A reference-unified slant-path ionospheric model

Abstract

The application discloses a benchmark-unified slant-path ionospheric model and relates to the technical field of satellite navigation precise positioning. The benchmark-unified slant-path ionospheric model comprises the following steps: S1, extracting ionospheric observation values of ambiguity fixing; S2, selecting a transfer benchmark and recovering ionospheric observations of non-visible satellites; and S3, slant-path ionospheric grid modeling. The benchmark-unified slant-path ionospheric model uses the recovered ionospheric observations of non-visible satellites to complete. For the ionospheric observations to be recovered, we select the ionospheric delay of the nearest neighbor station of the same satellite as the approximation, wherein, considering the influence of the receiver bias, the receiver bias benchmark is unified by selecting multiple transfer satellites, and the improved regional slant-path ionospheric modeling method increases the number of broadcast satellites.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and precise positioning technology, specifically to a standardized oblique path ionospheric model. Background Technology

[0002] High-precision positioning technology for satellite navigation has undergone multiple generations of updates and developments, from Real-Time Differential Dynamic Positioning (RTK), Precise Point Positioning (PPP and PPP-AR), Network RTK, to the latest emerging Wide Area Instantaneous Precise Positioning (PPP-RTK) technology. Among these, PPP-RTK technology retains the flexibility of PPP while also possessing the fast convergence capability of Network RTK, making it one of the current research hotspots in GNSS positioning technology. High-precision prior ionospheric information helps improve the convergence time of PPP-RTK, with a common approach being the use of a slanted path ionospheric model.

[0003] Due to the diffuse nature of the ionosphere, the extracted station-satellite ionospheric delay absorbs receiver-related biases. To eliminate the influence of receiver biases in ionospheric products, traditional slant-path ionospheric models only model common-view satellites within the reference network. This strategy cannot fully utilize all ionospheric information, reduces the number of broadcast satellites, and thus limits the effectiveness of PPP-RTK positioning. In view of this, we propose a benchmark-unified slant-path ionospheric model. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a standardized oblique path ionospheric model, which solves the problems mentioned in the background section.

[0006] (II) Technical Solution

[0007] To achieve the above objectives, the present invention provides the following technical solution: a standardized oblique path ionospheric model, wherein the ionospheric model includes the following steps:

[0008] S1. Extract ionospheric observations with fixed ambiguity, collect and organize existing known parameters, and then extract the ionospheric delay. The ionospheric observations include the original observations, which are denoted as:

[0009]

[0010] S2. Select the transfer reference and recover ionospheric observations from non-visible satellites. Assume there are n stations r1, r2, ..., r in the reference network. n m satellites s1, s2, ..., s m ;

[0011] S3. Oblique path ionospheric grid modeling: After the ionospheric observations of non-visible satellites are restored, the ionospheric observations of all stations and satellites are known. The ionospheric information of m satellites is modeled and broadcast.

[0012] Optionally, in S1, P and L are pseudorange and carrier observations, i is a frequency point, r is a receiver, s is a satellite, ρ is the station-satellite distance, c is the speed of light in vacuum, and dt r and dt s For receiver and satellite clock bias, T is tropospheric delay, I is ionospheric delay, λ is wavelength, and N is ambiguity. and For the observation noise of pseudorange and carrier, the b r and b s For the code hardware delay between the receiver and the satellite, the B r and B s For the carrier phase hardware delay of the receiver and the satellite.

[0013] Optionally, the known parameters include precision orbitals, clock errors, and upd products.

[0014] Optionally, the expression for the ionospheric delay is:

[0015]

[0016] The To extract the biased ionospheric delay, the The tropospheric dry delay, the The tropospheric wet delay, the and d r，1 It is the upd value of the satellite and receiver at the f1 frequency point, the DCB r，12 and DCB values ​​for the receiver and satellite,

[0017] Optionally, S2 further includes: restoring r n to s m The ionospheric observations are expressed by the following formula: For the extracted polarized ionosphere, r′ is the station closest to r, and s i Let i = 1, ..., k be the k selected transfer satellites. The accuracy of the ionospheric observation recovery is characterized by the difference between the recovered value and the true value, where the true value is:

[0018] Optionally, the accuracy of the recovered ionospheric observations is:

[0019]

[0020] The accuracy consists of two parts:

[0021] One part is the inter-station ionospheric difference for specific satellites;

[0022] The other part is the average inter-station ionospheric difference of the satellite.

[0023] Optionally, S3 further includes: modeling using a first-order polynomial:

[0024]

[0025] Where (φ r ,λ r (φ0,λ0) represents the latitude and longitude of the reference station r, (φ0,λ0) represents the latitude and longitude of the regional center, and a0, a1, a2, a3 represent the coefficients to be fitted.

[0026] Optionally, S3 further includes: projecting the residuals of each station onto the grid points using inverse distance weighting. Where d r Let r be the distance from the reference station to the grid, N be the number of stations participating in the modeling, and w be the distance from the reference station r to the grid. r The weight of the reference station r.

[0027] (III) Beneficial Effects

[0028] This invention provides a standardized oblique path ionospheric model. It offers the following advantages:

[0029] (1) The slant path ionospheric model of this benchmark is supplemented by restoring ionospheric observations from non-visible satellites. For the ionospheric observations that need to be restored, we select the ionospheric delay of the same satellite from the nearest neighbor station as an approximation. Considering the influence of receiver bias, we select multiple transmission satellites to achieve consistency of the receiver bias benchmark.

[0030] (2) The benchmark-unified oblique path ionospheric model and the improved regional oblique path ionospheric modeling method increase the number of satellites broadcast. Using the traditional oblique path ionospheric model, the percentage of satellites broadcast by GPS, Galileo, and BeiDou-3 systems is only 75.9%, 77.3%, and 76.0%, respectively. Using the improved oblique path ionospheric model, the percentage of satellites broadcast by GPS, Galileo, and BeiDou-3 systems increases to 93.0%, 93.9%, and 92.9%, respectively. Attached Figure Description

[0031] Figure 1 This is a flowchart of the regional oblique path ionosphere modeling method of the present invention;

[0032] Figure 2 This is a schematic diagram illustrating the recovery of ionospheric observations from non-visible satellites according to the present invention.

[0033] Figure 3 This invention provides a comparison of the accuracy of the traditional oblique path ionospheric model and the improved oblique path ionospheric model.

[0034] Figure 4 This is a scatter plot and a fitted straight line for this invention.

[0035] Figure 5 For the present invention Figure 4 Enlarged view of the dashed box;

[0036] Figure 6 The positioning errors of the E / N / U directions of this invention are measured in 1, 5, 10, and 60 minutes.

[0037] Figure 7 The positioning results of PPP, PPP-RTK(C), and PPP-RTK(M) in this invention;

[0038] Figure 8 This is a comparison chart of the total number of satellites and the number of co-viewed satellites under different systems of this invention;

[0039] Figure 9 A comparison chart showing the total number of satellites under different systems and the number of satellites broadcast by the improved oblique path ionospheric model.

[0040] In the picture: Figure 3 The value in square brackets is the average precision. Figure 7 The NAUG in the middle represents the number of satellites with ionospheric enhancement information, and the shaded area indicates that the NAUG of PPP-RTK(C) and PPP-RTK(M) are different; Figure 8 The numbers in square brackets indicate the ratio of shared satellites to the total number; Figure 9 The numbers in square brackets indicate the ratio of satellites broadcast to the total number of satellites. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Please see Figures 1-9 This invention provides a technical solution: a benchmark-unified oblique path ionospheric model, the ionospheric model comprising the following steps:

[0043] S1. Extract ionospheric observations with fixed ambiguity, collect and organize existing known parameters, and then extract the ionospheric delay. The ionospheric observations include the original observations, which are denoted as:

[0044]

[0045] Where P and L are pseudorange and carrier observations, i is the frequency point, r is the receiver, s is the satellite, ρ is the station-satellite distance, c is the speed of light in vacuum, and dt is the distance between the satellite and the station. r and dt s Here, T is the receiver and satellite clock bias, I is the tropospheric delay, λ is the wavelength, and N is the ambiguity. and For the observation noise of pseudorange and carrier, b r and b s For the code hardware delay between the receiver and the satellite, B r and B s For the carrier phase hardware delay of the receiver and the satellite.

[0046] In this embodiment, the known parameters include precise orbit, clock bias, and upd product. By statistically analyzing these known parameters, the wide-lane and narrow-lane ambiguities can be fixed and converted into integer ambiguity values ​​for each frequency point. Simultaneously, the satellite clock bias and tropospheric wet delay can be accurately estimated, and the upd value for each frequency point can also be converted from the upd values ​​of the wide-lane and narrow-lane ambiguities.

[0047] The expression for ionospheric delay is:

[0048]

[0049] To extract the biased ionospheric delay, As the tropospheric dry delay, it can be accurately modeled using classical models. This is the tropospheric wet delay. and d r，1 It is the upd value of the satellite and receiver at the f1 frequency, DCB r，12 and DCB values ​​for the receiver and satellite,

[0050] S2. Select the transfer reference and recover ionospheric observations from non-visible satellites. Assume there are n stations r1, r2, ..., r in the reference network. n m satellites s1, s2, ..., s mTo fill in the gaps, we use the recovery of ionospheric observations from non-visible satellites. For the ionospheric observations that need to be recovered, we select the ionospheric delay of the same satellite from the nearest neighbor station as an approximation. Considering the influence of receiver bias, we select multiple transfer satellites to achieve consistency of the receiver bias reference.

[0051] Restore r n to s m The ionospheric observations are expressed by the following formula: For the extracted polarized ionosphere, r′ is the station closest to r, and s i ,i=1,…k represents the k selected transfer satellites. The accuracy of ionospheric observation recovery is characterized by the difference between the recovered value and the true value, where the true value is: The choice of satellite for transmission greatly affects the accuracy of ionospheric observation recovery.

[0052] The accuracy of the ionospheric observation recovery is:

[0053]

[0054] Accuracy consists of two parts:

[0055] One part is the inter-station ionospheric difference for a specific satellite, which is a fixed value;

[0056] The other part is the average inter-station ionospheric difference of the transfer satellite, which can be minimized by selecting the transfer satellite. This optimal satellite can be expressed as:

[0057]

[0058] It is worth noting that the extracted ionospheric observations are all biased. In order to eliminate the influence of satellite and receiver bias in the biased ionosphere, a DD-ION method based on double-difference observations is proposed.

[0059]

[0060] Where ddI represents the value of DD-ION, and |·| is the absolute value.

[0061] The STD value of ddI is affected by ionospheric residuals, and therefore can be used as an indicator for evaluating ionospheric residuals. There are two methods for calculating STD:

[0062] Method 1: Calculate the STD for all values, which represents the ionospheric error of any satellite pair;

[0063] Method 2: Calculate the STD of the mean for each epoch, which represents the average ionospheric error of all satellite pairs.

[0064] To further investigate the influencing factors of ionospheric residuals, the total number of electrons on the oblique path (STEC) was projected onto the vertical path (VTEC). Where MF represents the projection function, and (φ,λ) are the latitude and longitude coordinates of the satellite-receiver path at the thin-layer puncture point. el represents the satellite elevation angle. Within a local reference network, the elevation angles of the satellite to different stations are very similar. Based on the above information, the formula can be transformed into:

[0065]

[0066]

[0067] The target expression is monotonically decreasing within the available interval, therefore it can be known that... The minimum value is obtained at this time. Therefore, we tend to choose satellites with large elevation angles. At the same time, considering that the PPP filter solution has a convergence process, the ionospheric accuracy is limited in the initial few epochs with fixed ambiguity, so the number of epochs with fixed ambiguity is also taken into consideration.

[0068] S3. Oblique-path ionospheric grid modeling: After recovering the ionospheric observations of non-visible satellites, the ionospheric observations of all stations and satellites are known, and the ionospheric information of m satellites can be successfully modeled and broadcast. Due to the small modeling area, the homogeneity and correlation of the ionosphere are strong, and modeling is performed using a first-order polynomial:

[0069]

[0070] Where (φ r ,λ r (φ0,λ0) represents the latitude and longitude of the reference station r, (φ0,λ0) represents the latitude and longitude of the regional center, and a0, a1, a2, a3 represent the coefficients to be fitted.

[0071] The residuals of each station are projected onto the grid points using inverse distance weighting: Where d r Let r be the distance from the reference station to the grid, N be the number of stations participating in the modeling, and w be the distance from the reference station r to the grid. r The weight of the reference station r is used; the final broadcast format is shown in the table below:

[0072]

[0073] Where *Nsat and Ngrid represent the number of satellites broadcast and the number of grids, respectively.

[0074] In this invention, selecting multiple transmission satellites that meet the requirements of an elevation angle greater than 40 degrees and a fixed ambiguity of more than 40 epochs can effectively ensure the accuracy of the ionospheric recovery value.

[0075] The improved regional oblique path ionospheric modeling method increases the number of satellites broadcast. Using the traditional oblique path ionospheric model, the percentage of satellites broadcast by GPS, Galileo, and BeiDou-3 systems is only 75.9%, 77.3%, and 76.0%, respectively. Figure 8 As shown; using the improved oblique path ionospheric model, the percentage of satellites broadcast by the GPS, Galileo, and BeiDou-3 systems increased to 93.0%, 93.9%, and 92.9%, respectively. Figure 9 As shown.

[0076] The improved regional oblique path ionospheric modeling method still maintains good product accuracy. Accuracy evaluation of the generated ionospheric products was conducted using five user stations. The traditional oblique path ionospheric model had an average accuracy of 0.046m, while the improved oblique path ionospheric model had an average accuracy of 0.053m. Figure 3 As shown, the improved oblique path ionospheric model not only broadcasts more ionospheric information but also ensures product accuracy.

[0077] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A standardized oblique path ionospheric model, characterized in that: The ionosphere model includes the following steps: S1. Extract ionospheric observations with fixed ambiguity, collect and organize precise orbit, clock error, and UPD product parameters, and then extract ionospheric delay. The ionospheric observations include the original observations, which are denoted as: ； and For pseudorange and carrier observations, For frequency points, For the receiver, For satellites, The distance to the star station. The speed of light in a vacuum. and For receiver and satellite clock bias, For tropospheric delay, For ionospheric delay, For wavelength, For ambiguity, and For pseudorange and carrier observation noise, and For the hardware delay of the code between the receiver and the satellite, and For the carrier phase hardware delay between the receiver and the satellite; S2. Select the reference point and recover ionospheric observations from non-visible satellites, assuming there are n stations in the reference network. m satellites The ionospheric observations of non-visible satellites are used to fill the gaps. For the ionospheric observations that need to be recovered, the ionospheric delay of the same satellite at the nearest neighbor station is selected as an approximation. In addition, considering the influence of receiver bias, multiple transmission satellites are selected to achieve consistency of the receiver bias reference. S2 further includes: recovery arrive The ionospheric observations are expressed by the following formula: , For the extraction of the polarized ionosphere, Distance The nearest monitoring station, For the selected k transfer satellites, the accuracy of ionospheric observation recovery is characterized by the difference between the recovered values ​​and the true values, where the true values ​​are: ; This refers to the nth station within the reference network; For the m-th satellite in the reference network; formula definition; The accuracy of the recovered ionospheric observations is: ； The accuracy consists of two parts: One part is the inter-station ionospheric difference for specific satellites; The other part is the average inter-station ionospheric difference of the satellite; S3. Oblique path ionospheric grid modeling: After the ionospheric observations of non-visible satellites are restored, the ionospheric observations of all stations and satellites are known. The ionospheric information of m satellites is modeled and broadcast.

2. The benchmark-unified oblique path ionospheric model according to claim 1, characterized in that: The expression for the ionospheric delay is: ； The To extract the biased ionospheric delay, the The tropospheric dry delay, the The tropospheric wet delay, the and It is the satellite and receiver in The upd value at the frequency point, the and DCB values ​​for the receiver and satellite, , .

3. The baseline-unified oblique path ionospheric model according to claim 1, characterized in that: The S3 further includes: modeling using a first-order polynomial: ； in The latitude and longitude of the reference station r The latitude and longitude of the regional center The coefficients are to be fitted.

4. A benchmark-unified oblique path ionospheric model according to claim 3, characterized in that: S3 further includes: projecting the residual of each station onto the grid points using inverse distance weighting. ,in Let r be the distance from the reference station to the grid, and N be the number of stations participating in the modeling. The weight of the reference station r.

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