CN116068598A - Wide-area distributed non-differential non-combination PPP-RTK positioning method - Google Patents

Wide-area distributed non-differential non-combination PPP-RTK positioning method Download PDF

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CN116068598A
CN116068598A CN202310357088.1A CN202310357088A CN116068598A CN 116068598 A CN116068598 A CN 116068598A CN 202310357088 A CN202310357088 A CN 202310357088A CN 116068598 A CN116068598 A CN 116068598A
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satellite
products
receiver
subnet
ppp
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CN116068598B (en
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张宝成
查九平
侯鹏宇
刘腾
潭冰峰
柴艳菊
张啸
刘洋
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Institute of Precision Measurement Science and Technology Innovation of CAS
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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
    • G01S19/38—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
    • G01S19/40—Correcting position, velocity or attitude
    • G01S19/41—Differential correction, e.g. DGPS [differential GPS]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

A wide area distributed non-differential non-combining PPP-RTK positioning method, the wide area distributed non-differential non-combining PPP-RTK positioning method comprising; dividing the whole network into a plurality of sub-networks, and ensuring that all receivers in each sub-network have the same common-view satellite; estimating satellite products and atmospheric correction products of the sub-networks by using GNSS data of the co-view satellites of the sub-networks; step three, according to the satellite products and the atmosphere correction products of the estimated subnetwork, adopting an S transformation theory to perform reference unification to obtain the satellite products and the atmosphere correction products with the consistent whole network reference; and fourthly, interpolating an atmospheric correction product consistent with the whole network standard to obtain the distance error between the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, and obtaining the atmospheric delay correction data. The design improves the accuracy of the observation value of the user side, and further improves the real-time positioning accuracy of the user.

Description

Wide-area distributed non-differential non-combination PPP-RTK positioning method
Technical Field
The invention relates to an improvement of a wide area PPP-RTK positioning technology, belongs to the field of GNSS precise positioning, and particularly relates to a wide area distributed non-differential non-combination PPP-RTK positioning method.
Background
PPP-RTK high-precision continuous positioning based on non-differential non-combination relies on the rapid generation of continuous high-precision satellite precision products and atmospheric correction products by using ground reference network data. Along with the increasing of the service range of the reference network, the number and the density of tracking stations are continuously increased, and the existing centralized reference network data processing technology processes all tracking station data in the network together, so that the problems of complex model, low calculation efficiency, prolonged product generation and the like exist, and the real-time high-precision positioning requirement of the wide-area PPP-RTK cannot be met.
The Chinese patent application with the application number of CN201910269641.X and the application date of 2019, 4 and 3 discloses a high-precision positioning method and a system based on a PPP algorithm, which can realize centimeter-level high-precision positioning by utilizing a double-frequency GNSS carrier phase and a pseudo-range observation value and combining a GNSS precise orbit and a clock error only by means of a mobile terminal without depending on a ground position base station. The system of the invention comprises: the system comprises a GNSS dual-frequency signal receiving module, a wireless wide area network module, a low-orbit navigation enhancement satellite signal receiving module and a microprocessor. The positioning method adopts GNSS dual-frequency observation data and GNSS precise correction to obtain original pseudo-range and carrier phase observation data, utilizes an LAMBDA algorithm to fix integer ambiguity, and finally adopts an extended Kalman filter equation to recursively observe a linear equation for ionosphere-removing combination observation, and obtains position information after convergence.
The disclosure of this background section is only intended to increase the understanding of the general background of the present patent application and should not be taken as an admission or any form of suggestion that this information forms the prior art already known to a person of ordinary skill in the art.
Disclosure of Invention
The invention aims to solve the problem of real-time high-precision positioning in the prior art and provides a wide-area distributed non-differential non-combination PPP-RTK positioning method capable of realizing real-time high-precision positioning.
In order to achieve the above object, the technical solution of the present invention is: a wide area distributed non-differential non-combining PPP-RTK positioning method, the wide area distributed non-differential non-combining PPP-RTK positioning method comprising:
dividing the whole network into a plurality of sub-networks, and ensuring that all receivers in each sub-network have the same common-view satellite;
estimating satellite products and atmospheric correction products of the sub-networks by using GNSS data of the co-view satellites of the sub-networks;
step three, according to the satellite products and the atmosphere correction products of the estimated subnetwork, adopting an S transformation theory to perform reference unification to obtain the satellite products and the atmosphere correction products with the consistent whole network reference;
interpolating an atmospheric correction product consistent with the whole network reference to obtain the distance error between the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, and obtaining the atmospheric delay correction data;
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized.
The whole network is as follows: assuming that the whole network has
Figure SMS_1
Synchronous observation of the individual reference stations>
Figure SMS_2
GNSS satellites with observation frequency +.>
Figure SMS_3
The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
Figure SMS_4
；
wherein the method comprises the steps of
Figure SMS_12
For the receiver number>
Figure SMS_7
Is satellite number>
Figure SMS_9
For frequency +.>
Figure SMS_16
Respectively observing values of pseudo range and phase; />
Figure SMS_19
And->
Figure SMS_18
Receiver clock error and satellite clock error respectively; />
Figure SMS_21
Delay for zenith troposphere; />
Figure SMS_13
Coefficients that are ionospheric bias delays; />
Figure SMS_15
A bias ionosphere delay for a first frequency point; />
Figure SMS_5
For frequency->
Figure SMS_11
A corresponding carrier phase wavelength; />
Figure SMS_8
Is integer ambiguity; />
Figure SMS_20
And->
Figure SMS_14
Receiver code bias and receiver differential code bias, respectively,/->
Figure SMS_17
For satellite code bias, +.>
Figure SMS_6
And->
Figure SMS_10
The receiver phase offset and the satellite phase offset, respectively.
The whole network is divided into a plurality of subnets specifically comprises: dividing the whole net into
Figure SMS_22
Subnetwork, th->
Figure SMS_23
The subnetwork has
Figure SMS_24
The station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
Figure SMS_25
；
the specific expression forms of various products are as follows:
Figure SMS_26
；
Figure SMS_27
representing subnet->
Figure SMS_28
Is->
Figure SMS_29
Number receiver, the satellite products obtained by each sub-network and the standard of the atmospheric correction product selection are differentFor example, the reference ambiguities selected in sub-networks 1 and 2 for satellite phase bias estimation are +.>
Figure SMS_30
And
Figure SMS_31
the formula for the user to perform ambiguity resolution in these 2 subnets is:
Figure SMS_32
。
the GNSS data using the common view satellites of each sub-network specifically comprises:
the satellite processor outputs signals from the transmitting antenna and the receiving antenna, and hardware delay exists between different frequencies and even between different codes and phases of the same frequency; because the hardware delay of all satellites at the receiver is consistent, the satellites are classified as the clock error of the receiver; the hardware delays of the satellite terminals are different in satellite sizes, the generated code delays are called satellite code deviations, the phase delays are called satellite phase deviations, and the satellite terminal code deviations are larger than the phase deviation in magnitude;
the atmospheric correction product utilizes GNSS observations of each subnet tracking station to estimate an atmospheric delay error, including tropospheric delay and ionospheric delay errors.
Satellite code/phase bias observed by a plurality of ground tracking stations (GNSS) can be regarded as code/phase distance error, and satellite clock difference is time bias multiplied by light velocity, namely distance error.
The unification of the benchmarks of the subnet satellite products by adopting the S transformation theory comprises any one or any combination of the following:
a satellite clock error reference unifying step, a satellite code deviation reference unifying step and a phase deviation reference unifying step.
The step of unifying satellite clock error references is as follows: the satellite clock difference obtained by each subnet is used as pseudo-observation, and the satellite clock difference and the receiver clock difference are parameterized again, and the formula is as follows:
Figure SMS_33
；
wherein the method comprises the steps of
Figure SMS_34
Where rank deficiency is 1, assume selection
Figure SMS_35
As a benchmark, the above formula is re-written as:
Figure SMS_36
Figure SMS_37
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-network
Figure SMS_38
As a benchmark, the benchmark unified model is:
Figure SMS_39
；
Figure SMS_40
；
the phase deviation reference unifying step refers to: the pseudo observation equation formula formed by the phase deviation obtained by each sub-network is as follows:
Figure SMS_41
；
rank deficiency of
Figure SMS_42
Select->
Figure SMS_43
As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
Figure SMS_44
；
wherein the method comprises the steps of
Figure SMS_45
At this time->
Figure SMS_46
And ambiguity->
Figure SMS_47
Linear correlation, introduce->
Figure SMS_48
Based on the equation:
Figure SMS_49
；
wherein the method comprises the steps of
Figure SMS_50
At this point the receiver phase deviation +.>
Figure SMS_51
And single difference ambiguity->
Figure SMS_52
Still related, rank deficient->
Figure SMS_53
Select->
Figure SMS_54
As a benchmark, the full rank formula is:
Figure SMS_55
；/>
Figure SMS_56
。
the satellite clock difference obtained by each subnet is used as pseudo observation, and the re-parameterized satellite clock difference and the receiver clock difference are specifically as follows: assuming that the reference receiver clock of the first subnet is used as a reference, the satellite clock of other subnets is simultaneously subtracted from the reference receiver clock of the first subnet to obtain a pseudo-observed value, and the receiver clock of each subnet is actually simultaneously subtracted from the clock of the reference receiver of the first subnet, wherein the satellite clock and the receiver clock are new satellite clock and receiver clock both comprising the reference receiver clock of the first subnet.
The satellite clock error reference unification, the satellite code deviation reference unification and the phase deviation reference unification and the related covariance matrix are solved together to obtain a satellite product under the unified reference
Figure SMS_57
And the covariance matrix is +.>
Figure SMS_58
；
The obtained satellite product under unified reference
Figure SMS_59
And the covariance matrix thereof>
Figure SMS_60
Substituting the calculated satellite products and atmospheric products of each subnet and the covariance matrix thereof to calculate the atmospheric correction product formulas of each subnet as follows:
Figure SMS_61
。
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized: substituting the calculated atmospheric products into each subnet, and releasing the atmospheric products together with satellite products to users in the subnet for PPP-RTK positioning, wherein the user positioning formula is as follows:
Figure SMS_62
；
wherein:
Figure SMS_63
and->
Figure SMS_64
For the tropospheric delay and ionospheric delay products interpolated into the subnetwork p.
Compared with the prior art, the invention has the beneficial effects that:
1. in the wide area distributed non-differential non-combination PPP-RTK positioning method, the atmospheric correction product is estimated to obtain the distance errors of the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, when a user positions in a network, the ionosphere delay and the troposphere delay can be interpolated to obtain troposphere delay and ionosphere delay data of the user receiver and the satellite in the connection direction, and the user observes and corrects the atmospheric errors, so that the accuracy of an observation value is improved, the positioning accuracy is further improved, and the positioning can be performed in real time. Therefore, the design can be used for positioning in real time, and the positioning accuracy is improved.
2. In the wide area distributed non-differential non-combination PPP-RTK positioning method, the design adopts non-differential non-combination to perform PPP-RTK positioning, which is favorable for the expansion and fusion of multi-frequency multi-mode GNSS observation information, and the distributed PPP-RTK positioning method is consistent with the positioning precision and continuity of a centralized PPP-RTK, so that the calculation efficiency is improved by 50%, and the user is ensured to realize the real-time high-precision continuous positioning of the wide area PPP-RTK. Therefore, the design is favorable for expansion and fusion of multi-frequency multi-mode GNSS observation information and can be used for continuous positioning.
3. In the wide area distributed non-differential non-combination PPP-RTK positioning method, the same processing mode is adopted for both the calculation of the server-side product and the utilization of the user-side product, so that the self-consistency is better, and the requirement of a service object on the precision is higher. Therefore, the design has better self-consistency and higher precision.
Drawings
Fig. 1 is a schematic diagram of the distribution of tracking stations and the division of subnets of the present invention.
FIG. 2 is a time-consuming schematic of a different product generation scheme of the present invention.
Fig. 3 is a graph of an alignment of satellite clock, satellite phase bias and ionospheric delay products generated by four schemes of the present invention.
Fig. 4 is a schematic diagram of the initial convergence time and positioning accuracy of two PPP-RTKs for all users of the present invention.
In the figure: the english letters in fig. 1 are each tracking station name, and the english letters in the horizontal axis portion in fig. 4 are each tracking station name.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings and detailed description.
Referring to fig. 1 to 4, a wide area distributed non-differential non-combining PPP-RTK positioning method includes:
dividing the whole network into a plurality of sub-networks, and ensuring that all receivers in each sub-network have the same common-view satellite;
estimating satellite products and atmospheric correction products of the sub-networks by using GNSS data of the co-view satellites of the sub-networks;
step three, according to the satellite products and the atmosphere correction products of the estimated subnetwork, adopting an S transformation theory to perform reference unification to obtain the satellite products and the atmosphere correction products with the consistent whole network reference;
interpolating an atmospheric correction product consistent with the whole network reference to obtain the distance error between the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, and obtaining the atmospheric delay correction data;
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized.
The whole network is as follows: assuming that the whole network has
Figure SMS_65
Synchronous observation of the individual reference stations>
Figure SMS_66
GNSS satellites with observation frequency +.>
Figure SMS_67
The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
Figure SMS_68
；
wherein the method comprises the steps of
Figure SMS_79
For the receiver number>
Figure SMS_69
Is satellite number>
Figure SMS_76
For frequency +.>
Figure SMS_78
Respectively observing values of pseudo range and phase; />
Figure SMS_81
And->
Figure SMS_83
Receiver clock error and satellite clock error respectively; />
Figure SMS_84
Delay for zenith troposphere; />
Figure SMS_82
Coefficients that are ionospheric bias delays; />
Figure SMS_85
A bias ionosphere delay for a first frequency point; />
Figure SMS_72
For frequency->
Figure SMS_75
Corresponding carrier waveA phase wavelength; />
Figure SMS_71
Is integer ambiguity; />
Figure SMS_73
And->
Figure SMS_77
Receiver code bias and receiver differential code bias, respectively,/->
Figure SMS_80
For satellite code bias, +.>
Figure SMS_70
And->
Figure SMS_74
The receiver phase offset and the satellite phase offset, respectively.
The whole network is divided into a plurality of subnets specifically comprises: dividing the whole net into
Figure SMS_86
Subnetwork, th->
Figure SMS_87
The subnetwork has
Figure SMS_88
The station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
Figure SMS_89
；
the specific expression forms of various products are as follows:
Figure SMS_90
；
Figure SMS_91
representing subnet->
Figure SMS_92
Is->
Figure SMS_93
The satellite receiver, the satellite product obtained by each sub-network and the reference of the atmospheric correction product selection are different, for example, the satellite phase deviation estimation has the reference ambiguity of +.>
Figure SMS_94
And
Figure SMS_95
the formula for the user to perform ambiguity resolution in these 2 subnets is:
Figure SMS_96
。
the GNSS data using the common view satellites of each sub-network specifically comprises:
the satellite processor outputs signals from the transmitting antenna and the receiving antenna, and hardware delay exists between different frequencies and even between different codes and phases of the same frequency; because the hardware delay of all satellites at the receiver is consistent, the satellites are classified as the clock error of the receiver; the hardware delays of the satellite terminals are different in satellite sizes, the generated code delays are called satellite code deviations, the phase delays are called satellite phase deviations, and the satellite terminal code deviations are larger than the phase deviation in magnitude;
the atmospheric correction product utilizes GNSS observations of each subnet tracking station to estimate an atmospheric delay error, including tropospheric delay and ionospheric delay errors.
Satellite code/phase bias observed by a plurality of ground tracking stations (GNSS) can be regarded as code/phase distance error, and satellite clock difference is time bias multiplied by light velocity, namely distance error.
The unification of the benchmarks of the subnet satellite products by adopting the S transformation theory comprises any one or any combination of the following:
a satellite clock error reference unifying step, a satellite code deviation reference unifying step and a phase deviation reference unifying step.
The step of unifying satellite clock error references is as follows: the satellite clock difference obtained by each subnet is used as pseudo-observation, and the satellite clock difference and the receiver clock difference are parameterized again, and the formula is as follows:
Figure SMS_97
；
wherein the method comprises the steps of
Figure SMS_98
Wherein the rank deficiency is 1, assuming selection +.>
Figure SMS_99
As a benchmark, the above formula is re-written as:
Figure SMS_100
Figure SMS_101
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-network
Figure SMS_102
As a benchmark, the benchmark unified model is:
Figure SMS_103
；
Figure SMS_104
；
the phase deviation reference unifying step refers to: the pseudo observation equation formula formed by the phase deviation obtained by each sub-network is as follows:
Figure SMS_105
；
rank deficiency of
Figure SMS_106
Select->
Figure SMS_107
As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
Figure SMS_108
；
wherein the method comprises the steps of
Figure SMS_109
At this time->
Figure SMS_110
And ambiguity->
Figure SMS_111
Linear correlation, introduce->
Figure SMS_112
Based on the equation:
Figure SMS_113
；
wherein the method comprises the steps of
Figure SMS_114
At this point the receiver phase deviation +.>
Figure SMS_115
And single difference ambiguity->
Figure SMS_116
Still related, rank deficient->
Figure SMS_117
Select->
Figure SMS_118
As a benchmark, the full rank formula is:
Figure SMS_119
；
Figure SMS_120
。
the satellite clock difference obtained by each subnet is used as pseudo observation, and the re-parameterized satellite clock difference and the receiver clock difference are specifically as follows: assuming that the reference receiver clock of the first subnet is used as a reference, the satellite clock of other subnets is simultaneously subtracted from the reference receiver clock of the first subnet to obtain a pseudo-observed value, and the receiver clock of each subnet is actually simultaneously subtracted from the clock of the reference receiver of the first subnet, wherein the satellite clock and the receiver clock are new satellite clock and receiver clock both comprising the reference receiver clock of the first subnet.
The satellite clock error reference unification, the satellite code deviation reference unification and the phase deviation reference unification and the related covariance matrix are solved together to obtain a satellite product under the unified reference
Figure SMS_121
And the covariance matrix is +.>
Figure SMS_122
；/>
The obtained satellite product under unified reference
Figure SMS_123
And the covariance matrix thereof>
Figure SMS_124
Substituting the calculated satellite products and atmospheric products of each subnet and the covariance matrix thereof to calculate the atmospheric correction product formulas of each subnet as follows:
Figure SMS_125
。
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized: substituting the calculated atmospheric products into each subnet, and releasing the atmospheric products together with satellite products to users in the subnet for PPP-RTK positioning, wherein the user positioning formula is as follows:
Figure SMS_126
；
wherein:
Figure SMS_127
and->
Figure SMS_128
For the tropospheric delay and ionospheric delay products interpolated into the subnetwork p.
Example 1:
a wide area distributed non-differential non-combining PPP-RTK positioning method, the wide area distributed non-differential non-combining PPP-RTK positioning method comprising;
dividing the whole network into a plurality of sub-networks, and ensuring that all receivers in each sub-network have the same common-view satellite;
estimating satellite products and atmospheric correction products of the sub-networks by using GNSS data of the co-view satellites of the sub-networks;
step three, according to the satellite products and the atmosphere correction products of the estimated subnetwork, adopting an S transformation theory to perform reference unification to obtain the satellite products and the atmosphere correction products with the consistent whole network reference;
interpolating an atmospheric correction product consistent with the whole network reference to obtain the distance error between the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, and obtaining the atmospheric delay correction data;
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized.
Example 2:
example 2 is substantially the same as example 1 except that:
the method comprises the following steps ofThe wide area distributed non-differential non-combined PPP-RTK positioning method includes: assuming that the whole network has
Figure SMS_129
Synchronous observation of the individual reference stations>
Figure SMS_130
GNSS satellites with observation frequency +.>
Figure SMS_131
The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
Figure SMS_132
；
wherein the method comprises the steps of
Figure SMS_141
For the receiver number>
Figure SMS_134
Is satellite number>
Figure SMS_138
For frequency +.>
Figure SMS_144
Respectively observing values of pseudo range and phase; />
Figure SMS_148
And->
Figure SMS_146
Receiver clock error and satellite clock error respectively; />
Figure SMS_149
Delay for zenith troposphere; />
Figure SMS_143
Coefficients that are ionospheric bias delays; />
Figure SMS_147
A bias ionosphere delay for a first frequency point; />
Figure SMS_135
For frequency->
Figure SMS_137
A corresponding carrier phase wavelength; />
Figure SMS_136
Is integer ambiguity; />
Figure SMS_140
And->
Figure SMS_142
Receiver code bias and receiver differential code bias, respectively,/->
Figure SMS_145
For satellite code bias, +.>
Figure SMS_133
And->
Figure SMS_139
Receiver phase bias and satellite phase bias, respectively;
the whole network is divided into a plurality of subnets specifically comprises: dividing the whole net into
Figure SMS_150
Subnetwork, th->
Figure SMS_151
The subnetwork has
Figure SMS_152
The station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
Figure SMS_153
；
the specific expression forms of various products are as follows:
Figure SMS_154
；
Figure SMS_155
representing subnet->
Figure SMS_156
Is->
Figure SMS_157
The satellite receiver, the satellite product obtained by each sub-network and the reference of the atmospheric correction product selection are different, for example, the satellite phase deviation estimation has the reference ambiguity of +.>
Figure SMS_158
And
Figure SMS_159
the formula for the user to perform ambiguity resolution in these 2 subnets is:
Figure SMS_160
。
example 3:
example 3 is substantially the same as example 1 except that:
a wide area distributed non-differential non-combination PPP-RTK positioning method, the GNSS data using each sub-network common view satellite specifically comprises:
the satellite processor outputs signals from the transmitting antenna and the receiving antenna, and hardware delay exists between different frequencies and even between different codes and phases of the same frequency; because the hardware delay of all satellites at the receiver end is consistent, the clock error of the receiver is included; the hardware delays of the satellite terminals are different in satellite sizes, the generated code delays are called satellite code deviations, the phase delays are called satellite phase deviations, and the satellite terminal code deviations are larger than the phase deviation in magnitude;
the satellite signals are from the satellite to the receiver, the time delay is generated for the observation signals through atmospheric refraction, the correction is needed when PPP positioning is carried out, the atmospheric correction product is to estimate the atmospheric delay errors including tropospheric delay and ionospheric delay errors by utilizing GNSS observation of each subnet tracking station, the tropospheric delay correction only needs to estimate the tropospheric delay in the zenith direction of each receiver, and then the tropospheric delay correction is projected onto the connection line of the receiver and the satellite through a projection function; the ionosphere requires an estimation of one parameter per receiver and satellite link, which is relatively large.
The satellite code/phase deviation obtained through the observation of a plurality of ground tracking stations GNSS can be regarded as a code/phase distance error, the satellite clock error is a time deviation, the satellite clock error is a distance error, the satellite error can be directly corrected when PPP-RTK positioning is carried out on users in a network, the troposphere and ionosphere delay errors are related to the position of a receiver, the atmospheric delay distance error caused by atmospheric refraction is obtained between the receiver and the direction of a satellite connecting line, the atmospheric delay of each satellite estimated by each tracking station in the network is needed to be interpolated to the position of the user, and the error correction is carried out in a positioning model;
the unification of the benchmarks of the subnet satellite products by adopting the S transformation theory comprises any one or any combination of the following:
a satellite clock error reference unifying step, a satellite code deviation reference unifying step and a phase deviation reference unifying step.
The step of unifying satellite clock error references is as follows: the satellite clock difference obtained by each subnet is used as pseudo-observation, and the satellite clock difference and the receiver clock difference are parameterized again, and the formula is as follows:
Figure SMS_161
；
wherein the method comprises the steps of
Figure SMS_162
Where rank deficiency is 1, assume selection
Figure SMS_163
As a benchmark, the above formula is re-written as:
Figure SMS_164
Figure SMS_165
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-network
Figure SMS_166
As a benchmark, the benchmark unified model is:
Figure SMS_167
；
Figure SMS_168
；
the phase deviation reference unifying step refers to: the pseudo observation equation formula formed by the phase deviation obtained by each sub-network is as follows:
Figure SMS_169
；
rank deficiency of
Figure SMS_170
Select->
Figure SMS_171
As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
Figure SMS_172
；
wherein the method comprises the steps of
Figure SMS_173
At this time->
Figure SMS_174
And ambiguity->
Figure SMS_175
Linear correlation, introduce->
Figure SMS_176
Based on the equation:
Figure SMS_177
wherein the method comprises the steps of
Figure SMS_178
At this point the receiver phase deviation +.>
Figure SMS_179
And single difference ambiguity->
Figure SMS_180
Still related, rank deficient->
Figure SMS_181
Select->
Figure SMS_182
As a benchmark, the full rank formula is: />
Figure SMS_183
；
Figure SMS_184
；
The satellite clock difference obtained by each subnet is used as pseudo observation, and the re-parameterized satellite clock difference and the receiver clock difference are specifically as follows: assuming that the reference receiver clock error of the first subnet is used as a reference, the satellite clock error products of other subnets and the reference receiver clock error are subjected to subtraction to be used as pseudo-observed values, the receiver clock error of each subnet is actually subtracted from the clock error of the reference receiver of the first subnet, the satellite clock error and the receiver clock error are new satellite clock error and receiver clock error which both comprise the reference receiver clock error of the first subnet, the reference unification is to select the product of one subnet as the reference, the products of other subnets and the reference net product are subjected to subtraction, the products of other subnets are converted into the reference net through S transformation, the reference unification of the whole net is realized, when a user positions in the whole net, if the products of different references are used in different subnets, when the user positions from one subnet to the other subnet, the user needs to continuously switch and correct product information due to the existence of systematic deviation, the positioning discontinuity is caused, the positioning discontinuity of the user is seriously influenced, the positioning performance of the user is also seriously influenced, the positioning precision of the whole net is realized, and the positioning precision of the whole standard is realized when the user is unified, and the positioning precision of the whole standard is realized;
the satellite clock error reference unification, the satellite code deviation reference unification and the phase deviation reference unification and the related covariance matrix are solved together to obtain a satellite product under the unified reference
Figure SMS_185
And the covariance matrix is +.>
Figure SMS_186
；
The obtained satellite product under unified reference
Figure SMS_187
And the covariance matrix thereof>
Figure SMS_188
Substituting the calculated satellite products and atmospheric products of each subnet and the covariance matrix thereof to calculate the atmospheric correction product formulas of each subnet as follows:
Figure SMS_189
。
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized: substituting the calculated atmospheric products into each subnet, and releasing the atmospheric products together with satellite products to users in the subnet for PPP-RTK positioning, wherein the user positioning formula is as follows:
Figure SMS_190
；
wherein:
Figure SMS_191
and->
Figure SMS_192
For the tropospheric delay and ionospheric delay products interpolated into the subnetwork p.
Example 4
Example 4 is substantially the same as example 1 except that:
a wide area distributed non-differential non-combination PPP-RTK positioning method selects 82 tracking stations in the United states NGS network for analysis of double-frequency GPS data for one week, the distribution is shown in figure 1, the sampling rate of the data is 30 seconds, 44 stations are used for generating satellite products and atmospheric correction products (dots), 38 stations are used as users to evaluate the products generated at the network end (triangle), and the 44 tracking stations are divided into four subnets, which are shown in the boundary in figure 1;
as shown in fig. 2: although subnet 1 is one more station than subnet 2, the processing time consumption is significantly increased compared with subnet 2, because adding one station greatly increases the complexity of matrix calculation, the product fusion time consumption is within 10ms, the time consumption of the distributed PPP-RTK product generation is equal to the sum of the processing time and the product fusion time of subnets 1 and 2, each epoch is about 1000 ms, and the calculation efficiency is improved by 50% compared with the time consumed by the generation of the centralized PPP-RTK product by about 2000 ms;
as shown in fig. 3: the obvious difference exists among all satellite phase deviation products generated by the subnets 1 and 2, because the standards selected by the two subnets are different, if the standards are not unified, the user must re-estimate the ambiguity when switching between the subnets, so that the positioning accuracy is reduced and the positioning is discontinuous, and the data of the distributed PPP-RTK selecting subnet 2 is used as the standard for fusing the two subnet products and is consistent with the satellite products generated by the centralized PPP-RTK;
as shown in FIG. 4, the distributed PPP-RTK and the centralized PPP-RTK can realize the fixation of integer ambiguity in one epoch, the positioning accuracy (RMS) reaches 1-2 cm, the distributed PPP-RTK positioning method is consistent with the positioning accuracy and continuity of the centralized PPP-RTK, the calculation efficiency is improved by 50%, and the user is ensured to realize the real-time high-accuracy continuous positioning of the wide PPP-RTK.
The above description is merely of preferred embodiments of the present invention, and the scope of the present invention is not limited to the above embodiments, but all equivalent modifications or variations according to the present disclosure will be within the scope of the claims.

Claims (10)

1. A wide area distributed non-differential non-combination PPP-RTK positioning method is characterized by comprising the following steps:
dividing the whole network into a plurality of sub-networks, and ensuring that all receivers in each sub-network have the same common-view satellite;
estimating satellite products and atmospheric correction products of the sub-networks by using GNSS data of the co-view satellites of the sub-networks;
step three, according to the satellite products and the atmosphere correction products of the estimated subnetwork, adopting an S transformation theory to perform reference unification to obtain the satellite products and the atmosphere correction products with the consistent whole network reference;
interpolating an atmospheric correction product consistent with the whole network reference to obtain the distance error between the receiver and the satellite in the observation direction caused by troposphere delay and ionosphere delay at each moment, and obtaining the atmospheric delay correction data;
substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized.
2. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 1, wherein: the whole network is as follows: assuming that the whole network has
Figure QLYQS_1
Synchronous observation of the individual reference stations>
Figure QLYQS_2
GNSS satellites with observation frequency +.>
Figure QLYQS_3
The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
Figure QLYQS_4
；
wherein the method comprises the steps of
Figure QLYQS_12
For the receiver number>
Figure QLYQS_6
Is satellite number>
Figure QLYQS_10
For frequency +.>
Figure QLYQS_9
Respectively observing values of pseudo range and phase; />
Figure QLYQS_15
And->
Figure QLYQS_16
Receiver clock error and satellite clock error respectively; />
Figure QLYQS_18
Delay for zenith troposphere;
Figure QLYQS_19
coefficients that are ionospheric bias delays; />
Figure QLYQS_21
A bias ionosphere delay for a first frequency point; />
Figure QLYQS_5
For frequency->
Figure QLYQS_13
A corresponding carrier phase wavelength; />
Figure QLYQS_11
Is integer ambiguity; />
Figure QLYQS_14
And->
Figure QLYQS_17
Receiver code bias and receiver differential code bias, respectively,/->
Figure QLYQS_20
For satellite code bias, +.>
Figure QLYQS_7
And->
Figure QLYQS_8
The receiver phase offset and the satellite phase offset, respectively.
3. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 1, wherein: the whole network is divided into a plurality of subnets specifically comprises: dividing the whole net into
Figure QLYQS_22
Subnetwork, th->
Figure QLYQS_23
The subnetwork has
Figure QLYQS_24
The station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
Figure QLYQS_25
；
the specific expression forms of various products are as follows:
Figure QLYQS_26
；/>
Figure QLYQS_27
representing subnet->
Figure QLYQS_28
Is->
Figure QLYQS_29
The satellite receiver, the satellite product obtained by each sub-network and the reference of the atmospheric correction product selection are different, for example, the satellite phase deviation estimation has the reference ambiguity of +.>
Figure QLYQS_30
And
Figure QLYQS_31
the formula for the user to perform ambiguity resolution in these 2 subnets is:
Figure QLYQS_32
。
4. the method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 1, wherein: the GNSS data using the common view satellites of each sub-network specifically comprises:
the satellite processor outputs signals from the transmitting antenna and the receiving antenna, and hardware delay exists between different frequencies and even between different codes and phases of the same frequency; because the hardware delay of all satellites at the receiver end is consistent, the clock error of the receiver is included; the hardware delays of the satellite terminals are different in satellite sizes, the generated code delays are called satellite code deviations, the phase delays are called satellite phase deviations, and the satellite terminal code deviations are larger than the phase deviation in magnitude;
the atmospheric correction product utilizes GNSS observations of each subnet tracking station to estimate an atmospheric delay error, including tropospheric delay and ionospheric delay errors.
5. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 4, wherein: satellite code/phase bias observed by a plurality of ground tracking stations (GNSS) can be regarded as code/phase distance error, and satellite clock difference is time bias multiplied by light velocity, namely distance error.
6. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 1, wherein: the unification of the benchmarks of the subnet satellite products by adopting the S transformation theory comprises any one or any combination of the following:
a satellite clock error reference unifying step, a satellite code deviation reference unifying step and a phase deviation reference unifying step.
7. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 6, wherein:
the step of unifying satellite clock error references is as follows: the satellite clock difference obtained by each subnet is used as pseudo-observation, and the satellite clock difference and the receiver clock difference are parameterized again, and the formula is as follows:
Figure QLYQS_33
；
wherein the method comprises the steps of
Figure QLYQS_34
Wherein the rank deficiency is 1, assuming selection +.>
Figure QLYQS_35
As a benchmark, the above formula is re-written as:
Figure QLYQS_36
；
Figure QLYQS_37
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-network
Figure QLYQS_38
As a benchmark, the benchmark unified model is:
Figure QLYQS_39
；
Figure QLYQS_40
；
the phase deviation reference unifying step refers to: the pseudo observation equation formula formed by the phase deviation obtained by each sub-network is as follows:
Figure QLYQS_41
；
rank deficiency of
Figure QLYQS_42
Select->
Figure QLYQS_43
As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
Figure QLYQS_44
；
wherein the method comprises the steps of
Figure QLYQS_45
At this time->
Figure QLYQS_46
And ambiguity->
Figure QLYQS_47
Linear correlation, introduce->
Figure QLYQS_48
Based on the equation:
Figure QLYQS_49
；
wherein the method comprises the steps of
Figure QLYQS_50
At this point the receiver phase deviation +.>
Figure QLYQS_51
And single difference ambiguity->
Figure QLYQS_52
Still related, rank deficient->
Figure QLYQS_53
Select->
Figure QLYQS_54
As a benchmark, the full rank formula is:
Figure QLYQS_55
；
Figure QLYQS_56
。
8. the method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 7, wherein: the satellite clock difference obtained by each subnet is used as pseudo observation, and the re-parameterized satellite clock difference and the receiver clock difference are specifically as follows: assuming that the reference receiver clock of the first subnet is used as a reference, the satellite clock of other subnets is simultaneously subtracted from the reference receiver clock of the first subnet to obtain a pseudo-observed value, and the receiver clock of each subnet is actually simultaneously subtracted from the clock of the reference receiver of the first subnet, wherein the satellite clock and the receiver clock are new satellite clock and receiver clock both comprising the reference receiver clock of the first subnet.
9. The method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 7, wherein: the satellite clock error reference unification, the satellite code deviation reference unification and the phase deviation reference unification and the related covariance matrix are solved together to obtain a satellite product under the unified reference
Figure QLYQS_57
And the covariance matrix is +.>
Figure QLYQS_58
；
The obtained satellite product under unified reference
Figure QLYQS_59
And the covariance matrix thereof>
Figure QLYQS_60
Substituting the calculated satellite products and atmospheric products of each subnet and the covariance matrix thereof to calculate the atmospheric correction product formulas of each subnet as follows:
Figure QLYQS_61
。
10. the method for locating a wide area distributed non-differential non-combining PPP-RTK according to claim 9, wherein: substituting the atmospheric delay correction data and satellite products into PPP-RTK positioning models adopted by users under all subnets, so that accurate positioning of the users is realized: substituting the calculated atmospheric products into each subnet, and releasing the atmospheric products together with satellite products to users in the subnet for PPP-RTK positioning, wherein the user positioning formula is as follows:
Figure QLYQS_62
；
wherein:
Figure QLYQS_63
and->
Figure QLYQS_64
For the tropospheric delay and ionospheric delay products interpolated into the subnetwork p. />
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