A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement

Abstract

The present invention discloses a multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement, which includes: using regional sparse reference stations, constructing zenith troposphere and satellite-tilt ionospheric delay models through PPP solutions with known precise coordinates, and providing atmospheric enhancement information for users; users constructing a full-rank estimable solution model with atmospheric enhancement according to the multi-frequency GNSS non-combination model; performing integer transformation on the ambiguities and their variance-covariance obtained from the non-combination model, and mapping them into the forms of ultra-wide lane, wide lane, and narrow lane; adopting an integer ambiguity search method to sequentially fix the ultra-wide lane, wide lane, and narrow lane ambiguities in sequence, and obtaining the positioning solution under the corresponding ambiguity-fixed state. Through sparse reference station atmospheric enhancement and multi-frequency ambiguity sequential solution, the present invention can achieve rapid fixation of single-epoch PPP ambiguities. In local time periods where the narrow lane ambiguity cannot be reliably fixed, a high-precision positioning solution better than 10 cm can still be achieved relying on the wide lane solution.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS (Global Navigation Satellite System) positioning and navigation, relates to GNSS precise point positioning technology, and particularly relates to a multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement. Background Art

[0002] The Global Navigation Satellite System (GNSS) has become one of the main means for people to obtain accurate spatio-temporal information due to its many advantages such as all-weather operation, high global coverage, high positioning accuracy, and real-time efficiency. It is widely used in many fields such as deformation monitoring, precise timekeeping, and precise orbit determination. As a major national infrastructure, it is also an extremely important part of the national Positioning Navigation and Timing (PNT) system. Currently, the internationally recognized four major GNSS systems include the GPS of the United States, the GLONASS of Russia, the Galileo of the European Union, and the BDS system independently developed by China. In recent years, with the modernization of GPS, the continuous improvement of the GLONASS and Galileo systems, and the global networking of China's BDS-3 system, the new generation of navigation satellites can transmit navigation signals at three or more frequencies, and GNSS has officially entered the era of multi-mode and multi-frequency compatibility and interoperability.

[0003] Precise Point Positioning (PPP) technology is one of the main methods for high-precision GNSS positioning. By accurately considering various error corrections, it can achieve absolute high-precision positioning globally based on a single receiver, with the advantages of high positioning flexibility and convenience. However, it is often limited by external precise orbit and clock error products. At the same time, the model has many parameters to be estimated and strong correlations, and it usually takes a long time to reach centimeter-level accuracy. In addition, due to the influence of the fractional cycle bias (FCB), conventional PPP data processing can only obtain a floating-point solution, and the reliability of positioning is relatively low. Even on the basis of FCB correction, reliable ambiguity fixing requires a considerable initialization time. With the rise of new location-based service industries such as autonomous driving, in addition to positioning accuracy, users pay more attention to the real-time, continuous, and reliable nature of positioning. Especially in complex application scenarios such as urban canyons, due to the vulnerability of GNSS signals themselves, once cycle slips or signal outages occur, PPP will face the problems of re-convergence or re-initialization, and these difficulties have also become bottlenecks for the large-scale popularization and application of PPP.

[0004] As multi-mode and multi-frequency gradually become the new development trend in the GNSS field, compared with single systems, multi-mode GNSS means more visible satellites and better geometric distribution, and multi-frequency information means more combinations of observations with excellent characteristics. All of these can strengthen the model strength of PPP, shorten its convergence and initialization time to a certain extent, and improve the continuity and reliability of positioning, but there is still a certain gap from real-time applications. To achieve quasi-real-time fixing of PPP ambiguities, it is usually necessary to introduce additional enhancement information (such as atmospheric constraint information, etc.), and by means of additional constraints, weaken the correlation between the parameters to be estimated in the model and achieve rapid fixing of ambiguities. Summary of the Invention

[0005] To solve the above problems, the present invention discloses a multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement. Through sparse reference station atmospheric enhancement and multi-frequency ambiguity sequential solution, it can achieve rapid fixing of PPP ambiguities in a single epoch. In local time periods where the narrow-lane ambiguity cannot be reliably fixed, high-precision positioning solutions can still be achieved relying on the wide-lane solution.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement, comprising the following steps:

[0008] (1) Using regional sparse reference stations, through PPP solution with known accurate coordinates, construct a zenith tropospheric delay model and an inclined ionospheric delay model for each satellite, and provide atmospheric enhancement information for the positioning site;

[0009] (2) The user-end site constructs a full-rank estimable solution model with atmospheric enhancement according to the multi-frequency GNSS non-combination model;

[0010] (3) For the ambiguity parameters estimated by the user-end non-combination model, perform integer transformation according to the combination coefficients, and transform the non-combination ambiguity floating-point solution parameters and their variance-covariance matrix into ultra-wide-lane, wide-lane, and narrow-lane forms;

[0011] (4) Adopt an integer ambiguity search method to sequentially fix the ultra-wide-lane, wide-lane, and narrow-lane ambiguities in sequence, and obtain the positioning solution under the corresponding ambiguity fixed state.

[0012] Furthermore: In step (1), the process of regional atmospheric error modeling using regional sparse reference stations includes:

[0013] First, construct a PPP solution model with known accurate coordinates (not regarded as unknown parameters) for the reference stations. The non-combination full-rank estimable model after re-parameterization is shown in Equation (1)

[0014]

[0015] Where the superscript s of the relevant variables on the left side of the equal sign and the subscripts r and i represent satellite, receiver, and frequency respectively; and are the basic pseudorange observation value and carrier observation value respectively; represents the station-satellite distance; represents the tropospheric delay on the signal propagation path; c represents the speed of light in vacuum; and are the satellite clock error and receiver clock error after re-parameterization respectively; represents the ionospheric delay parameter (the first frequency point) after re-parameterization of the ionosphere and pseudorange hardware delay; γ i is the ionospheric delay amplification coefficient at each frequency; D r,i and are the receiver end inter-frequency bias (IFB) and satellite end differential code bias (DCB) corrections for frequency i respectively; is the floating-point ambiguity after re-parameterization; ζ i is the hardware bias remaining in the pseudorange equation; δ i is the inter-frequency clock bias (IFCB) correction that needs to be additionally considered in the carrier equation, and its essence is the linear combination of the satellite end phase hardware bias varying with time ; and represent the pseudorange and carrier observation value noises including multipath respectively.

[0016] The tropospheric delay parameters of the above-mentioned satellites use the empirical model to correct their dry components The wet component uses the wet delay projection function to be converted into the product of the projection function and the zenith tropospheric wet delay T r,zwd , that is

[0017]

[0018] Using the full-rank model with known coordinates shown in Equation (1) and the tropospheric projection model of Equation (2), combined with precise satellite orbits, satellite clock errors, and satellite phase bias products, the receiver clock error zenith tropospheric wet delay T r,zwd , receiver end IFB D r,i and the inclined ionospheric delay of each satellite and ambiguity parameters Each reference station further constrains and extracts the zenith tropospheric wet delay and the re-parameterized inclined ionospheric delay of each satellite After that, according to the spatial distribution of the user and the reference station, interpolate the atmospheric delay at the user's position,

[0019]

[0020]

[0021] In the formula, the subscripts u and r represent the user and different reference stations; n is the number of reference stations; and are the interpolated slant ionospheric and zenith tropospheric wet delays at the user side respectively; a r is the interpolation coefficient corresponding to the reference station r. For the ionospheric delay, the interpolation coefficient is calculated according to the difference in the latitudes and longitudes of the piercing points of each satellite

[0022]

[0023] In the formula, and are the differences in the latitudes and longitudes of the piercing points of the satellite s corresponding to the user and the reference station respectively. For the zenith tropospheric wet delay, according to the difference in the Gaussian plane coordinates between the user and the base station, a method similar to that of formula (5) is used to calculate the interpolation coefficient by least squares solution.

[0024] Furthermore: In step (2), the process of constructing a full-rank estimable solution model with atmospheric enhancement at the user-side site includes:

[0025] Similar to the above formula (1), a full-rank estimable PPP solution model is constructed at the user side, and the atmospheric error modeled in the above step (1) is used to enhance the model. The parameters to be estimated are constrained in the form of a pseudo-observation equation, thereby shortening the initialization time. For the zenith tropospheric wet delay, the constraint equation is as follows,

[0026]

[0027] where represents the variance of the tropospheric pseudo-observations. For the ionospheric delay, since the non-combination PPP model reparameterizes it during the parameter estimation process, the interpolated value includes the DCB at the receiver end of each reference station. Unlike the troposphere, the non-differenced ionospheric parameters at the user side cannot be directly constrained. In order to eliminate the influence of the receiver-end DCB, the method of inter-satellite single difference is used to eliminate the influence of the receiver DCB, and the PPP is enhanced with the ionospheric enhancement information in the form of inter-satellite single difference

[0028]

[0029] In the formula, s and s 0 are the non-reference star and the reference star respectively; is the variance of the ionospheric pseudo-observations.

[0030] Further: The process of transforming the client ambiguity into the ultra-wide lane, wide lane, and narrow lane forms through integer transformation in step (3) includes:

[0031] Through the atmospheric enhancement solution model in step (2), the non-combination ambiguities at each frequency are solved, and integer transformation is performed through the ultra-wide lane, wide lane, and narrow lane combination coefficients to obtain the ultra-wide lane, wide lane, and narrow lane combination ambiguities and their variance-covariance matrices. Assume that the integer transformation matrices of the ultra-wide lane, wide lane, and narrow lane are D e 、D w and D n respectively, and the transformed parameters and their covariance matrices are

[0032]

[0033] where, and are the parameters to be estimated before and after transformation respectively, and are the variance-covariance matrices before and after transformation respectively. I is the identity matrix, corresponding to the non-ambiguity parameter part.

[0034] Further: In step (4), the process of sequentially fixing the ultra-wide lane, wide lane, and narrow lane ambiguities to obtain the positioning solution in the corresponding ambiguity-fixed state includes:

[0035] The least squares reduction correlation method (LAMBDA) is used to sequentially fix the ultra-wide lane, wide lane, and narrow lane ambiguities obtained in the above step (3), and the fixing method is:

[0036] (1) First, fix the ultra-wide lane. When the ultra-wide lane meets the Ratio threshold for LAMBDA fixing, the remaining parameters are constrained by the ambiguity-fixed ultra-wide lane to obtain the ultra-wide lane fixed positioning solution and other parameters; when the Ratio threshold condition is not met, the floating-point solution is maintained for the current epoch.

[0037] (2) From the parameters in the ultra-wide lane fixed solution state, extract the wide lane ambiguity part, and use the LAMBDA method for search and fixing. When the Ratio threshold condition is met, the remaining parameters are constrained by the ambiguity-fixed wide lane to obtain the wide lane fixed positioning solution and other parameters; when the Ratio threshold condition is not met, the ultra-wide lane solution is maintained for the current epoch.

[0038] (3) From the parameters in the wide lane fixed solution state, extract the narrow lane ambiguity part, and use the LAMBDA method for search and fixing. When the Ratio threshold condition is met, the remaining parameters are constrained by the ambiguity-fixed narrow lane to obtain the narrow lane fixed positioning solution; when the Ratio threshold condition is not met, the wide lane solution is maintained for the current epoch.

[0039] The beneficial effects of the present invention include:

[0040] The multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement proposed by the present invention extracts high-precision atmospheric enhancement information such as troposphere and inclined ionosphere of sparse reference stations through step-by-step ambiguity fixing, and interpolates according to the user's location. By adding pseudo-observation equations, the parameter estimation model at the user end is constrained, weakening the correlation between the parameters to be estimated in the user-end positioning model. Compared with the conventional PPP model that fixes the non-combined ambiguity, it can effectively shorten the PPP initialization time; the ultra-wide lane, wide lane, and narrow lane sequential solution methods adopted at the user end can also obtain a high-precision wide lane solution (accuracy better than 10 cm) in the local time period when the narrow lane ambiguity cannot be fixed. Description of the Drawings

[0041] Figure 1 is the implementation flowchart of the positioning method described in the present invention;

[0042] Figure 2 is the schematic diagram of the sparse reference station network and user sites used in the numerical example;

[0043] Figure 3 is the modeling effect of the ionospheric error region at the LILY site;

[0044] Figure 4 is the modeling effect of the tropospheric error region at the LILY site;

[0045] Figure 5 is the positioning accuracy of different modes at 6 user sites. Detailed Embodiment

[0046] The following further clarifies the present invention in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0047] As Figure 1 shown, this embodiment discloses a method for generating multi-reference station differential positioning information based on a dynamic grid, and the specific steps are as follows:

[0048] Step (1): Use regional sparse reference stations to model regional atmospheric errors

[0049] First, a PPP solution model with accurately known reference station coordinates (not regarded as unknown parameters) is constructed. The non-combined full-rank estimable model after re-parameterization is shown in Equation (1)

[0050]

[0051] where the superscript s and subscripts r, i of the relevant variables on the left side of the equal sign represent satellite, receiver, and frequency respectively; and are the basic pseudo-range observation value and carrier observation value respectively; Denotes the station-satellite distance; Denotes the tropospheric delay on the signal propagation path; c denotes the speed of light in vacuum; And Are the satellite clock error and receiver clock error after re-parameterization, respectively; Denotes the ionospheric delay parameter (first frequency point) after re-parameterization of the ionosphere and pseudorange hardware delay; γ i Is the ionospheric delay amplification factor at each frequency; D r,i And Are the receiver end inter-frequency bias (IFB) and satellite end differential code bias (DCB) corrections for frequency i, respectively; Is the floating-point ambiguity after re-parameterization; ζ i Is the hardware bias remaining in the pseudorange equation; δ i Is the inter-frequency clock bias (IFCB) correction that needs to be additionally considered in the carrier equation, and its essence is the linear combination of the satellite end phase hardware bias varying with time Of; And Denote the pseudorange and carrier observation noises including multipath, respectively.

[0052] The tropospheric delay parameters of the above-mentioned satellites adopt an empirical model to correct their dry components The wet component adopts a wet delay projection function To be transformed into the product of the projection function and the zenith tropospheric wet delay T r,zwd That is

[0053]

[0054] Using the full-rank model with known coordinates shown in Equation (1) and the tropospheric projection model in Equation (2), combined with precise satellite orbits, satellite clock errors, and satellite phase bias products, the receiver clock error Zenith tropospheric wet delay T r,zwd The receiver end IFB D r,i And the inclined ionospheric delay of each satellite And the ambiguity parameter Each reference station further constrains and extracts the zenith tropospheric wet delay And the re-parameterized inclined ionospheric delay of each satellite After that, according to the spatial distribution of the user and the reference station, interpolate the atmospheric delay at the user's position,

[0055]

[0056]

[0057] where the subscripts u and r represent the user and different reference stations, respectively; n is the number of reference stations; and are the interpolated slant ionospheric and zenith tropospheric wet delays at the user side, respectively; a r is the interpolation coefficient corresponding to the reference station r. For the ionospheric delay, the interpolation coefficient is calculated based on the difference in the latitudes and longitudes of the piercing points of each satellite.

[0058]

[0059] where and are the differences in the latitudes and longitudes of the piercing points of the satellite s corresponding to the user and the reference station, respectively. For the zenith tropospheric wet delay, based on the difference in the Gauss plane coordinates between the user and the base station, a method similar to that of Equation (5) is used to calculate the interpolation coefficient by least squares solution.

[0060] Step (2): The user-side site constructs a full-rank estimable solution model with atmospheric augmentation

[0061] Similar to the above Equation (1), the user side constructs a full-rank estimable PPP solution model and uses the atmospheric error modeled in the above Step (1) to perform atmospheric augmentation on the model. The parameters to be estimated are constrained in the form of pseudo-observation equations, thereby shortening the initialization time. For the zenith tropospheric wet delay, its constraint equation is as follows.

[0062]

[0063] where represents the variance of the tropospheric pseudo-observations. For the ionospheric delay, since the non-combination PPP model reparameterizes it during the parameter estimation process, the interpolated value contains the DCB at the receiver end of each reference station and cannot directly constrain the undifferenced ionospheric parameters at the user side like the troposphere. To eliminate the influence of the receiver-end DCB, the method of inter-satellite single difference is used to eliminate the influence of the receiver DCB, and the PPP is enhanced with the ionospheric augmentation information in the form of inter-satellite single difference.

[0064]

[0065] where s and s 0 are the non-reference satellite and the reference satellite, respectively; is the variance of the ionospheric pseudo-observations.

[0066] Step (3): The user-side ambiguity is transformed into the ultra-wide lane, wide lane, and narrow lane forms through integer transformation

[0067] Through the atmospheric enhancement solution model in step (2), the non-combination ambiguities at each frequency are solved, and integer transformation is performed through the ultra-wide-lane, wide-lane, and narrow-lane combination coefficients to obtain the ultra-wide-lane, wide-lane, and narrow-lane combined ambiguities and their variance-covariance matrices. Assume that the integer transformation matrices for the ultra-wide-lane, wide-lane, and narrow-lane are D e 、D w and D n respectively, and the transformed parameters and their covariance matrix are

[0068]

[0069] where and are the parameters to be estimated before and after transformation respectively, and are the variance-covariance matrices before and after transformation respectively. I is the identity matrix, corresponding to the non-ambiguity parameter part.

[0070] Step (4): Sequentially fix the ultra-wide-lane, wide-lane, and narrow-lane ambiguities to obtain the positioning solution under the corresponding ambiguity-fixed state

[0071] Adopt the least squares de-correlation method (LAMBDA) to fix the ultra-wide-lane, wide-lane, and narrow-lane ambiguities obtained in the above step (3) in sequence. The fixing method is as follows:

[0072] (1) First, fix the ultra-wide-lane. When the ultra-wide-lane meets the Ratio threshold for LAMBDA fixing, use the ambiguity-fixed ultra-wide-lane to constrain the remaining parameters to obtain the ultra-wide-lane fixed positioning solution and other parameters; when it does not meet the Ratio threshold condition, keep the floating-point solution at the current epoch.

[0073] (2) Extract the wide-lane ambiguity part from the parameters in the ultra-wide-lane fixed solution state, and use the LAMBDA method to search and fix it. When it meets the Ratio threshold condition, use the ambiguity-fixed wide-lane to constrain the remaining parameters to obtain the wide-lane fixed positioning solution and other parameters; when it does not meet the Ratio threshold condition, keep the ultra-wide-lane solution at the current epoch.

[0074] (3) Extract the narrow-lane ambiguity part from the parameters in the wide-lane fixed solution state, and use the LAMBDA method to search and fix it. When it meets the Ratio threshold condition, use the ambiguity-fixed narrow-lane to constrain the remaining parameters to obtain the narrow-lane fixed positioning solution; when it does not meet the Ratio threshold condition, keep the wide-lane solution at the current epoch.

[0075] Appendix Figure 2 is for regional atmospheric modeling using sparse reference stations with an average spacing of 369.5 km, which includes 6 user sites for positioning verification. Appendix Figure 3 and Appendix Figure 4The modeling effects of the zenith troposphere and the ionospheric delays of each satellite are respectively shown. The modeling accuracy of the zenith troposphere delay is 1.7 cm (RMS), and the modeling accuracy of the ionospheric delay is 5.2 cm. The positioning accuracy statistics of 6 user sites are as Figure 5 shown. In the case of no atmospheric constraint, the planar and elevation positioning accuracies of the single-epoch wide-lane solution are 25.8 cm and 56.1 cm respectively; in the case of having atmospheric constraints, the accuracy of the ultra-wide-lane solution is 12.7 cm in the plane and 22.7 cm in elevation, the accuracy of the wide-lane solution is 7.7 cm in the plane and 9.8 cm in elevation, and the accuracy of the narrow-lane solution is 4.0 cm in the plane and 6.0 cm in elevation. It can be seen from this that when the narrow-lane solution cannot be fixed, relying on the wide-lane solution can still obtain a positioning accuracy better than 10 cm.

[0076] The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, and also include technical solutions composed of any combination of the above technical features. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement, characterized in that: It includes the following steps: (1) Using regional sparse reference stations, through PPP solutions with known accurate coordinates, construct zenith tropospheric delay models and inclined ionospheric delay models for each satellite, and provide atmospheric enhancement information for the positioning site; (2) The user-side site constructs a full-rank estimable solution model with atmospheric enhancement according to the multi-frequency GNSS non-combination model; (3) For the ambiguity parameters estimated by the user-side non-combination model, perform integer transformation according to the combination coefficients, and transform the non-combination ambiguity floating-point solution parameters and their variance-covariance matrix into ultra-wide lane, wide lane, and narrow lane forms; (4) Adopt the integer ambiguity search method to sequentially fix the ultra-wide lane, wide lane, and narrow lane ambiguities, and obtain the positioning solution under the corresponding ambiguity-fixed state.

2. A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement according to claim 1, characterized in that: In step (1), the process of using regional sparse reference stations to model regional atmospheric errors includes: First, construct a PPP solution model with known accurate coordinates for the reference station. The re-parameterized non-combination full-rank estimable model is shown in Equation (1) Where the superscript s and subscripts r, i of the relevant variables on the left side of the equal sign represent satellite, receiver, and frequency respectively; and are the basic pseudorange observation and carrier observation respectively; represents the station-satellite distance; represents the tropospheric delay on the signal propagation path; c represents the speed of light in vacuum; and are the satellite clock error and receiver clock error after re-parameterization respectively; represents the ionospheric delay parameter after re-parameterization of the ionosphere and pseudorange hardware delay corresponding to the first frequency point; γ i is the ionospheric delay amplification factor at each frequency; D r,i and are the receiver inter-frequency bias and satellite differential code bias correction at frequency i respectively; is the floating ambiguity after re-parameterization; ζ i is the hardware bias remaining in the pseudorange equation; δ i is the inter-frequency clock error correction that needs to be additionally considered in the carrier equation, and its essence is the linear combination of the satellite-side phase hardware bias varying with time ; and represent the pseudorange and carrier observation noise including multipath respectively; The tropospheric delay parameters of the above satellites use an empirical model to correct their dry components The wet component uses a wet delay projection function to be converted into the product of the projection function and the zenith tropospheric wet delay T r,zwd That is Using the full-rank model with known coordinates shown in Equation (1) and the tropospheric projection model of Equation (2), combined with precise satellite orbits, satellite clock biases, and satellite phase bias products, the receiver clock bias is estimated in real time Zenith tropospheric wet delay T r,zwd , receiver inter-frequency bias D r,i and the inclined ionospheric delay of each satellite and ambiguity parameters Based on the fixed ambiguity, each reference station further constrains the extraction of the zenith tropospheric wet delay and the reparameterized inclined ionospheric delay of each satellite After that, according to the spatial distribution of the user and the reference station, the atmospheric delay at the user location is interpolated where the subscripts u and r represent the user and different reference stations, respectively; n is the number of reference stations; and are the interpolated slant ionospheric and zenith tropospheric wet delays at the user side, respectively; a r is the interpolation coefficient corresponding to the reference station r; for the ionospheric delay, the interpolation coefficient is calculated based on the difference in the puncture point latitudes and longitudes of each satellite In the formula, and are the differences in the puncture point latitudes and longitudes of the satellite s corresponding to the user and the reference station respectively; for the zenith tropospheric wet delay, according to the difference in the Gauss plane coordinates between the user and the base station, the interpolation coefficients are calculated by the least squares solution using the method of Equation (5).

3. A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement according to claim 1, characterized in that: In step (2), the process of the user-side site constructing a full-rank estimable solution model with atmospheric enhancement includes: Adopt the method of Equation (1). The user-side constructs a full-rank estimable PPP solution model, and uses the atmospheric errors modeled in the above step (1) to enhance the model; the parameters to be estimated are constrained in the form of pseudo-observation equations, thereby shortening the initialization time; for the zenith tropospheric wet delay, its constraint equation is as follows, Among them, represents the variance of the tropospheric pseudo-observations; for the ionospheric delay, since the non-combination PPP model re-parameterizes it during the parameter estimation process, the interpolated values contain the differential code biases at the receiver ends of each reference station. Therefore, unlike the troposphere, the undifferenced ionospheric parameters at the user end cannot be directly constrained. To eliminate the influence of the receiver-end differential code biases, the method of inter-satellite single difference is used to eliminate the influence of the receiver differential code biases, and the PPP is enhanced with the ionospheric enhancement information in the form of inter-satellite single difference. where s and s 0 are the non-reference satellite and the reference satellite, respectively; is the variance of the ionospheric pseudo-observations.

4. A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement according to claim 1, characterized in that: The process of the user-side ambiguity being transformed into ultra-wide lane, wide lane, and narrow lane forms through integer transformation in step (3) includes: Through the atmospheric enhancement solution model in step (2), the uncombined ambiguities at each frequency are solved, and integer transformation is performed through the ultra-wide lane, wide lane, and narrow lane combination coefficients to obtain the ultra-wide lane, wide lane, and narrow lane combined ambiguities and their variance-covariance matrices; assuming that the integer transformation matrices of the ultra-wide lane, wide lane, and narrow lane are D e , D w , and D n , the transformed parameters and their covariance matrix are Among them, and are the parameters to be estimated before and after transformation respectively, and are the variance-covariance matrices before and after transformation respectively; I is the identity matrix, corresponding to the non-ambiguity parameter part.

5. A multi-frequency PPP sequential single-epoch positioning method based on atmospheric error enhancement according to claim 1, characterized in that: In step (4), the process of sequentially fixing the ultra-wide lane, wide lane, and narrow lane ambiguities to obtain the positioning solution under the corresponding ambiguity-fixed state includes: Adopt the LAMBDA algorithm to sequentially fix the ultra-wide lane, wide lane, and narrow lane ambiguities obtained in the above step (3). The fixing method is: (1) First, fix the ultra-wide lane. When the ultra-wide lane meets the Ratio threshold for LAMBDA fixing, use the ambiguity-fixed ultra-wide lane to constrain the remaining parameters to obtain the ultra-wide lane-fixed positioning solution and other parameters; when the Ratio threshold condition is not met, keep the floating-point solution for the current epoch; (2) Extract the wide lane ambiguity part from the parameters in the ultra-wide lane-fixed solution state, and use the LAMBDA method for search and fixing. When the Ratio threshold condition is met, use the ambiguity-fixed wide lane to constrain the remaining parameters to obtain the wide lane-fixed positioning solution and other parameters; when the Ratio threshold condition is not met, keep the ultra-wide lane solution for the current epoch; (3) Extract the narrow-lane ambiguity part from the parameters in the fixed solution state of the wide-lane, and use the LAMBDA method for search and fixation. When the Ratio threshold condition is satisfied, use the narrow-lane with fixed ambiguity to constrain the remaining parameters to obtain the narrow-lane fixed positioning solution; when the Ratio threshold condition is not satisfied, keep the wide-lane solution at the current epoch.

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