CN114662268B - Improved GNSS network sequential adjustment calculation method - Google Patents

Improved GNSS network sequential adjustment calculation method Download PDF

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CN114662268B
CN114662268B CN202111290536.8A CN202111290536A CN114662268B CN 114662268 B CN114662268 B CN 114662268B CN 202111290536 A CN202111290536 A CN 202111290536A CN 114662268 B CN114662268 B CN 114662268B
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error
value
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CN114662268A (en
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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 adjustment equations and a second group of error adjustment equations of a sequential adjustment model, and performing single adjustment on the first group of error adjustment equations to obtain a parameter correction matrix and a parameter covariance matrix; calculating to obtain a first adjustment value and a first error of the unknown parameters; determining a fuzzy center and a fuzzy amplitude of the correction number of the unknown parameter according to a fuzzy theory, and solving to obtain the correction number of the unknown parameter during the second adjustment according to the constructed adjustment function constraint model; calculating to obtain a second adjustment value of the unknown parameter according to the correction number of the unknown parameter during the second adjustment 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 control networks of various levels, which is widely applied in various 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 a 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 calculation is carried out, the prior art generally adopts sequential adjustment estimation to complete the coordinate calculation 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. And the sequential adjustment estimation utilizes the adjustment result in the early stage and the observation sample in the current stage to obtain the same optimal solution 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 gross error of an observation sample 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 independent measuring station of a front-stage subnet, coordinate parameters of a common measuring station among subnets and coordinate parameters of a newly added measuring station of a rear-stage subnet in a GNSS network;
performing adjustment on the first group of error equations separately to obtain a parameter correction matrix and a parameter covariance matrix;
calculating to obtain a first adjustment value of the unknown parameter according to the parameter correction matrix;
calculating the diagonal of the parameter covariance matrix to obtain a median error of the unknown parameter;
substituting the first-time adjustment value of the unknown parameter into a second set of error equations as an approximate value of a second set of adjustment values to calculate a new constant term, and defining a new second observation value correction number as V' 2 Obtaining a new error equation;
according to a fuzzy theory, taking a difference value of approximate values obtained during the first adjustment value and the second adjustment value as a fuzzy center of a public parameter correction number, taking three times of the medium error as a fuzzy amplitude of the public parameter correction number, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
solving the adjustment function constraint model to obtain a second correction number of the unknown parameter;
calculating a second adjustment value of the unknown parameter according to the second correction number 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 V 1 ＝A 11 X a +A 12 X b -f 1 ；
The second set of error equations is V 2 ＝B 22 X b +B 23 Y-f 2 ；
Wherein, V 1 For first observation correction, A 11 And A 12 Is a first set of error equation coefficient matrix, V 2 Number of second observation correction, B 22 And B 23 Is a second set of error equation coefficient matrix, X a For the coordinate parameter, X, of the preceding sub-network stand-alone station b For the coordinate parameter of the common station between the subnets, Y for the coordinate parameter of the newly added station of the later subnet, f 1 Is a constant term of the first set of error equations,
Figure GDA0003880475400000031
f 2 is a constant term of the second set of error equations, is->
Figure GDA0003880475400000032
L 1 And L 2 Respectively, a first observation and a second observation, in combination>
Figure GDA0003880475400000033
And Y 0 And an approximate value taken when the unknown parameters are solved for the first time.
Preferably, the parameter correction matrix is
Figure GDA0003880475400000034
The parameter covariance matrix is
Figure GDA0003880475400000035
Wherein the content of the first and second substances,
Figure GDA0003880475400000036
and &>
Figure GDA0003880475400000037
Is the correction of said unknown parameter, P 1 For a first observation weight matrix>
Figure GDA0003880475400000038
Is the variance of the unit weight, and r is the number of redundant observations at the first adjustment.
Preferably, the first adjustment value is
Figure GDA0003880475400000039
Preferably, the first adjustment value of the common parameter is substituted into the second set of error equations to calculate a new constant term, and a new second observation value modified number is defined as V' 2 Obtaining a new error equation, specifically including:
the first adjustment value
Figure GDA00038804754000000310
Substituting the approximate value of the second adjustment into the second set of error equations to obtain a new constant term l 2 Defining a new second observation value modified number as V' 2 Obtaining a new error equation;
wherein the content of the first and second substances,
Figure GDA00038804754000000311
preferably, according to a fuzzy theory, the difference between the first adjustment value and the second adjustment value is used as a fuzzy center of a public parameter correction number, the triple error is used as a fuzzy amplitude of the public parameter correction number, and a adjustment function constraint model is constructed according to the constant term, the fuzzy center and the fuzzy amplitude, specifically including:
the adjustment value of the unknown parameter at the first adjustment
Figure GDA0003880475400000041
As the blur center for the parameter, the blur center for the common parameter correction is ≥>
Figure GDA0003880475400000042
Figure GDA0003880475400000043
The approximate value of the unknown parameter is obtained during the second adjustment, and the value which is 3 times of the medium error is taken as the fuzzy amplitude delta Front side ；
Constructing the adjustment function constraint model according to the membership function, the fuzzy center and the fuzzy amplitude:
Figure GDA0003880475400000044
wherein, x ″ b And y' is the correction of the unknown parameter at the second adjustment, μ A (x″ b ) Is x ″) b The membership function of (a) is selected,
Figure GDA0003880475400000045
further, the solving the adjustment function constraint model to obtain a second correction number of the parameter specifically includes:
taking the minimum value of the sum of squares of the observed residuals, and x ″) b Membership function mu of A (x″ b ) Taking the maximum value to obtain a criterion function
Figure GDA0003880475400000046
Establishing an operator according to the fuzzy amplitude
Figure GDA0003880475400000047
Converting the criterion function into a criterion function matrix according to the operator
Figure GDA0003880475400000048
Calculating the partial derivative of the criterion function matrix and making the partial derivative equal to 0, and calculating to obtain a second correction number of the unknown parameter
Figure GDA0003880475400000049
Wherein, 0<τ<1，W＝diag[w 1 w 2 … w t ]，p i Weighted by a second observation, P 2 Is a second observation weight matrix, v i For the second observation residual, n =1,2,3 \ 8230, t =1,2,3 \ 8230, j =1,2 xb ＝x″ b -x b front of And represents the deviation of the parameter correction from its a priori blur center.
Preferably, the calculating the second adjustment value of the unknown parameter according to the second correction number and the first adjustment value specifically includes:
correcting the second number
Figure GDA0003880475400000051
And said first difference value->
Figure GDA0003880475400000052
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 GDA0003880475400000053
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 in a previous period and a later period; performing adjustment on the first group of error equations separately to obtain a parameter correction matrix and a parameter covariance matrix; calculating to obtain a first adjustment value of the unknown parameter according to the parameter correction matrix; calculating the diagonal of the parameter covariance matrix to obtain the median error of the unknown parameters; according to a fuzzy theory, taking the difference value of the approximate values obtained during the first adjustment and the second adjustment as a fuzzy center of a public parameter correction number, taking three times of the medium error as a fuzzy amplitude of the public parameter correction number, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude; solving the adjustment function constraint model to obtain a second correction number of the parameter; calculating a second adjustment value of the unknown parameter according to the second correction number 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 flowchart illustrating an improved method for calculating 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 making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides an improved method for calculating the sequential adjustment of a GNSS network, which is shown in FIG. 1 and is a schematic flow chart of the improved method for calculating the sequential adjustment of the GNSS network provided by the embodiment of the invention, and the method comprises steps S1-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 a geometric relation of base line vectors among measuring stations by defining coordinate parameters of an independent measuring station of a front-stage subnet, coordinate parameters of a common measuring station among subnets and coordinate parameters of a newly added measuring station of a rear-stage subnet in a GNSS network;
s2, performing single adjustment on the first group of error equations to obtain a parameter correction matrix and a parameter covariance matrix;
s3, calculating according to the parameter correction matrix to obtain a first adjustment value of the unknown parameter;
s4, calculating the diagonal of the parameter covariance matrix to obtain the median error of the unknown parameter;
s5, substituting the first-time adjustment value as an approximate value of a second-time adjustment value into the second group of error equations to calculate a new constant term, and defining a new second observation value correction number as V' 2 Obtaining a new error equation;
s6, according to a fuzzy theory, taking the difference value of the approximate values obtained during the first adjustment value and the second adjustment value as a fuzzy center of a public parameter correction number, taking three times of the medium error as a fuzzy amplitude of the public parameter correction number, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
s7, solving the adjustment function constraint model to obtain a second correction number of the parameter;
s8, calculating a second adjustment value of the unknown parameter according to the second correction value and the first adjustment value;
and S9, calculating to obtain 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 measuring stations of the subnet at the early stage, the coordinate parameters of the public measuring stations among the subnets and the coordinate parameters of the newly added measuring stations of the subnet 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 matrix and a parameter covariance matrix;
calculating according to the parameter correction matrix to obtain a first adjustment value of the unknown parameter;
calculating a diagonal line of the parameter covariance matrix to obtain a medium error of the unknown parameter;
substituting the first-time adjustment value as an approximate value of the second-time adjustment value into the second group of error equations to calculate a new constant term, and defining a new second observation value correction number as V' 2 Obtaining a new error equation;
according to a fuzzy theory, taking a difference value of approximate values obtained during the first adjustment value and the second adjustment value as a fuzzy center of a public parameter correction number, taking three times of the medium error as a fuzzy amplitude of the public parameter correction number, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude;
solving the adjustment function constraint model to obtain a second correction number of the parameter;
calculating a second adjustment value of the unknown parameter according to the second correction number 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 brought into 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 V 1 ＝A 11 X a +A 12 X b -f 1 ；
The second set of error equations is V 2 ＝B 22 X b +B 23 Y-f 2 ；
Wherein, V 1 For first observation correction, A 11 And A 12 Is a first set of error equation coefficient matrix, V 2 Number of second observation correction, B 22 And B 23 Is a second set of error equation coefficient matrix, X a Coordinate parameters, X, for said prophase sub-network independent stations b For the coordinate parameter of the common station between the subnets, Y for the coordinate parameter of the newly added station of the later subnet, f 1 Is a constant term of the first set of error equations,
Figure GDA0003880475400000081
f 2 is a constant term of the second set of error equations, is->
Figure GDA0003880475400000082
L 1 And L 2 Respectively, a first observation and a second observation, in combination>
Figure GDA0003880475400000083
And Y 0 And the approximate value is taken when the unknown parameter is 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 network 1 And a second set of error equations V 2 ；
Wherein, V 1 ＝A 11 X a +A 12 X b -f 1 ，V 2 ＝B 22 X b +B 23 Y-f 2 ，V 1 For first observation correction, A 11 、A 12 Is firstSet of error equation coefficient arrays, f 1 Is a constant term thereof
Figure GDA0003880475400000084
V 2 Number of second observation correction, B 22 、B 23 Is a second set of error equation coefficient matrix, f 2 Is its constant term->
Figure GDA0003880475400000085
X a For coordinate parameters, X, of the preceding sub-network independent stations b Coordinate parameters of a common measuring station among the subnetworks, and Y is coordinate parameters of a newly added measuring station of a later subnet; l is 1 、L 2 Is the first and second adjustment observed value, A 11 、A 12 、B 22 、B 23 Respectively is its coefficient array>
Figure GDA0003880475400000086
Y 0 And the approximate value of the unknown parameter taken when the unknown parameter participates in adjustment calculation for the first time.
In another embodiment of the present invention, the parameter correction matrix is
Figure GDA0003880475400000087
The parameter covariance matrix is
Figure GDA0003880475400000088
/>
Wherein the content of the first and second substances,
Figure GDA0003880475400000089
and &>
Figure GDA00038804754000000810
Is the correction of said unknown parameter, P 1 For the first observation the weight matrix is asserted>
Figure GDA00038804754000000811
Is a unit weightThe difference r is the number of redundant observations at the first adjustment.
In the embodiment, the first set of error equations V is applied 1 Separately adjusting to obtain parameter correction matrix
Figure GDA0003880475400000091
And obtaining a parameter covariance matrix of
Figure GDA0003880475400000092
In the formula (I), the compound is shown in the specification,
Figure GDA0003880475400000093
for parameter correction, P 1 For the observation weight matrix, an observation weight matrix is asserted>
Figure GDA0003880475400000094
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 GDA0003880475400000095
In the specific implementation of this embodiment, the first adjustment value of the unknown parameter is calculated according to the parameter correction matrix
Figure GDA0003880475400000096
Wherein the content of the first and second substances,
Figure GDA0003880475400000097
for the first adjustment of the value of the unknown parameter, is adjusted>
Figure GDA0003880475400000098
Is a correction of the parameter at the first adjustment, is determined>
Figure GDA0003880475400000099
For the unknown parameterThe approximate value taken during the first adjustment calculation.
Conventional sequential adjustment based on post-adjustment parameter estimation
Figure GDA00038804754000000910
And its covariance matrix>
Figure GDA00038804754000000911
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 gross error, 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 improve the sequential adjustment, parameter information obtained by the adjustment in the early stage is brought into a later adjustment model in a constraint condition mode for resolving, the prior information obtained in the early stage is utilized to constrain the parameters, and the error interference resistance of the model is improved.
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 is compared
Figure GDA0003880475400000101
As an approximate value in the second adjustment, substituting the approximate value into the second set of error equations to calculate a new constant term l 2 And a new second observation value correction number is defined as V' 2 Obtaining a new error equation;
wherein the content of the first and second substances,
Figure GDA0003880475400000102
in another embodiment provided by the present invention, according to a fuzzy theory, a difference value between the first adjustment value and the second adjustment value is used as a fuzzy center of a common parameter correction number, three times of the medium error is used as a fuzzy amplitude of the common parameter correction number, and a adjustment function constraint model is constructed according to the constant term, the fuzzy center, and the fuzzy amplitude, specifically including:
with the first adjustment of said unknown parameter
Figure GDA0003880475400000103
As the blur center of the common parameter correction, the blur center of the common parameter correction->
Figure GDA0003880475400000104
Figure GDA0003880475400000105
The approximate value of the unknown parameter is obtained during the second adjustment, and the value which is 3 times of the medium error is taken as the fuzzy amplitude delta Front side ；
Constructing the adjustment function constraint model according to the membership function, the fuzzy center and the fuzzy amplitude:
Figure GDA0003880475400000106
wherein, x ″ b And y' is the correction of the unknown parameter at the second adjustment, μ A (x″ b ) Is x ″) b Is a function of the membership of (a) to (b),
Figure GDA0003880475400000107
V′ 2 number of corrections for new second observation, B 22 、B 23 Is a second set of error equation coefficient matrix, l 2 Is 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 in the case of a normal fuzzy number, the probability distribution of a parameter can be expressed as
Figure GDA0003880475400000108
In another embodiment provided by the present invention, the solving the adjustment function constraint model to obtain a second correction of the parameter specifically includes:
taking the minimum value of the sum of squares of the observed residuals, and x ″) b Membership function mu of A (x″ b ) Taking the maximum value to obtain a criterion function
Figure GDA0003880475400000111
Establishing an operator according to the fuzzy amplitude
Figure GDA0003880475400000112
Converting the criterion function into a criterion function matrix according to the operator
Figure GDA0003880475400000113
Calculating the partial derivative of the criterion function matrix, wherein the partial derivative is equal to 0, and calculating to obtain a second correction number of the unknown parameter
Figure GDA0003880475400000114
Wherein, 0<τ<1，W＝diag[w 1 w 2 … w t ]，P i Is the weight of the second observed value, P 2 Is a second observation weight matrix, v i For the second observation residual, n =1,2,3 \ 8230, t =1,2,3 \ 8230, j =1,2 xb ＝x″ b -x b front of And represents the deviation of the parameter correction from its a priori blur center.
In the embodiment, an operator is constructed
Figure GDA0003880475400000115
To avoid the occurrence of delta Front side =0 results in w j In the case of infinity, an operator can be set to +>
Figure GDA0003880475400000116
Is suitable forWhen it is a small number. />
Take W = diag [ W ] 1 w 2 … w t ]；
The criterion function can be written as a criterion function matrix
Figure GDA0003880475400000117
If the alignment is carried out, the function matrix is used for solving the partial derivative and the partial derivative is equal to zero, so that a parameter solution can be solved;
parameter solution
Figure GDA0003880475400000118
Wherein, x ″) b Y' is the correction of the unknown parameter at the second adjustment, P 2 As a second adjustment observation weight matrix, B 22 、B 23 Is a coefficient matrix of 2 Is a constant term, x b front of The number is modified for unknown parameters to blur the center.
In another embodiment provided by the present invention, the calculating, according to the second correction number and the first adjustment value, a second adjustment value of the unknown parameter is obtained, specifically:
correcting the second number
Figure GDA0003880475400000121
The first difference of level->
Figure GDA0003880475400000122
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 GDA0003880475400000123
In the specific implementation of this embodiment, the first adjustment value is used
Figure GDA0003880475400000124
And parameter solution
Figure GDA0003880475400000125
Substituting into the equation of the difference value>
Figure GDA0003880475400000126
Calculating a second difference value->
Figure GDA0003880475400000127
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 is shown in fig. 2, which is a network diagram of a GNSS network provided by the embodiment of the present invention;
two GNSS receivers are adopted for synchronous observation, LC01 and LC03 are receivers of known points, and LC02 and LC04 are regarded as unknown points for adjustment calculation;
the theoretical coordinate values of the four stations of LC01, LC03, LC02 and LC04 are shown in Table 1:
TABLE 1 theoretical values of coordinates of four stations
Figure GDA0003880475400000128
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 GDA0003880475400000131
Resolving by using sequential least squares and a constrained sequential algorithm respectively, wherein a coordinate resolving result and a coordinate residual are shown in a table 3 and a table 4 respectively;
TABLE 3 unknown Point coordinate calculation result/m
Figure GDA0003880475400000132
TABLE 4 coordinate residuals/m
Figure GDA0003880475400000133
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 error
Figure GDA0003880475400000134
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 of the coordinate estimation value obtained by the constrained 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 anti-error interference performance of the GNSS network and improve the resolving precision of the GNSS network point coordinates while ensuring the resolving 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 in a previous period and a later period; performing adjustment on the first group of error equations separately to obtain a parameter correction matrix and a parameter covariance matrix; calculating to obtain a first adjustment value of the unknown parameter according to the parameter correction matrix; calculating a diagonal line of the parameter covariance matrix to obtain a median error of the unknown parameter; according to a fuzzy theory, taking a difference value of approximate values obtained during the first adjustment value and the second adjustment value as a fuzzy center of a public parameter correction number, taking three times of the medium error as a fuzzy amplitude of the public parameter correction number, and constructing an adjustment function constraint model according to the constant term, the fuzzy center and the fuzzy amplitude; solving the adjustment function constraint model to obtain a second correction number of the parameter; calculating a second adjustment value of the unknown parameter according to the second correction number 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-stage 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 calculation 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 (1)

1. An improved GNSS network sequential adjustment calculation method is characterized by comprising the following steps:
establishing a first group of error adjustment equations and a second group of error adjustment equations of a front and rear adjustment model according to the geometric relationship of a baseline vector among measurement stations by defining coordinate parameters of an independent measurement station of a front-stage subnet, coordinate parameters of a common measurement station among subnets and coordinate parameters of a newly added measurement station of a rear-stage subnet in the GNSS network;
performing adjustment on the first group of error adjustment equations separately to obtain a parameter correction matrix and a parameter covariance matrix;
calculating according to the parameter correction matrix to obtain a first average value of the coordinate parameters of the independent stations of the previous sub-networks and the coordinate parameters of the common stations among the sub-networks;
calculating the diagonal of the parameter covariance matrix to obtain a median error of the coordinate parameters of the independent measuring stations of the previous sub-networks and the coordinate parameters of the common measuring stations among the sub-networks;
substituting the first adjustment value of the coordinate parameters of the public measuring station between the subnets as an approximate value of the second adjustment value into the second group of error adjustment equations, calculating a new constant item, redefining an observed value correction number, and obtaining a new error adjustment equation;
determining a fuzzy center and a fuzzy amplitude of a correction number of coordinate parameters of the common observation station between the subnets according to a fuzzy theory and the first adjustment value and the medium error, and constructing an adjustment function constraint model according to the new constant term, the fuzzy center and the fuzzy amplitude;
solving the adjustment function constraint model to obtain the correction numbers of the coordinate parameters of the public measuring station between the subnets during the second adjustment and the coordinate parameters of the newly added measuring station of the later subnet;
calculating according to the correction number of the coordinate parameters of the public measuring station between the subnets during the second adjustment and the coordinate parameters of the newly increased measuring station of the later subnet and the first adjustment value to obtain a second adjustment value of the coordinate parameters of the public measuring station between the subnets and the coordinate parameters of the newly increased measuring station of the later subnet;
calculating to obtain the coordinates of each GNSS network point according to the second adjustment value;
the first set of error adjustment equations is V 1 ＝A 11 X a +A 12 X b -f 1 ；
The second set of error adjustment equations is V 2 ＝B 22 X b +B 23 Y-f 2 ；
Wherein, V 1 For the first set of observations, A 11 And A 12 Is a first set of error adjustment equation coefficient matrix, V 2 Correcting the second set of observations, B 22 And B 23 Is a second set of error adjustment equation coefficient matrix, X a For the coordinate parameter, X, of the preceding sub-network stand-alone station b For the coordinate parameter of the common station between the subnets, Y is the coordinate parameter of the newly added station of the later subnet, f 1 As constant terms of the first set of error adjustment equations,
Figure FDA0004064717190000021
f 2 as constant terms of the second set of error adjustment equations,
Figure FDA0004064717190000022
L 1 and L 2 Respectively a first and a second set of observations, <' > based on>
Figure FDA0004064717190000023
Are each X a And X b Approximate values taken during the first adjustment;
the parameter correction matrix is
Figure FDA0004064717190000024
The parameter covariance matrix is
Figure FDA0004064717190000025
Wherein the content of the first and second substances,
Figure FDA0004064717190000026
and &>
Figure FDA0004064717190000027
Are each X a And X b Number of corrections, P 1 For the first observation weight matrix, <' > based on the evaluation value>
Figure FDA0004064717190000028
Is the unit weight variance, and r is the number of redundant observations in the first adjustment; the first difference of level is->
Figure FDA0004064717190000029
Substituting the first adjustment value of the coordinate parameters of the public measuring station between the subnets as an approximate value of the second adjustment value into the second group of error adjustment equations, calculating a new constant term, redefining an observed value correction number, and obtaining a new error adjustment equation, wherein the method specifically comprises the following steps:
the adjustment value of the coordinate parameters of the common measuring station among the sub-networks in the first adjustment value is obtained
Figure FDA00040647171900000210
As second adjustment time X b Is substituted into the second set of error adjustment equations to calculate a new constant term l 2 Defining a new second set of observation value correction numbers as V' 2 Obtaining a new error adjustment equation;
wherein the content of the first and second substances,
Figure FDA00040647171900000211
according to a fuzzy theory, determining a fuzzy center and a fuzzy amplitude of a correction number of coordinate parameters of a common survey station between subnets according to the first adjustment value and the medium error, and constructing an adjustment function constraint model according to the new constant term, the fuzzy center and the fuzzy amplitude, specifically comprising:
in the first adjustment
Figure FDA0004064717190000031
As X b Fuzzy center of (2), then X b Positive fuzzy center->
Figure FDA0004064717190000032
Taking the value of 3 times of the medium error as the fuzzy amplitude delta Front side ；
According to membership function, fuzzy center x b front of And the blur amplitude Δ Front part Constructing the adjustment function constraint model:
Figure FDA0004064717190000033
wherein, x' b And y' are each X b And the number of corrections of Y,. Mu. A (x″ b ) Is x ″) b The membership function of (a) is selected,
Figure FDA0004064717190000034
the solving of the adjustment function constraint model to obtain the correction numbers of the coordinate parameters of the common measuring station between the subnets during the second adjustment and the coordinate parameters of the newly added measuring station of the later subnet specifically comprises:
calculating the second adjustment time X b And the number of corrections of Y
Figure FDA0004064717190000035
Wherein, W = diag [ W [ ] 1 w 2 … w t ]，P 2 Is a second set of observation weight matrices;
the second adjustment value of the coordinate parameter of the public measuring station between the sub-networks and the coordinate parameter of the newly increased measuring station of the later sub-network is obtained by calculation according to the correction number of the coordinate parameter of the public measuring station between the sub-networks and the coordinate parameter of the newly increased measuring station of the later sub-network during the second adjustment and the first adjustment value, and the method specifically comprises the following steps:
adjusting time X for the second time b Substituting the corrected number of Y and the first adjustment value into an adjustment value calculation formula to calculate a second adjustment value;
the average value is calculated by the formula
Figure FDA0004064717190000036
/>
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