A customized weighted ionosphere modeling method applied to PPP-RTK
By introducing a user position-related weight matrix into PPP-RTK and constructing a customized weighted ionospheric model, the model self-consistency problem caused by differences in user spatial distribution is solved, the accuracy and adaptability of ionospheric modeling are improved, and personalized services are achieved.
Patent Information
- Application Number
- CN202510165783.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-14
- Publication Date
- 2025-10-10
- Estimated Expiration
- 2045-02-14
AI Technical Summary
The existing PPP-RTK regional ionospheric modeling method fails to effectively consider the spatial distribution differences of different users, resulting in poor model self-consistency, difficulty in providing personalized customized services, and inability to reasonably reflect the spatiotemporal irregularities of the ionosphere.
A weight matrix related to the user's spatial position is introduced, and a customized ionospheric model is constructed for each user through the weighted least squares method. The ionospheric information weight of the reference station is adjusted to improve the self-consistency and adaptability of the model.
It realizes personalized modeling for different users, improves the accuracy and self-consistency of the ionosphere model, provides a more reasonable reflection of the ionosphere spatial distribution, and improves the positioning accuracy of PPP-RTK.
Smart Images
Figure CN119986700B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and relates to GNSS real-time kinematic precise point positioning (PPP-RTK) technology, and specifically to a customized weighted ionospheric modeling method applied to PPP-RTK. Background Art
[0002] PPP-RTK is a precision positioning technology that achieves comparable performance to network RTK through non-differential absolute positioning. It has become a hot topic in the field of satellite navigation and positioning in recent years. However, regional atmospheric modeling is crucial to PPP-RTK service performance, particularly the regional ionosphere. Due to its irregular temporal and spatial distribution, real-time, high-precision modeling remains challenging.
[0003] Conventional regional ionospheric modeling typically constructs a specific fitting function model based on ionospheric information extracted from regional reference stations. Commonly used models include linear interpolation models, inverse distance interpolation models, Kriging interpolation models, and polynomial fitting models. During the construction of these models, only reference station-related information is considered, without taking into account the spatial distribution differences between different users. This model is a public model, and its construction is only related to the reference station, not the user. Even if no user exists, it does not affect the establishment of the model. In other words, the model is the same for all users, which is obviously unreasonable. It is difficult to adapt to the diverse characteristics of different users and it is difficult to more objectively describe the spatiotemporal irregularities of the ionosphere.
[0004] To address the above problems, the present invention fully considers the differences between different users, introduces weight factors related to spatial position, improves the self-consistency of modeling, realizes personalized modeling for different users, provides customized services for different users, and reasonably reflects the ionospheric spatial distribution of user locations. Summary of the Invention
[0005] To solve the above problems, the present invention discloses a customized weighted ionospheric modeling method applied to PPP-RTK. By introducing a weight matrix related to the user's spatial position on the basis of a conventional regional ionospheric model, the self-consistency of the model is improved, customized modeling for different users is realized, and the irregularity of the spatial distribution of the ionosphere can be more effectively reflected.
[0006] To achieve the above object, the technical solution of the present invention is as follows:
[0007] A customized weighted ionospheric modeling method for PPP-RTK includes the following steps:
[0008] (1) Based on the dual-frequency / multi-frequency non-combined precise point positioning (PPP) floating point solution, the high-precision undifferenced slant ionospheric delay of each reference station is extracted by implementing ambiguity fixation;
[0009] (2) Select a reference satellite as the benchmark, eliminate the hardware bias of the receiver end through inter-satellite single difference, and map the undifferenced slanted ionospheric delay into the inter-satellite single differenced slanted ionospheric delay;
[0010] (3) Construct a surface fitting function model for the inter-satellite single-difference slant ionospheric delay of multiple reference stations in the region;
[0011] (4) Considering the differences in spatial distribution of different users, an independent weight matrix is constructed for each user, and the coefficients of the constructed fitting function model are solved to achieve customized ionospheric modeling for different users.
[0012] Furthermore, in step (1), the process of extracting high-precision undifferenced slant ionospheric delay based on the non-combined PPP model includes:
[0013] For the regional reference station network, a dual-frequency (or multi-frequency) non-combined PPP model is constructed. This model retains atmospheric parameters such as the ionosphere and supports flexible processing of observation information of any number of frequencies. The full-rank mathematical model of its floating-point solution can be expressed as:
[0014]
[0015] In the formula, the superscript s and subscript r represent different satellites and receivers respectively; the subscript j represents different frequency numbers; and are pseudorange and carrier observation values, respectively; is the station-to-star distance; t r and t s are the receiver and satellite clock errors respectively; c represents the speed of light; and T r,w represent the zenith tropospheric wet delay and the corresponding projection function respectively; is the reparameterized undifferenced tilted ionospheric delay; γ j is the ionospheric amplification factor; is the floating point ambiguity; λ j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and satellite respectively.
[0016] Based on the model shown in formula (1), the floating point ambiguity is fixed to an integer using the LAMBDA algorithm, and the centimeter-level reparameterized undifferenced slant ionospheric delay can be obtained. Its specific composition includes the real non-differential ionospheric delay and related hardware bias. The specific expression is as follows:
[0017]
[0018] Where, is the true undifferenced slant ionospheric delay; D r and D s They represent the hardware deviations of the receiver and satellite, respectively; f1 and f2 represent the frequencies corresponding to the first and second frequency points, respectively.
[0019] Furthermore, in step (2), the process of eliminating the hardware bias of the receiver end by the inter-satellite single difference method includes:
[0020] For the reference station network, the satellite hardware bias D in formula (2) is s The impact on all stations is consistent and will not affect the overall modeling effect of the subsequent ionosphere. In contrast, the receiver hardware bias D r Differences often exist, and these effects need to be accounted for before modeling. To this end, a satellite is selected as a reference, and inter-satellite single-difference methods are used to eliminate these effects. During the reference selection process, satellites with higher elevation angles are typically chosen to ensure visibility of the reference satellite. It's important to note that the hardware biases at the receiver end vary for different navigation systems (such as GPS, BDS, and Galileo), so independent reference satellites must be selected for each navigation system.
[0021] After inter-satellite single difference, the ionospheric delay of each satellite pair can be expressed as,
[0022]
[0023] Where, ref represents the reference satellite benchmark; Represents the symbol of the intersatellite single difference operator.
[0024] Furthermore, the process of constructing a surface fitting function model for the regional inter-satellite single-difference tilt ionospheric delay in step (3) includes:
[0025] Compared to tropospheric delay, there is currently no ideal ionospheric projection function. If the slant ionosphere is first mapped to the vertical direction and then the vertical ionospheric delay is modeled, errors of the order of decimeters may be introduced, and the modeling effect will not meet the performance requirements of PPP-RTK. Therefore, for different satellite pairs, a regional interpolation model is directly established for the inter-satellite single-difference slant ionospheric delay.
[0026] Based on the slant ionospheric delay of multiple reference stations in a region, a plane or surface model is usually used to describe the spatial distribution of the ionosphere. Polynomial models are widely used in regional ionosphere modeling. Depending on the redundancy of prior information, polynomial models of different orders can be selected. The third-order polynomial expression is used as an example to illustrate.
[0027]
[0028] Where x r and y r They represent the Gaussian plane coordinates of the measuring station; a i Represents the model coefficient to be determined.
[0029] For a regional reference station network consisting of n stations, a least squares solution model can be constructed.
[0030] V=BX-L (5)
[0031] Where L and V represent the ionosphere and modeling residual vector of the reference station, respectively; B represents the design matrix; and X represents the model coefficient vector to be solved.
[0032] The expressions of L and V are as follows,
[0033]
[0034] The expressions of B and X are as follows,
[0035]
[0036] At this point, only the least squares method needs to be used to determine the model coefficient a i , the regional ionospheric model can be obtained.
[0037] Furthermore, in step (4), the customized modeling process taking into account the spatial distribution differences of different users includes:
[0038] Based on the regional ionosphere fitting model constructed in step (3), the conventional model coefficient determination process usually does not consider the spatial distribution differences of different users, and adopts the equal weight strategy to solve the model coefficient, that is,
[0039] X=(B T B) -1 B T L (8)
[0040] The above model only considers the factors of the reference stations involved in the modeling, and is unrelated to the users. Whether there are users or where they are distributed has no effect on the establishment of the model. Therefore, the conventional model established based on formula (8) is an ionospheric model that is common to all users, that is, the model coefficients are the same for different users. This is obviously unreasonable and difficult to adapt to the differences of users in different regions. In addition, the irregular characteristics of the spatial distribution of the ionosphere are difficult to objectively describe using a specific polynomial model. Even for the stations involved in the modeling, the above common model still has modeling residuals, that is, the self-consistency of the model at the reference station needs to be improved.
[0041] To address these issues, we introduce a user-location-dependent weight matrix P to adjust the weights of ionospheric information from different reference stations. We implement personalized modeling for each user through weighted least squares, while also improving the model's consistency across the modeling sites.
[0042] The weight matrix can be expressed as,
[0043] P=diag[p1,p2,…,p n ] (9)
[0044] Where p i is the weight corresponding to each reference station, and its value is related to the spatial distribution of users.
[0045] Considering the spatial distribution and correlation between users and reference stations, a distance-related weight coefficient is used.
[0046]
[0047] Where, d i is the distance between the user and each reference station; α is the order, usually 1 or 2.
[0048] Furthermore, weighted least squares is used to solve different model coefficients for each user.
[0049] X=(B T PB) -1 B T PL (11)
[0050] By introducing a user-position-related weight matrix into the conventional equal-weighted polynomial model, the closer the reference station is to the user, the greater the weight it is assigned. When the two are infinitely close, the model value is naturally infinitely close to the ionospheric delay of the reference station itself, ensuring that the modeling residual of the modeling site is 0 and improving the self-consistency of the model. In addition, since different weight matrices are established for different users, customized modeling for different users is also achieved.
[0051] The beneficial effects of the present invention include:
[0052] The present invention proposes a customized weighted ionospheric modeling method for PPP-RTK. In the PPP-RTK regional ionospheric modeling, a weight factor related to the user's location is introduced. Compared with the common model established for all users with the conventional equal-weight strategy, the method proposed in the present invention improves the modeling self-consistency at the reference station, realizes personalized modeling for different users, provides customized services for different users, and more reasonably reflects the spatial distribution of the ionosphere at the user's location. BRIEF DESCRIPTION OF THE DRAWINGS
[0053] Figure 1 is a flow chart for implementing the method of the present invention;
[0054] Figure 2 This is a comparison chart of the modeling effects of the Galileo navigation system E03 satellite;
[0055] Figure 3 This is a comparison chart of the modeling effects of the GPS navigation system G07 satellite;
[0056] Figure 4 This is a comparison chart of the modeling effects of the BDS navigation system C39 satellite;
[0057] Figure 5 This is a comparison chart of the modeling effects of different spatially distributed sites. DETAILED DESCRIPTION
[0058] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.
[0059] like Figure 1 As shown, this embodiment discloses a customized weighted ionospheric modeling method applied to PPP-RTK, and the specific steps are as follows:
[0060] Step (1): Extract high-precision slant ionospheric delay based on dual-frequency / multi-frequency non-combined PPP model
[0061] For the regional reference station network, a dual-frequency (or multi-frequency) non-combined PPP model is constructed. This model retains atmospheric parameters such as the ionosphere and supports flexible processing of observation information of any number of frequencies. The full-rank mathematical model of its floating-point solution can be expressed as:
[0062]
[0063] In the formula, the superscript s and subscript r represent different satellites and receivers respectively; the subscript j represents different frequency numbers; and are pseudorange and carrier observation values, respectively; is the station-to-star distance; t r and ts are the receiver and satellite clock errors respectively; c represents the speed of light; and T r,w represent the zenith tropospheric wet delay and the corresponding projection function respectively; is the reparameterized undifferenced tilted ionospheric delay; γ j is the ionospheric amplification factor; is the floating point ambiguity; λ j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and satellite respectively.
[0064] Based on the model shown in formula (1), the floating point ambiguity is fixed to an integer using the LAMBDA algorithm, and the centimeter-level reparameterized undifferenced slant ionospheric delay can be obtained. Its specific composition includes the real non-differential ionospheric delay and related hardware bias, and the specific expression is as follows:
[0065]
[0066] Where, is the true undifferenced slant ionospheric delay; D r and D s They represent the hardware deviations of the receiver and satellite, respectively; f1 and f2 represent the frequencies corresponding to the first and second frequency points, respectively.
[0067] Step (2): Eliminate the hardware bias of the receiver by using the inter-satellite single difference method to construct the satellite-to-slant ionospheric delay
[0068] For the reference station network, the satellite hardware bias D in formula (2) is s The impact on all stations is consistent and will not affect the overall modeling effect of the subsequent ionosphere. In contrast, the receiver hardware bias D r Differences often exist, and these effects need to be accounted for before modeling. To this end, a satellite is selected as a reference, and inter-satellite single-difference methods are used to eliminate these effects. During the reference selection process, satellites with higher elevation angles are typically chosen to ensure visibility of the reference satellite. It's important to note that the hardware biases at the receiver end vary for different navigation systems (such as GPS, BDS, and Galileo), so independent reference satellites must be selected for each navigation system.
[0069] After inter-satellite single difference, the ionospheric delay of each satellite pair can be expressed as,
[0070]
[0071] Where, ref represents the reference satellite benchmark; Represents the symbol of the intersatellite single difference operator.
[0072] Step (3): Constructing regional fitting model for inter-satellite single-difference ionospheric delay of the region
[0073] Compared with tropospheric delay, there is no ideal ionospheric projection function at present. If the slant ionosphere is mapped to the vertical direction first, and then the vertical ionospheric delay is modeled, a decimeter-level error may be introduced, and the modeling effect will be difficult to meet the performance requirements of PPP-RTK. Therefore, for different satellite pairs, a regional interpolation model is directly established for the slant ionospheric delay of the inter-satellite single difference.
[0074] Based on the slant ionospheric delay of multiple reference stations in a region, a certain plane or curved surface model is usually used to describe the spatial distribution of the ionosphere. Polynomial models are widely used in regional ionospheric modeling. According to the prior information redundancy, a polynomial model of different order can be selected. Taking a 3rd order polynomial expression as an example,
[0075]
[0076] In the formula, x r and y r represent the Gaussian plane coordinates of the station; a i represents the model coefficients to be solved.
[0077] For a regional reference station network consisting of n stations, a least squares solution model can be constructed,
[0078] V = BX - L (5)
[0079] In the formula, L and V represent the ionospheric and modeling residual vectors of the reference stations, respectively; B represents the design matrix; X represents the model coefficient vector to be solved.
[0080] The expressions of L and V are as follows,
[0081]
[0082] The expressions of B and X are as follows,
[0083]
[0084] At this point, only the least squares method is used to determine the model coefficients a i , and the regional ionospheric model can be obtained.
[0085] Step (4): Customized modeling considering the spatial distribution difference of different users
[0086] Based on the regional ionospheric fitting model constructed in step (3), the spatial distribution difference of different users is usually not considered in the conventional model coefficient determination process, and the model coefficients are solved by using the equal weight strategy, that is,
[0087] X = (B T B) -1 B T L (8)
[0088] The above model only considers the factors of the reference stations involved in modeling, and is irrelevant to the user, regardless of whether the user exists or not and where the user is distributed, which has no effect on the establishment of the model. Therefore, the conventional model established based on formula (8) is an ionospheric model common to all users, that is, the model coefficients are the same for different users. This is obviously unreasonable and difficult to adapt to the differences of users in different regions. In addition, the irregular characteristics of the spatial distribution of the ionosphere are difficult to objectively describe by a certain polynomial model, and even for the stations involved in modeling, the above common model still has modeling residuals, that is, the self-consistency of the model at the reference stations also needs to be improved.
[0089] In view of the above problems, a weight matrix P related to the user position is introduced to adjust the ionospheric information weight of different reference stations. Through weighted least squares, personalized modeling for different users is realized, and the self-consistency of the model at the modeling stations is improved.
[0090] The weight matrix can be expressed as,
[0091] P = diag[p1, p2, …, p n ] (9)
[0092] In the formula, p i is the weight corresponding to each reference station, which is related to the spatial distribution of the user.
[0093] Considering the spatial distribution and correlation of the user and the reference station, a distance-related weight coefficient is adopted,
[0094]
[0095] In the formula, d i is the distance between the user and each reference station; and α is the order, which is usually 1 or 2.
[0096] Further, the weighted least squares is used to solve different model coefficients for each user,
[0097] X = (B T PB) -1 B T PL (11)
[0098] By introducing a user-position-related weight matrix into the conventional equal-weighted polynomial model, the closer the reference station is to the user, the greater the weight it is assigned. When the two are infinitely close, the model value is naturally infinitely close to the ionospheric delay of the reference station itself, ensuring that the modeling residual of the modeling site is 0 and improving the self-consistency of the model. In addition, since different weight matrices are established for different users, customized modeling for different users is also achieved.
[0099] Attachment Figure 1 It is the basic flow chart of the present invention;
[0100] Attachment Figure 2 ~Attachment Figure 4 A comparison of the modeling results for the E03, G07, and C39 satellites of the Galileo, GPS, and BDS navigation systems, respectively, reveals that compared to conventional models, the proposed model has smaller modeling error magnitudes and fluctuations, and is more accurate than conventional models. Using first- and second-order weighting factors, the accuracy of the E03 satellite increased from 9.7 cm to 4.5 cm and 2.7 cm; the accuracy of the G07 satellite increased from 7.1 cm to 2.9 cm and 1.6 cm; and the accuracy of the C39 satellite increased from 4.6 cm to 1.7 cm and 1.5 cm, significantly improving the ionospheric modeling accuracy of all three navigation systems.
[0101] Attachment Figure 5 It is the accuracy statistics of all 31 test sites. It can be found intuitively that compared with the conventional model, after adopting the method of the present invention, the ionospheric modeling accuracy of different stations is improved to varying degrees, which further verifies the universality of the method of the present invention at different stations.
[0102] It should be noted that the above content merely illustrates the technical idea of the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.
Claims
1. A customized weighted ionospheric modeling method for PPP-RTK, characterized by: The following steps are involved: (1) Based on the dual-frequency / multi-frequency non-combined precise point positioning PPP floating point solution, the high-precision undifferenced slant ionospheric delay of each reference station is extracted by implementing ambiguity fixation; (2) Select a reference satellite as the benchmark, eliminate the hardware bias of the receiver end through inter-satellite single difference, and map the undifferenced slanted ionospheric delay into the inter-satellite single differenced slanted ionospheric delay; (3) Construct a surface fitting function model for the inter-satellite single-difference slant ionospheric delay of multiple reference stations in the region; The process includes: Corresponding to different satellite pairs, a regional interpolation model is directly established for the inter-satellite single-difference slant ionospheric delay; Based on the slant ionospheric delay of multiple reference stations in the region, the spatial distribution of the ionosphere is described using a plane or curved surface model; a third-order polynomial expression is used to illustrate, Where x r and y r They represent the Gaussian plane coordinates of the measuring station; a i represents the model coefficient to be determined; For a regional reference station network consisting of n stations, a least squares solution model is constructed. V=BX-L (2) Where L and V represent the ionosphere and modeling residual vector of the reference station, respectively; B represents the design matrix; X represents the model coefficient vector to be solved; The expressions of L and V are as follows, The expressions of B and X are as follows, At this point, the least squares method is used to determine the model coefficient a i , get the regional ionospheric model; (4) Considering the differences in spatial distribution of different users, an independent weight matrix is constructed for each user, and the coefficients of the constructed fitting function model are solved to achieve customized ionospheric modeling for different users; The customized modeling process that considers the differences in spatial distribution of different users includes: Based on the regional ionosphere fitting model constructed in step (3), the model coefficients are solved using an equal weight strategy, that is, X=(B T B) -1 B T L (5) The user position-related weight matrix P is introduced to adjust the weight of ionospheric information of different reference stations; The weight matrix is expressed as, P=diag[p1,p2,…,p n ] (6) Where p i is the weight corresponding to each reference station, and its value is related to the spatial distribution of users; Considering the spatial distribution and correlation between users and reference stations, a distance-related weight coefficient is used. Where, d i is the distance between the user and each reference station; α is the order, which can be 1 or 2; Furthermore, weighted least squares is used to solve different model coefficients for each user. X=(B T PB) -1 B T PL (8) By introducing a user position-related weight matrix into the conventional equal-weighted polynomial model, the closer the reference station is to the user, the greater the weight it is assigned. When the two are infinitely close, the model value is naturally infinitely close to the ionospheric delay of the reference station itself, ensuring that the modeling residual of the modeling site is 0 and improving the self-consistency of the model.
2. The customized weighted ionospheric modeling method for PPP-RTK according to claim 1, characterized in that: In step (1), the process of extracting high-precision undifferenced slant ionospheric delay based on the non-combined PPP model includes: For the regional reference station network, a dual-frequency / multi-frequency non-combined PPP model is constructed, and the full-rank mathematical model of its floating-point solution is expressed as: In the formula, the superscript s and subscript r represent different satellites and receivers respectively; the subscript j represents different frequency numbers; and are pseudorange and carrier observation values, respectively; is the station-to-star distance; t r and t s are the receiver and satellite clock errors respectively; c represents the speed of light; and T r,w represent the zenith tropospheric wet delay and the corresponding projection function respectively; is the reparameterized undifferenced tilted ionospheric delay; γ j is the ionospheric amplification factor; is the floating point ambiguity; λ j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and satellite respectively; Based on the model shown in formula (9), the LAMBDA algorithm is used to fix the floating point ambiguity to an integer, and the centimeter-level reparameterized undifferenced slant ionospheric delay is obtained. Its specific composition includes the real non-differential ionospheric delay and related hardware bias, and the specific expression is as follows: Where, is the true undifferenced slant ionospheric delay; D r and D s They represent the hardware deviations of the receiver and satellite, respectively; f1 and f2 represent the frequencies corresponding to the first and second frequency points, respectively.
3. The customized weighted ionospheric modeling method for PPP-RTK according to claim 2, characterized in that: In step (2), the process of eliminating the hardware bias of the receiver by the inter-satellite single difference method includes: A certain satellite is selected as a reference, and the inter-satellite single difference method is used to eliminate its influence. Each navigation system selects an independent reference satellite. After inter-satellite single difference, the ionospheric delay of each satellite pair is expressed as, Where, ref represents the reference satellite benchmark; Represents the symbol of the intersatellite single difference operator.