CN116068598B - 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 PDFInfo
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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
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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
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 hasSynchronous observation of the individual reference stations>GNSS satellites with observation frequency +.>The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
；
wherein the method comprises the steps ofFor the receiver number>Is satellite number>For frequency +.>Respectively observing values of pseudo range and phase; />And->Receiver clock error and satellite clock error respectively; />Delay for zenith troposphere; />Coefficients that are ionospheric bias delays; />A bias ionosphere delay for a first frequency point; />For frequency->A corresponding carrier phase wavelength; />Is integer ambiguity; />And->Receiver code bias and receiver differential code bias, respectively,/->For satellite code bias, +.>And->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 intoSubnetwork, th->The subnetwork hasThe station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
；
the specific expression forms of various products are as follows:
；
representing subnet->Is->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 +.>Andthe formula for the user to perform ambiguity resolution in these 2 subnets is:
。
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:
；
wherein the method comprises the steps ofWherein the rank deficiency is 1, assuming selection +.>As a benchmark, the above formula is re-written as:
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-networkAs a reference, then baseThe quasi-uniform model is:
；
；
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:
；
rank deficiency ofSelect->As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
；
wherein the method comprises the steps ofAt this time->And ambiguity ofLinear correlation, introduce->Based on the equation:
；
wherein the method comprises the steps ofAt this time, the receiver phase is deviatedAnd single difference ambiguity->Still related, rank deficient->Select->As a benchmark, the full rank formula is:
；
。
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 referenceAnd the covariance matrix is +.>；
Unifying the obtainedSatellite products on a referenceAnd the covariance matrix thereof>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:
。
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:
；
wherein:and->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 hasSynchronous observation of the individual reference stations>GNSS satellites with observation frequency +.>The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
；
wherein the method comprises the steps ofFor the receiver number>Is satellite number>For frequency +.>Pseudo-range and phase respectivelyIs a measurement of the observed value of (2); />And->Receiver clock error and satellite clock error respectively; />Delay for zenith troposphere; />Coefficients that are ionospheric bias delays; />A bias ionosphere delay for a first frequency point; />For frequency->A corresponding carrier phase wavelength; />Is integer ambiguity; />And->Receiver code bias and receiver differential code bias, respectively,/->For satellite code bias, +.>And->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 intoSubnetwork, th->The subnetwork hasThe station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
；
the specific expression forms of various products are as follows:
；
representing subnet->Is->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 +.>Andthe formula for the user to perform ambiguity resolution in these 2 subnets is:
。
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:
；
wherein the method comprises the steps ofWhere rank deficiency is 1, assume selectionAs a benchmark, the above formula is re-written as:
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-networkAs a benchmark, the benchmark unified model is:
；
；
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:
；
rank deficiency ofSelect->As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
；
wherein the method comprises the steps ofAt this time->And ambiguity->Linear correlation, introduce->Based on the equation:
；
wherein the method comprises the steps ofAt this time, the receiver phase is deviatedAnd single difference ambiguity->Still related, rank deficient->Select->As a benchmark, the full rank formula is:
；
。
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 unified baseQuasi-satellite productAnd the covariance matrix is +.>；
The obtained satellite product under unified referenceAnd the covariance matrix thereof>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:
。
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:
；
wherein:and->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:
a wide area distributed non-differential non-combined PPP-RTK positioning method, the whole network refers to: assuming that the whole network hasSynchronous observation of the individual reference stations>GNSS satellites with observation frequency +.>The whole network full rank satellite product and atmospheric product solution formulas are expressed as follows:
；
wherein the method comprises the steps ofFor the receiver number>Is satellite number>For frequency +.>Respectively observing values of pseudo range and phase; />And->Receiver clock error and satellite clock error respectively; />Delay for zenith troposphere;coefficients that are ionospheric bias delays; />A bias ionosphere delay for a first frequency point; />For frequency->A corresponding carrier phase wavelength; />Is integer ambiguity; />And->Receiver code bias and receiver differential code bias, respectively,/->For satellite code bias, +.>And->Receiver phase bias and satellite phase bias, respectively;
the whole network is divided into a plurality of subnets specifically comprises: dividing the whole net intoSubnetwork, th->The subnetwork hasThe station receiver, satellite products and atmospheric products and their covariance matrix that each subnet calculates are:
；
the specific expression forms of various products are as follows:
；
representing subnet->Is->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 +.>Andthe user is at these 2The formula for ambiguity resolution in the subnet is:
。
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:
；
wherein the method comprises the steps ofWherein the rank deficiency is 1, assuming selection +.>As a benchmark, the above formula is re-written as:
；
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-networkAs a benchmark, the benchmark unified model is:
；
；
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:
；
rank deficiency ofSelect->As a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
；
wherein the method comprises the steps ofAt this time->And ambiguity->Linear correlation, introduce->Based on the equation:
wherein the method comprises the steps ofAt this time, the receiver phase is deviatedAnd single difference ambiguity->Still related, rank deficient->Select->As a benchmark, the full rank formula is:
；
；
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 referenceAnd the covariance matrix is +.>；
The obtained satellite product under unified referenceAnd the covariance matrix thereof>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:
。
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:
；/>
wherein:and->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 (6)
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;
the standard unification by adopting the S transformation theory according to the satellite products and the atmospheric correction products of the estimated subnetwork comprises any one or any combination of the following:
a satellite clock error reference unification step, a satellite code deviation reference unification step and a phase deviation reference unification 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:
wherein the method comprises the steps ofWherein the rank deficiency is 1, assuming that +.>As a benchmark, the above formula is re-written as:
wherein q is greater than 1;
the step of unifying satellite code deviation references is as follows: selecting receiver code bias in a first sub-networkAs a benchmark, the benchmark unified model is:
where j > 2, q=1, …, p;
wherein q is greater than 1;
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:
wherein q=1, …, p;
rank deficiency f, selectAs a reference, the equation after re-parameterizing the satellite phase offset and the receiver phase offset is:
wherein the method comprises the steps ofWherein q is > 1, in which case->And ambiguity->Linear correlation, introduce->Based on the equation:
wherein the method comprises the steps ofWhere q > 1, where the receiver phase deviation +.>And single difference ambiguity->Still related, rank deficient q-1, select +.>As a benchmark, the full rank formula is:
wherein q is greater than 1, s is greater than 1;
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 difference of the first subnet is taken as a reference, the satellite clock difference products of other subnets and the reference receiver clock difference are subjected to subtraction to obtain pseudo-observed values, and the receiver clock differences of all subnets are subtracted from the clock difference of the reference receiver of the first subnet, wherein the satellite clock difference and the receiver clock difference are new satellite clock differences and receiver clock differences which comprise the reference receiver clock difference 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 Y under the unification reference sat ＝[Y sck Y scb Y spb ] T And its covariance matrix as
The obtained satellite product Y under unified reference sat And a covariance matrix thereofSubstituting 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:
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 n reference stations to synchronously observe m GNSS satellites, the observation frequency is f, and the calculation formulas of the whole network full rank satellite products and the atmospheric products are expressed as follows:
where r=1, …, n is the receiver number, s=1, …, m is the satellite number, j=1, …, f is the frequency,respectively observing values of pseudo range and phase; />And->Receiver clock error and satellite clock error respectively; />Delay for zenith troposphere;coefficients that are ionospheric bias delays; />A bias ionosphere delay for a first frequency point; lambda (lambda) j For carrier phase corresponding to frequency jA wavelength; />Is integer ambiguity; />And->Receiver code bias and receiver differential code bias, respectively,/->For satellite code bias, +.>And->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 network into p sub-networks, the q-th sub-network having n q Station receiver, where q=1, …, p,the satellite products and the atmospheric products and the covariance matrix of each subnet are calculated as follows:
Y(q)＝[Y sat (q) Y atm (q)] T ，
the specific expression forms of various products are as follows:
where j > 2, (. Cndot.) where j is equal to or greater than 2 r (q) r receivers in sub-network q, the reference for selection of satellite and atmospheric correction products obtained for each sub-network being different, the reference ambiguity for selection of satellite phase bias estimates in sub-networks 1 and 2, respectivelyAndthe formula for the user to perform ambiguity resolution in these 2 subnets is:
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 and phase bias observed by a plurality of ground tracking stations (GNSS) can be regarded as code and 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: 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:
wherein:and->For the tropospheric delay and ionospheric delay products interpolated into the subnetwork p.
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