Customized weighted ionosphere modeling method applied to PPP-RTK

Abstract

The invention discloses a customized weighted ionosphere modeling method applied to PPP-RTK. The method comprises the following steps: extracting high-precision non-difference inclined ionosphere delay based on a double-frequency / multi-frequency non-combined precision single-point positioning model; a reference satellite is selected as a benchmark, related hardware deviation of a receiver end is eliminated through inter-satellite single difference, and non-difference tilt ionosphere delay is mapped into inter-satellite single-difference tilt ionosphere delay; constructing a curved surface fitting function model corresponding to each satellite pair; the difference of spatial distribution of different users is considered, an independent weight matrix is constructed for each user, and a model coefficient is solved based on weighted least squares. According to the method, on the basis of conventional equal-weight modeling, weight factors related to user positions are introduced, and different weight matrixes are constructed for different users, so that customized modeling oriented to different users is realized, meanwhile, the self-consistency of the model at a modeling site is also improved, and the spatial change of an ionized layer is objectively described.

Description

Technical Field

[0001] The present invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, relates to GNSS real-time kinematic precise point positioning (PPP-RTK) technology, and specifically relates to a customized weighted ionospheric modeling method applied to PPP-RTK. Background Art

[0002] PPP-RTK is a precision positioning technology that can achieve performance comparable to network RTK in a non-differential absolute positioning manner, and has been a hot topic in the field of satellite navigation and positioning in recent years. Among them, regional atmospheric modeling is the key to the performance of PPP-RTK services, especially the regional ionosphere. Due to its irregular temporal and spatial distribution, real-time high-precision modeling still faces challenges.

[0003] In conventional regional ionosphere modeling, a specific fitting function model is usually constructed based on the ionosphere information extracted from the regional reference station. Commonly used models include linear interpolation model, inverse distance interpolation model, Kriging interpolation model, polynomial fitting model, etc. In the construction process of these models, only the relevant information of the reference station is considered, and the spatial distribution differences of different users are not taken into account. This model is a public model, and its construction is only related to the reference station, not the user. Even if there is no user, it does not affect the establishment of the model, that is, 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 irregular spatiotemporal properties of the ionosphere.

[0004] In response to the above problems, the present invention fully considers the differences between different users, introduces weight factors related to spatial positions, 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 ionosphere 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 ionosphere 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 tilt 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] Further: in step (1), the process of extracting high-precision non-difference tilted 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-satellite 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; j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and the 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] In the formula, 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] Further: 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 There are usually differences, and this part of the impact needs to be deducted before modeling. For this reason, a certain satellite is selected as the benchmark, and the inter-satellite single difference method is used to eliminate its influence. In the benchmark selection process, in order to ensure the visibility of the reference satellite, a satellite with a higher elevation angle is usually selected. It should be noted that the hardware deviations of the receiving end of different navigation systems (such as GPS, BDS, Galileo, etc.) are also different, so it is necessary to select an independent reference satellite 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] Further: the process of constructing a surface fitting function model for the inter-satellite single-difference tilt ionospheric delay of the region in step (3) includes:

[0025] Compared with the tropospheric delay, there is no ideal ionospheric projection function. If the tilted ionosphere is first mapped to the vertical direction and then the vertical ionospheric delay is modeled, it may introduce decimeter-level errors, and the modeling effect will be difficult to meet the performance requirements of PPP-RTK. Therefore, corresponding to different satellite pairs, a regional interpolation model is directly established for the tilted ionospheric delay of the inter-satellite single difference.

[0026] Based on the tilted ionospheric delay of multiple reference stations in the region, a certain plane or surface model is usually used to describe the spatial distribution of the ionosphere. Polynomial models are widely used in regional ionosphere modeling. According to 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] In the formula, x r and r They represent the Gaussian plane coordinates of the measuring station respectively; a i represents the model coefficients to be sought.

[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, we only need to use the least squares method to determine the model coefficient a i , the regional ionospheric model can be obtained.

[0037] Further: In step (4), the customized modeling process taking into account the differences in spatial distribution 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 an 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 has nothing to do with the users. Whether there are users or where the users are distributed 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 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 also needs to be improved.

[0041] To address the above problems, a user location-related weight matrix P is introduced to adjust the weights of ionospheric information at different reference stations. Through weighted least squares, personalized modeling for different users is achieved, while improving the self-consistency of the model at the modeling site.

[0042] The weight matrix can be expressed as,

[0043] P=diag[p1,p2,…,p n ] (9)

[0044] In the formula, 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 position is introduced. Compared with the common model established for all users by the conventional equal-weight strategy, the method proposed by the present invention improves the modeling self-consistency of the model at the reference station, realizes personalized modeling for different users, provides customized services for different users, and more reasonably reflects the ionospheric spatial distribution of the user's position. 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 C39 satellite of the BDS navigation system;

[0057] Figure 5 It is a comparison chart of modeling effects of different sites in spatial distribution. DETAILED DESCRIPTION

[0058] The present invention will be further explained below in conjunction with 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-satellite distance; t r and ts are the receiver and satellite clock errors respectively; c represents the speed of light; and T r,w denote 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; j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and the 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. The specific expression is as follows:

[0065]

[0066] In the formula, is the true undifferenced slant ionospheric delay; D r and D s They represent the hardware deviations of the receiver and the 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 There are usually differences, and this part of the impact needs to be deducted before modeling. For this reason, a certain satellite is selected as the benchmark, and the inter-satellite single difference method is used to eliminate its influence. In the benchmark selection process, in order to ensure the visibility of the reference satellite, a satellite with a higher elevation angle is usually selected. It should be noted that the hardware deviations of the receiving end of different navigation systems (such as GPS, BDS, Galileo, etc.) are also different, so it is necessary to select an independent reference satellite 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): Construct a regional fitting model for the regional inter-satellite single-difference ionospheric delay

[0073] Compared with the tropospheric delay, there is no ideal ionospheric projection function. If the tilted ionosphere is first mapped to the vertical direction and then the vertical ionospheric delay is modeled, it may introduce decimeter-level errors, and the modeling effect will be difficult to meet the performance requirements of PPP-RTK. Therefore, corresponding to different satellite pairs, a regional interpolation model is directly established for the tilted ionospheric delay of the inter-satellite single difference.

[0074] Based on the tilted ionospheric delay of multiple reference stations in the region, a certain plane or surface model is usually used to describe the spatial distribution of the ionosphere. Polynomial models are widely used in regional ionosphere modeling. According to 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.

[0075]

[0076] In the formula, x r and r They represent the Gaussian plane coordinates of the measuring station respectively; a i represents the model coefficients to be sought.

[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] 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.

[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, we only need to use the least squares method to determine the model coefficient a i , the regional ionospheric model can be obtained.

[0085] Step (4): Customized modeling to take into account the differences in spatial distribution of different users

[0086] 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 an equal weight strategy to solve the model coefficient, 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 the modeling, and has nothing to do with the users. Whether there are users or where the users are distributed 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 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 also needs to be improved.

[0089] To address the above problems, a user location-related weight matrix P is introduced to adjust the weights of ionospheric information at different reference stations. Through weighted least squares, personalized modeling for different users is achieved, while improving the self-consistency of the model at the modeling site.

[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, and its value is related to the spatial distribution of users.

[0093] Considering the spatial distribution and correlation between users and reference stations, a distance-related weight coefficient is used.

[0094]

[0095] Where, d i is the distance between the user and each reference station; α is the order, usually 1 or 2.

[0096] Furthermore, 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] Attached Figure 1 It is the basic flow chart of the present invention;

[0100] Attached Figure 2 ~Attached Figure 4 The modeling effects of the E03, G07 and C39 satellites of the Galileo, GPS and BDS navigation systems are compared. It can be found that compared with conventional models, the modeling error magnitude and fluctuation of the model of the present invention are smaller, and the accuracy is better than that of conventional models. After using the first-order and second-order weighting factors, the accuracy of the E03 satellite is improved from 9.7 cm to 4.5 cm and 2.7 cm; the accuracy of the G07 satellite is improved from 7.1 cm to 2.9 cm and 1.6 cm; the accuracy of the C39 satellite is improved from 4.6 cm to 1.7 cm and 1.5 cm. The ionospheric modeling accuracy of the three navigation systems has been significantly improved;

[0101] Attached 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 test sites is improved to varying degrees, which further verifies the universality of the method of the present invention at different test sites.

[0102] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope 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 tilt ionospheric delay of multiple reference stations in the region; (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.

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. This model retains the atmospheric parameters and supports flexible processing of observation information of any number of frequencies. 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-satellite 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; j is the wavelength; B r,j and Represent the inter-frequency deviation of the receiver and the satellite respectively; Based on the model shown in formula (1), 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. The specific expression is as follows: In the formula, 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 1, 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 the reference, and its influence is eliminated by using the inter-satellite single difference method. 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.

4. The customized weighted ionospheric modeling method for PPP-RTK according to claim 1, characterized in that: In step (3), the process of constructing a surface fitting function model for the regional inter-satellite single-difference tilt ionospheric delay 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 tilted ionospheric delay of multiple reference stations in the 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 ionosphere modeling. According to the redundancy of prior information, polynomial models of different orders are selected. The third-order polynomial expression is used as an example to illustrate. In the formula, x r and r They represent the Gaussian plane coordinates of the measuring station respectively; a i represents the model coefficient to be sought; For a regional reference station network consisting of n stations, a least squares solution model is constructed. V=BX-L (5) 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, we only need to use the least squares method to determine the model coefficient a i , and obtain the regional ionospheric model.

5. The customized weighted ionospheric modeling method for PPP-RTK according to claim 1, characterized in that: In step (4), the customized modeling process that takes into account 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 (8) The weight matrix P related to the user's position is introduced to adjust the weight of the ionospheric information of different reference stations; personalized modeling for different users is achieved through weighted least squares, while improving the self-consistency of the model at the modeling site; The weight matrix is ​​expressed as, P=diag[p1,p2,…,p n ] (9) In the formula, 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, usually 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 (11) 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.

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