrier phase deviation parameter of zero difference IF-LC
Figure FDA0003300850480000027
The parameters to be estimated are given by the equations (5) and (6)
Figure FDA0003300850480000028
And (3) carrying out linearization, and combining the obtained linear equation with the formula (4) to obtain a PPP linearization model with elevation constraint:
Figure FDA0003300850480000029
wherein the content of the first and second substances,
Figure FDA00033008504800000210
will be provided with
Figure FDA00033008504800000211
Referred to as the design matrix of the PPP linearized model with elevation constraints.
2. The method for precise point positioning with elevation constraint according to claim 1, wherein the method comprises the following steps: and secondly, dividing a PPP calculation model with elevation constraints into an epoch-by-epoch model, a satellite-by-satellite model and an observation-by-observation value model according to the difference of the added positions of the constraint conditions, wherein the epoch-by-epoch model is formed by adding an elevation constraint value to an observation epoch, when the satellite-by-satellite observation model is used for calculation, an elevation constraint value is added to an effective satellite observed in a certain epoch, and the observation-by-observation value model is a model formed by adding elevation constraints to each effective carrier phase observation value and each effective pseudo-range observation value.
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