CN114662268A - Improved GNSS network sequential adjustment calculation method - Google Patents

Improved GNSS network sequential adjustment calculation method Download PDF

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CN114662268A
CN114662268A CN202111290536.8A CN202111290536A CN114662268A CN 114662268 A CN114662268 A CN 114662268A CN 202111290536 A CN202111290536 A CN 202111290536A CN 114662268 A CN114662268 A CN 114662268A
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刘洋
赵哲
柳翠明
杨友生
李奇
胡昌华
伍锡锈
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Guangzhou Urban Planning Survey and Design Institute
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Abstract

The invention discloses an improved GNSS network sequential adjustment calculation method, which comprises the steps of establishing a first group of error equations and a second group of error equations of a sequential adjustment model, and performing single adjustment on the first group of error equations to obtain a parameter correction value matrix and a parameter covariance matrix; calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter; calculating a diagonal value according to the parameter covariance matrix to obtain a medium error of an unknown parameter; determining a fuzzy center and a fuzzy amplitude of a public parameter correction value according to a fuzzy theory, and solving to obtain a parameter second correction value according to a constructed constrained adjustment function model; calculating a second adjustment value of the unknown parameter according to the second parameter correction value and the first adjustment value; and calculating to obtain the coordinates of each GNSS network point according to the second adjustment value. The parameter estimation distortion caused by gross error can be effectively weakened, error accumulation is reduced, and the resolving precision is improved.

Description

Improved GNSS network sequential adjustment calculation method
Technical Field
The invention relates to the technical field of satellite positioning, in particular to an improved GNSS network sequential adjustment calculation method, an improved GNSS network sequential adjustment calculation device, a storage medium and terminal equipment.
Background
With the rapid development of Global Navigation Satellite Systems (GNSS), GNSS is utilized to establish various levels of control networks, which are widely applied in various industries, and a GNSS reference station network meeting the requirements of the users is established in various countries, regions and industries. The GNSS is used for establishing the reference station networks of all levels, the relative positioning technology is adopted, namely, the relative position relation between measurement points is determined, the relative position quantity between the points is called as a baseline vector coordinate, an observation network formed by the baseline vector is called as a baseline vector network, and the GNSS network adjustment is the process of performing adjustment calculation by taking the GNSS baseline vector as an observation value to obtain the coordinate of each GNSS network point and performing precision evaluation.
When large-scale GNSS network integral solution is carried out, the prior art generally adopts sequential adjustment estimation to complete the coordinate solution and the precision evaluation of GNSS network points. Dividing the whole GNSS network into a plurality of subnets, independently resolving each subnet to obtain parameter estimation values and covariance matrixes thereof under loose constraint, and then jointly processing each subnet. The sequential adjustment estimation utilizes the adjustment result in the early stage and the observation sample in the current stage to obtain the best solution which is the same as the integral adjustment result.
In the GNSS observation value, due to the influence of an observation signal, a propagation path, a receiver and the like, gross errors inevitably exist in the observation value, but in the prior art, joint processing among sub-networks is completed through normal equation superposition, the essence of the prior art is least square, the prior art has no resistance to the gross errors, and when an observation sample contains the gross errors, an accurate adjustment value cannot be obtained.
Disclosure of Invention
The embodiment of the invention provides an improved GNSS network sequential adjustment calculation method, which can reduce the influence of the observed sample gross error on the subsequent adjustment estimation, reduce the error accumulation effect and output an accurate adjustment value.
The embodiment of the invention provides an improved GNSS network sequential adjustment calculation method, which comprises the following steps:
establishing a first group of error equations and a second group of error equations of a front-stage adjustment model and a rear-stage adjustment model according to the geometrical relationship of a baseline vector among measuring stations by defining coordinate parameters of an early-stage subnet independent measuring station, coordinate parameters of an inter-subnet common measuring station and coordinate parameters of a later-stage subnet independent measuring station in the GNSS network;
performing adjustment on the first set of adjustment error equations separately to obtain a parameter correction value matrix and a parameter covariance matrix;
calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter;
calculating the diagonal value of the parameter variance-covariance matrix to obtain a medium error of an unknown parameter;
substituting the first adjustment value of the public parameter into a second adjustment error equation to calculate a new constant term and define a new observation information correction number as V'2Obtaining a new error equation;
according to a fuzzy theory, determining a fuzzy center and a fuzzy amplitude of a public parameter correction value according to the first adjustment value and the medium error, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
solving the constructed constraint adjustment function model to obtain a second correction value of the parameter;
calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value;
and calculating to obtain the coordinates of each GNSS network point according to the second adjustment value.
Preferably, the first set of error equations is V1＝A11Xa+A12Xb-f1；
The second set of error equations is V2＝B22Xb+B23Y-f2；
Wherein, V1For first observation correction, A11And A12Is a first adjustment model coefficient matrix, V2Number of second observation correction, B22And B23Is a second adjustment model coefficient matrix, XaIs the coordinate parameter, X, of the independent station of the preceding sub-networkbIs the coordinate parameter of the common station among the subnets, Y is the coordinate parameter of the newly added station of the later subnet, f1Is a constant term of the first adjustment error equation,
Figure BDA0003334540950000031
f2is a constant term of the second adjustment error equation,
Figure BDA0003334540950000032
L1and L2Respectively a first adjustment observed value and a second adjustment observed value,
Figure BDA0003334540950000033
and Y0And the approximate value is taken when the unknown parameters are solved for the first adjustment.
Preferably, the parameter correction value matrix is
Figure BDA0003334540950000034
The parameter covariance matrix is
Figure BDA0003334540950000035
Wherein,
Figure BDA0003334540950000036
and
Figure BDA0003334540950000037
as a correction of an unknown parameter, P1In order to obtain a matrix of weights of the observations,
Figure BDA0003334540950000038
is the unit weight variance, and r is the number of redundant observations at the first adjustment. .
Preferably, the first adjustment value is
Figure BDA0003334540950000039
Preferably, the common parameter covariance is
Figure BDA00033345409500000310
Is the posterior unit weight variance.
Preferably, the first adjustment value of the common parameter is substituted into the second adjustment error equation to calculate a new constant term, and a new observation information correction number is defined as V'2Obtaining a new error equation, specifically including:
the first adjustment value is compared
Figure BDA00033345409500000311
Substituting the approximate value of the second adjustment into the second adjustment error equation to obtain a new constant term l2Defining the new observation information correction number as V'2Obtaining a new error equation;
wherein,
Figure BDA00033345409500000312
preferably, the determining a fuzzy center and a fuzzy amplitude of the parameter correction value according to the fuzzy theory by using the first adjustment value of the common parameter and the median error and constructing a adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude specifically includes:
by first adjustment of a common parameter
Figure BDA0003334540950000041
As the fuzzy center of the parameter, the fuzzy center of the parameter correction value
Figure BDA0003334540950000042
And the parameters are taken as approximate values during the second adjustment. Taking the value of 3 times of the medium error as the fuzzy amplitude deltaFront side；
Constructing the adjustment function model according to the membership function, the fuzzy center and the fuzzy amplitude:
Figure BDA0003334540950000043
wherein, x ″)bAnd y' is the correction of the parameter at the second adjustment, μA(x″b) Is x ″)bThe membership function of (a) is selected,
Figure BDA0003334540950000044
further, the solving of the constructed adjustment constraint function model to obtain a second correction value of the parameter specifically includes:
taking the minimum value of the sum of squares of the observed residuals, and x ″)bMembership function mu ofA(x″b) Taking the maximum value to obtain the criterion function
Figure BDA0003334540950000045
Establishing an operator from the fuzzy magnitude
Figure BDA0003334540950000046
Converting the criterion function into a criterion function matrix according to the operator
Figure BDA0003334540950000047
Calculating the deviation of the criterion function matrix and making it equal to 0, calculating to obtain the second correction value of the parameter
Figure BDA0003334540950000048
Wherein τ is any number, 0<τ<1，W＝diag[w1 w2 … wt]，PiIn order to obtain a weighted array of observations,
Figure BDA0003334540950000049
for the observed residuals, n is 1, 2, 3 …, t is 1, 2, 3 …, j is 1, 2xb＝x″b-xb front ofAnd represents the deviation of the parameter correction value from its a priori blur center.
Preferably, the calculating according to the second correction value and the first adjustment value to obtain a second adjustment value of the unknown parameter specifically includes:
correcting the second value
Figure BDA0003334540950000051
And the first adjustment value
Figure BDA0003334540950000052
Substituting the average value into an average value calculation formula to calculate a secondary average value;
the average value is calculated by the formula
Figure BDA0003334540950000053
The invention provides an improved GNSS network sequential adjustment calculation method, which comprises the steps of establishing a first group of error equations and a second group of error equations of an adjustment model of a preceding period and a following period; performing adjustment on the first group of error equations separately to obtain a parameter correction value matrix and a parameter covariance matrix; calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter; calculating the diagonal value of the parameter covariance matrix to obtain a medium error of the public parameter; determining a fuzzy center and a fuzzy amplitude of parameters according to the first adjustment value and the medium error according to a fuzzy theory, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude; solving the constructed constraint adjustment function model to obtain a second correction value of the parameter; calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value; and calculating to obtain the coordinates of each GNSS network point according to the second adjustment value. When the later observation information contains the gross error, the parameter estimation distortion caused by the gross error can be effectively weakened, the error accumulation is reduced, and the resolving precision is improved.
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FIG. 1 is a flow chart illustrating a method for computing sequential adjustment of a GNSS network according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a GNSS network according to an embodiment of the present invention;
fig. 3 is a data schematic diagram of a sequential least squares and constrained sequential algorithm provided by an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without any inventive step, shall fall within the scope of the present invention.
The embodiment of the present invention provides an improved GNSS network sequential adjustment calculation method, which is shown in fig. 1, and is a schematic flow chart of the improved GNSS network sequential adjustment calculation method provided in the embodiment of the present invention, and includes steps S1 to S9:
S1，
establishing a first group of error equations and a second group of error equations of a front-stage adjustment model and a rear-stage adjustment model according to the geometrical relationship of a baseline vector among measuring stations by defining coordinate parameters of an early-stage subnet independent measuring station, coordinate parameters of an inter-subnet common measuring station and coordinate parameters of a later-stage subnet independent measuring station in the GNSS network;
s2, performing single adjustment on the first set of adjustment error equations to obtain a parameter correction value matrix and a parameter covariance matrix;
s3, calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter;
s4, calculating the diagonal value of the parameter covariance matrix to obtain the median error of the public parameter;
s5, substituting the first adjustment value as an approximate value of a second adjustment value into the second group of error equation, calculating a new constant term, and defining a new observation information correction number as V'2Obtaining a new error equation;
s6, determining a fuzzy center and a fuzzy amplitude of the parameters according to the fuzzy theory and the first adjustment value and the median error of the public parameters, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
s7, solving the constructed adjustment constraint function model to obtain a second correction value of the parameter;
s8, calculating a second average value of the unknown parameter according to the second correction value and the first average value;
and S9, calculating and obtaining the coordinates of each GNSS network point according to the second adjustment value.
In this embodiment, when the method is specifically implemented, the obtaining of the common parameter and the independent parameter of the adjustment model in the previous and subsequent stages in the GNSS network sequential adjustment algorithm includes: the coordinate parameters of the independent sites of the subnets at the early stage, the coordinate parameters of the common sites among the subnets and the coordinate parameters of the newly added sites of the subnets at the later stage; constructing a first set of error equations and a second set of error equations of a front-stage adjustment model and a rear-stage adjustment model;
performing single adjustment on the first group of error equations to obtain a parameter correction value matrix and a parameter covariance matrix;
calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter;
calculating the diagonal value of the parameter covariance matrix to obtain the median error of the public parameter;
taking the first average value as a second average valueAnd substituting the approximate value of the equation of balance time into the second group of error equations to calculate a new constant term and define a new observation information correction number as V'2Obtaining a new error equation;
determining a fuzzy center and a fuzzy amplitude of the parameters according to the fuzzy theory and the first adjustment value and the median error of the public parameters, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
solving the constructed adjustment constraint function model to obtain a second correction value of the parameter;
calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value;
and calculating to obtain the coordinates of each GNSS network point according to the second adjustment value.
By improving the sequential adjustment, parameter information obtained by the adjustment in the early stage is contained in the adjustment model in the later stage in a constraint condition mode for resolving, and the prior information obtained in the early stage is utilized to constrain the parameters, so that the error interference resistance of the model is improved.
In yet another embodiment of the present invention, the first set of error equations is V1＝A11Xa+A12Xb-f1；
The second set of error equations is V2＝B22Xb+B23Y-f2；
Wherein, V1For first observation correction, A11And A12Is a first adjustment model coefficient matrix, V2Number of second observation correction, B22And B23Is a second adjustment model coefficient matrix, XaIs the coordinate parameter, X, of the independent station of the previous sub-networkbIs the coordinate parameter of the common station among the subnets, Y is the coordinate parameter of the newly added station of the later subnet, f1Is a constant term of the first adjustment error equation,
Figure BDA0003334540950000081
f2is a second timeThe constant term of the adjustment error equation,
Figure BDA0003334540950000082
L1and L2Respectively a first adjustment observed value and a second adjustment observed value,
Figure BDA0003334540950000083
and Y0And the approximate value is taken when the unknown parameters are solved for the first adjustment.
In the specific implementation of the embodiment, a first set of error equations V is constructed in the sequential adjustment algorithm of the GNSS network1And a second set of error equations V2；
Wherein, V1＝A11Xa+A12Xb-f1，V2＝B22Xb+B23Y-f2，V1For the first observation value correction, A11、A12Is a first adjustment model coefficient array, f1Is its constant term
Figure BDA0003334540950000084
V2Number of second observation correction, B22、B23Is a second order flat difference model coefficient array, f2Is a constant term thereof
Figure BDA0003334540950000085
XaIs coordinate parameter, X, of the independent site of the previous subnetbCoordinate parameters of public stations among the subnetworks, and Y is coordinate parameters of newly added stations of later subnetworks; l is1、L2Is the first and second adjustment observed value, A11、A12、B22、B23Respectively, the coefficient arrays are the coefficient arrays of the linear motion vector,
Figure BDA0003334540950000086
Y0and the approximate value of the parameter which is taken when the parameter participates in the adjustment calculation for the first time.
In yet another embodiment of the present invention, the parameter correction value matrix is
Figure BDA0003334540950000087
The parameter covariance matrix is
Figure BDA0003334540950000088
Wherein,
Figure BDA0003334540950000089
and
Figure BDA00033345409500000810
as a correction of an unknown parameter, P1In order to obtain a weight matrix of the observed values,
Figure BDA00033345409500000811
is the unit weight variance, and r is the number of redundant observations at the first adjustment. .
In the embodiment, the first set of error equations V is applied1Separately adjusting to obtain parameter correction value matrix
Figure BDA0003334540950000091
And obtaining a parameter covariance matrix of
Figure BDA0003334540950000092
In the formula,
Figure BDA0003334540950000093
for parameter correction, P1In order to obtain a weighted array of observations,
Figure BDA0003334540950000094
is the variance of the unit weight, and r is the number of redundant observations at the first adjustment.
In another embodiment of the present invention, the first adjustment value is
Figure BDA0003334540950000095
In the specific implementation of this embodiment, the first quadratic adjustment value of the unknown parameter is calculated according to the parameter correction value matrix
Figure BDA0003334540950000096
Wherein,
Figure BDA0003334540950000097
for the second adjustment of the unknown parameter adjustment value,
Figure BDA0003334540950000098
is the difference value of the first adjustment unknown parameter, x ″)bY' is the number of parameter corrections during the second adjustment,
Figure BDA0003334540950000099
is a weight matrix of the public parameter and is obtained by the first adjustment result. B is22、B23Is a second adjustment model coefficient array, P2As a second observation, a weight matrix2Is a constant term thereof.
In yet another embodiment provided by the present invention, the covariance is
Figure BDA00033345409500000910
From the covariance, the conventional sequential adjustment estimates from the parameters after the early adjustment
Figure BDA00033345409500000911
And their covariance matrix
Figure BDA00033345409500000912
And the integral adjustment is carried out by combining current observation data, and the calculation effect consistent with the integral adjustment can be realized without the early observation value. However, if the prior parameter or the current observation information contains a coarse difference, the distortion of the posterior parameter and the covariance matrix thereof will be caused. In order to weaken the influence of the prior parameter abnormity and the observation gross error on parameter estimation, the method combines a GNSS network to sequential averageAnd improving the difference, incorporating the parameter information obtained by the adjustment in the early stage into the adjustment model in the later stage in a constraint condition mode for resolving, and constraining the parameter by using the prior information obtained in the early stage to improve the error interference resistance of the model.
In another embodiment provided by the present invention, substituting the first adjustment value as an approximate value of the second adjustment value into the second set of error equations to calculate a new constant term, so as to obtain a new error equation, specifically including:
the first adjustment value
Figure BDA0003334540950000101
As an approximate value in the second adjustment, substituting the approximate value into the second adjustment error equation to calculate a new constant term l2Defining the new observation information correction number as V'2Obtaining a new error equation;
wherein,
Figure BDA0003334540950000102
in the particular implementation of the present embodiment,
according to the early adjustment result, the coordinate (namely unknown parameter) of the survey station can be considered to be in a certain space range, and can be vividly expressed as that the estimated value of the parameter in the early period is taken as the center, and delta is taken as the radius range, and the information obtained by the early adjustment of the parameter is constructed into a fuzzy number by combining the fuzzy theory: x belongs to [ X ]0 Δ]， X～μ(X)；
X0For the fuzzy center, the early adjustment estimation of the parameter can be taken, Δ is the fuzzy range, the parameter can be taken as Δ n × σ, and σ is the error in the parameter, which can be obtained from the early adjustment result. In the theory of measurement error, the occasional error follows a normal distribution, and P { -3 σ { (S) }<Δ<Since 3 σ ═ 99.7%, that is, the probability of an error exceeding 3 times the median error is 0.3%, and this is a small probability event, n may be 3. Mu (X) is a membership function, which represents the degree of membership of an element to a fuzzy set, and common membership functions include normal fuzzy numbers, sinusoidal fuzzy numbers and the like.
In another embodiment provided by the present invention, the determining a fuzzy center and a fuzzy amplitude of the parameter according to the fuzzy theory by using the first leveling value and the median error, and constructing a leveling function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude specifically includes:
by first adjustment of a common parameter
Figure BDA0003334540950000103
As the fuzzy center of the parameter, the fuzzy center of the parameter correction value
Figure BDA0003334540950000111
And the parameters are taken as approximate values during the second adjustment. Taking the value of 3 times of the medium error as the fuzzy amplitude deltaFront side；
Constructing the adjustment function model according to the membership function, the fuzzy center and the fuzzy amplitude:
Figure BDA0003334540950000112
wherein, x ″)bAnd y' is the number of parameter corrections in the second adjustment, μA(x″b) Is x ″)bThe membership function of (a) is selected,
Figure BDA0003334540950000113
，V′2for second adjustment of the observed information, B22、B23Is a second adjustment model coefficient array, l2Is a constant term thereof.
A model of the adjustment function is understood to mean a model of the adjustment of a part of the parameters with constraints, mu (x ″)b) The degree of membership of an element to a fuzzy number is expressed as a membership function, and the probability distribution of a parameter can be expressed as a normal fuzzy number for example
Figure BDA0003334540950000114
In another embodiment provided by the present invention, the solving the constructed adjustment constraint function model to obtain the second correction value of the parameter specifically includes:
taking the minimum value of the sum of squares of the observed residuals, and x ″)bMembership function mu ofA(x″b) Taking the maximum value to obtain a criterion function
Figure BDA0003334540950000115
Establishing an operator from the fuzzy magnitude
Figure BDA0003334540950000116
Converting the criterion function into a criterion function matrix according to the operator
Figure BDA0003334540950000117
Calculating the deviation of the criterion function matrix and the deviation is equal to 0, and calculating to obtain a second correction value of the parameter
Figure BDA0003334540950000118
Wherein τ is any number, 0<τ<1，W＝diag[w1 w2 … wt]，PiIn order to obtain a weighted array of observations,
Figure BDA0003334540950000121
for the observed residuals, n is 1, 2, 3 …, t is 1, 2, 3 …, j is 1, 2xb＝x″b-xb front ofAnd represents the deviation of the parameter correction value from its a priori blur center.
In the embodiment, an operator is constructed
Figure BDA0003334540950000122
To avoid the occurrence of deltaFront side0 results in wjIn the case of infinity, the operator can be set to
Figure BDA0003334540950000123
0<τ<1 is a suitably small number.
Taking W as diag1 w2 … wt]；
The criterion function can be written as a criterion function matrix
Figure BDA0003334540950000124
In alignment, the function matrix calculates the partial derivative and makes it equal to zero to calculate the parameter solution;
parameter solution
Figure BDA0003334540950000125
Wherein, x ″)bY' is the number of parameter corrections during the second adjustment, P2As a weighted array of second-order adjustment observations, B22、B23Is a coefficient array of2Is a constant term, xb front ofThe center is blurred for parameter corrections.
In another embodiment of the present invention, the calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value specifically includes:
correcting the second value
Figure BDA0003334540950000126
The first order adjustment value
Figure BDA0003334540950000127
Substituting the average value into an average value calculation formula to calculate a secondary average value;
the average value is calculated by the formula
Figure BDA0003334540950000128
In the specific implementation of this embodiment, the first adjustment value is used
Figure BDA0003334540950000129
And parameter solution
Figure BDA00033345409500001210
Substituting into equation of mean value
Figure BDA0003334540950000131
Calculating the second adjustment value
Figure BDA0003334540950000132
And the calculated secondary adjustment value is used for GNSS reference station network resolving to obtain the coordinates of each GNSS network point.
In another embodiment provided by the present invention, the improved GNSS network sequential adjustment calculation method is applied to a GNSS network, and fig. 2 is a network diagram of the GNSS network provided by the embodiment of the present invention;
two GNSS receivers are adopted for synchronous observation, LC01 and LC03 are receivers with known points, and LC02 and LC04 are used as unknown points for adjustment calculation;
the coordinate theoretical values of four stations of LC01, LC03, LC02 and LC04 are shown in the following table 1:
TABLE 1 theoretical values of coordinates of four stations
Figure BDA0003334540950000133
Three baseline vectors of 1, 2, and 3 were selected for the first phase, and two baseline vectors of 4 and 5 were selected for the second phase. The MATLAB simulation system adds accidental errors to theoretical values of coordinate differences of each base line and adds rough differences to base lines 4 and 5 to form observation base line information as shown in Table 2. And obtaining a unit matrix from the baseline variance matrix in the resolving process.
TABLE 2 Observation of Baseline information
Figure BDA0003334540950000134
Resolving by using sequential least squares and a constrained sequential algorithm respectively, wherein coordinate resolving results and coordinate residuals are shown in tables 3 and 4 respectively;
TABLE 3 unknown Point coordinate calculation results/m
Figure BDA0003334540950000135
TABLE 4 coordinate residuals/m
Figure BDA0003334540950000141
Comparing the coordinate error and the coordinate residual error of the sequential least square and the constrained sequential algorithm respectively as shown in table 5 and fig. 3;
TABLE 5 unknown Point coordinate errors
Figure RE-GDA0003589279770000142
By analyzing the above results, it is possible to obtain: the coordinate residuals of the constraint sequential solution are respectively 0.0215m and 0.0229m, and both are smaller than the solution result of the sequential least square; and the residual errors between the coordinate estimated value obtained by constraining the sequential solution and the theoretical value are both smaller than the sequential least square. The description constraint sequential solution makes full use of parameter prior information obtained by adjustment in the early stage, and has better coarse error interference resistance compared with the traditional least square.
The constraint sequential adjustment model provided by the invention can improve the error interference resistance of the GNSS network and improve the resolution precision of the coordinates of the GNSS network points while ensuring the resolution efficiency. Can be applied to the following fields: resolving a large-scale GNSS reference station network; and the GNSS technology carries out data processing of the control network by stages.
The invention provides an improved GNSS network sequential adjustment calculation method, which comprises the steps of establishing a first group of error equations and a second group of error equations of an adjustment model of a preceding period and a following period; performing adjustment on the first group of error equations separately to obtain a parameter correction value matrix and a parameter covariance matrix; calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter; taking the diagonal value of the parameter covariance matrix to calculate to obtain the medium error of the public parameter; determining a fuzzy center and a fuzzy amplitude of the parameters according to a fuzzy theory and the first adjustment value and the medium error of the public parameters, and constructing an adjustment function restriction model according to the constant term, the fuzzy center and the fuzzy amplitude; solving the constructed adjustment constraint function model to obtain a second correction value of the parameter; calculating a second adjustment value of the unknown parameter according to the second adjustment value and the first adjustment value; and calculating to obtain the coordinates of each GNSS network point according to the second average difference value. When the later observation information contains the gross error, the parameter estimation distortion caused by the gross error can be effectively weakened, the error accumulation is reduced, and the resolving precision is improved.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (9)

1. An improved GNSS network sequential adjustment calculation method is characterized by comprising the following steps:
establishing a first group of error equations and a second group of error equations of a front-stage adjustment model and a rear-stage adjustment model according to the geometrical relationship of a baseline vector among measuring stations by defining coordinate parameters of an early-stage subnet independent measuring station, coordinate parameters of an inter-subnet common measuring station and coordinate parameters of a later-stage subnet independent measuring station in the GNSS network;
performing adjustment on the first group of error equations separately to obtain a parameter correction value matrix and a parameter covariance matrix;
calculating according to the parameter correction value matrix to obtain a first adjustment value of the unknown parameter;
calculating a diagonal value of the parameter covariance matrix to obtain a medium error of an unknown parameter;
substituting the first adjustment value of the public parameter as an approximate value of a second adjustment value into the second adjustment error equation, calculating a new constant term, redefining an observed value correction number, and obtaining a new error equation;
determining a fuzzy center and a fuzzy amplitude of a correction value of a common parameter according to the fuzzy theory and the first adjustment value and the median error, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
solving the constructed adjustment constraint function model to obtain a second correction value of the parameter;
calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value;
and calculating to obtain the coordinates of each GNSS network point according to the second adjustment value.
2. The method for improved GNSS network sequential adjustment computation of claim 1, wherein the first set of adjustment error equations is V1＝A11Xa+A12Xb-f1；
The second set of adjustment error equations is V2＝B22Xb+B23Y-f2；
Wherein, V1For first observation correction, A11And A12Is a first adjustment model coefficient matrix, V2Number of second observation correction, B22And B23Is a second adjustment model coefficient matrix, XaIs the coordinate parameter, X, of the preceding subnet independent stationbFor the coordinate parameter of the common station between the subnets, Y is the coordinate parameter of the newly added station of the later subnet, f1Is a constant term of the first adjustment error equation,
Figure FDA0003334540940000021
f2is a constant term of the second adjustment error equation,
Figure FDA0003334540940000022
L1and L2A first set of observations and a second set of observations,
Figure FDA0003334540940000023
and Y0For the first time for unknown parametersAnd (4) an approximate value taken in the adjustment calculation.
3. The improved GNSS network sequential adjustment calculation method of claim 2, wherein the parameter correction value matrix is
Figure FDA0003334540940000024
The parameter covariance matrix is
Figure FDA0003334540940000025
Wherein,
Figure FDA0003334540940000026
and
Figure FDA0003334540940000027
as a correction of an unknown parameter, P1In order to obtain a matrix of weights of the observations,
Figure FDA0003334540940000028
is the variance of the unit weight, and r is the number of redundant observations at the first adjustment.
4. The method as recited in claim 3, wherein the first adjustment value is the sequential adjustment of the GNSS network
Figure FDA0003334540940000029
5. The method for improved GNSS network sequential adjustment computation of claim 4, wherein the covariance is
Figure FDA00033345409400000210
6. The improved GNSS network sequential adjustment calculation method according to claim 5, wherein the substituting the first adjustment value of the common parameter as an approximate value of a second set of adjustments into the second set of adjustment error equations to calculate a new constant term, redefining an observation value correction, and obtaining a new error equation specifically includes:
the adjustment value of the common parameter in the first adjustment
Figure FDA0003334540940000031
As an approximate value in the second adjustment, substituting the approximate value into the second adjustment error equation, and calculating a new constant term l2Defining a new observation information correction number as V2', obtaining a new error equation;
wherein,
Figure FDA0003334540940000032
7. the improved GNSS network sequential adjustment calculation method according to claim 6, wherein the determining a fuzzy center and a fuzzy magnitude of parameter correction values according to the fuzzy theory with the first adjustment value and the median error, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy magnitude specifically comprises:
by first adjustment of a common parameter
Figure FDA0003334540940000033
As the fuzzy center of the parameter, the fuzzy center of the parameter correction value
Figure FDA0003334540940000034
Figure FDA0003334540940000035
And the parameters are taken as approximate values during the second adjustment. Taking the value of 3 times of the medium error as the fuzzy amplitude deltaFront side；
Constructing the constraint according to membership functions, the fuzzy center and the fuzzy amplitudeAdjustment function model:
Figure FDA0003334540940000036
wherein, x ″)bAnd y' is the correction of the parameter at the second adjustment, μA(x″b) Is x ″)bIs a function of the membership of (a) to (b),
Figure FDA0003334540940000037
8. the improved GNSS network sequential adjustment calculation method according to claim 6, wherein the solving the constructed constrained adjustment function model to obtain a second correction value of the parameter specifically includes:
taking the minimum value of the sum of squares of the observed residuals, x ″)bMembership function μ ofA(x″b) Taking the maximum value to obtain a criterion function
Figure FDA0003334540940000038
Establishing an operator from the fuzzy magnitude
Figure FDA0003334540940000041
Converting the criterion function into a criterion function matrix according to the operator
Figure FDA0003334540940000042
Calculating the deviation of the criterion function matrix and making it equal to 0, calculating to obtain the second correction value of the parameter
Figure FDA0003334540940000043
Wherein τ is any number, 0<τ<1，W＝diag[w1 w2 … wt]，PiIn order to obtain a weighted array of observations,
Figure FDA0003334540940000044
for the observed residuals, n is 1, 2, 3 …, t is 1, 2, 3 …, j is 1, 2xb＝x″b-xb front ofAnd represents the deviation of the parameter correction value from its a priori blur center.
9. The improved GNSS network sequential adjustment calculation method according to claim 8, wherein the second adjustment value of the unknown parameter is calculated according to the second correction value and the first adjustment value, and specifically includes:
correcting the second value
Figure FDA0003334540940000045
And the first adjustment value
Figure FDA0003334540940000046
Substituting the average value into an average value calculation formula to calculate a secondary average value;
the average value is calculated by the formula
Figure FDA0003334540940000047
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