GNSS-TEC projection function estimation method with additional azimuth angle parameter

Abstract

A GNSS-TEC projection function estimation method with additional azimuth angle parameters comprises the following steps: obtaining observation data of a plurality of GNSS monitoring stations, and then extracting STEC from the observation data; the IPP point position with the satellite elevation angle larger than 70 degrees and the IPP point position with the satellite elevation angle smaller than 40 degrees are obtained respectively, and then satellites with the satellite elevation angle larger than 70 degrees and satellites with the satellite elevation angle smaller than 40 degrees located at the same IPP point position at the same moment are matched; projecting the STEC of the IPP point position of which the satellite elevation angle is greater than 70 degrees to the zenith direction to obtain a VTEC, and then calculating the STEC projection function value MFV of the IPP point position of which the satellite elevation angle is less than 40 degrees according to the corresponding VTEC; and obtaining an ionosphere projection conversion model, and solving to obtain a to-be-estimated coefficient of the projection function model of the additional azimuth angle parameter. According to the method, the TEC projection conversion error of the ionized layer is relatively small under the condition of a low satellite elevation angle.

Description

Technical Field

[0001] The invention relates to an improvement of an ionospheric delay error correction technology, belongs to the field of GNSS data processing, and in particular to a GNSS-TEC projection function estimation method with an additional azimuth parameter. Background Art

[0002] Ionospheric delay is one of the main error sources that affect the performance of the Global Navigation Satellite System (GNSS). Accurate ionospheric error correction plays an important role in improving the positioning accuracy of single-frequency GNSS users and shortening the convergence time of GNSS precise positioning. At present, eliminating or weakening the influence of the ionosphere on GNSS signals through ionospheric TEC modeling is an important way to correct ionospheric delay errors. High-precision ionospheric delay correction models are helpful to promote the development of satellite navigation technology. The GNSS-TEC projection function is an important factor affecting the accuracy of the construction and application of ionospheric delay correction models. When the satellite elevation angle is 20°, the vertical total electron content (VerticalTEC, VTEC) at the zenith direction of the ionospheric pierce point (IPP) at different azimuths can reach 12TECu in the slant total electron content STEC (Slant TEC) projection, and the difference is the largest in the north-south direction and the smallest in the east-west direction. The commonly used projection function based on the isotropic assumption of ionospheric TEC ignores the differences in ionospheric changes at different azimuths, resulting in GNSS-TEC (Total Electron Content) Under low altitude angle conditions, the ionospheric delay correction error obtained by projection transformation is large.

[0003] A Chinese patent application with application number CN201110444513.8 and application date December 27, 2011 discloses a Beidou navigation system ionospheric delay estimation method, the method comprising: a rough longitude and latitude calculation step, in which a Beidou navigation receiver calculates satellite positions and pseudoranges according to satellite ephemeris to obtain rough longitude and latitude position information of the receiver; a penetration point longitude and latitude calculation step, in which the penetration point longitude and latitude information of the participating positioning satellites is calculated according to the obtained rough longitude and latitude position information and the position information of the participating positioning satellites; an ionospheric delay correction step, in which a grid point containing a penetration point and the ionospheric correction delay information of the penetration point are determined according to the received grid ionospheric delay information sent by the GEO satellite of the Beidou satellite navigation system and the longitude and latitude information of the penetration point; and an accurate longitude and latitude calculation step, in which the observation equation of the Beidou navigation receiver is corrected according to the ionospheric correction delay information of the penetration point to calculate the accurate longitude and latitude. After adopting this technical solution, the grid ionospheric information of the GEO satellite ephemeris of the Beidou navigation system can be used to reduce the ionospheric error and improve the navigation positioning accuracy. However, the above solution does not solve the problem of large errors in the ionospheric delay correction obtained by projection conversion at low altitude angles.

[0004] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of this patent application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0005] The purpose of the present invention is to overcome the problem in the prior art that the ionospheric delay correction error obtained by projection conversion at low altitude angles is large, and a GNSS-TEC projection function estimation method with additional azimuth parameters is provided. The GNSS-TEC projection function estimation method with additional azimuth parameters comprises the following steps:

[0006] The first step is to use GNSS observation data to extract clean STEC information without satellite and receiver differential code bias DCB;

[0007] The second step is to obtain the ionospheric intersection point IPP positions with satellite elevation angles greater than 70° and the IPP point positions with satellite elevation angles less than 40° for each satellite at multiple times, and then match the satellites with satellite elevation angles greater than 70° and less than 40° at the same IPP point position at the same time to obtain multiple groups of high-low matching "conjugate" IPP point groups;

[0008] Step 3: Project the STEC with satellite elevation angle greater than 70° in each high-low conjugate IPP point group to the zenith direction to obtain VTEC, and then calculate the projection function value MFV at low satellite elevation angle based on the STEC with satellite elevation angle less than 40°;

[0009] Step 4: Combine the projection function value MFV to build the GNSS-TEC ionospheric projection function model with additional azimuth parameters;

[0010] The fifth step is to solve the estimated coefficients of the GNSS-TEC ionospheric projection function model with additional azimuth parameters based on the least squares method in the latitude band, and then substituted the altitude angle, azimuth angle and local time of the IPP point into the GNSS-TEC ionospheric projection function model with additional azimuth parameters to obtain the APMF projection function values ​​at different low altitude angles.

[0011] In the first step, GNSS observation data is used to extract clean STEC information without satellite and receiver differential code bias DCB, wherein the GNSS observation data sampling epoch interval is selected to be 30s and the satellite cutoff elevation angle is 10°.

[0012] In the second step, the satellites with a satellite elevation angle greater than 70° and the satellites with a satellite elevation angle less than 40° at the same IPP point position at the same time are matched to obtain multiple sets of high-low matching "conjugate" IPP point groups. Specifically, it is assumed that the longitude and latitude of the two GNSS station-satellite lines of sight at the ionospheric piercing point at the same time are If the distance relationship between two points meets the following conditions, then these two puncture points are "conjugate" puncture points, and the "conjugate" puncture points are the high-low matching IPP point group, and the conditions are as follows:

[0013]

[0014] In the third step, the STEC with a satellite elevation angle greater than 70° in each high-low "conjugate" IPP point group is projected to the zenith direction to obtain VTEC, and then the projection function value MFV at a low satellite elevation angle is calculated based on the STEC with a satellite elevation angle less than 40°. The specific calculation formula is as follows:

[0015]

[0016] In the fourth step, a GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, as follows:

[0017]

[0018] Where E′ is the satellite altitude angle at the IPP point in the ionosphere, ω is the GNSS satellite azimuth, t is the local time at the IPP point, E0, E 1，n , E 2，n , E 3，m , E 4，m is the estimated coefficient of the APMF projection function, n and m are the APMF coefficient orders, n max With m max is the maximum order of coefficients.

[0019] In the fourth step, a GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, including local time, altitude angle, and azimuth angle as parameters.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] 1. In a GNSS-TEC projection function estimation method with additional azimuth parameters of the present invention, the STEC at the IPP point with an altitude angle greater than 70° is first projected to the zenith direction as the "true value" of VTEC, and the projection function value MFV at the ionospheric puncture point at a low altitude angle is calculated with time, altitude angle, azimuth angle, longitude, and latitude. At the same time, the projection function introduces satellite azimuth and local time as parameters, which can effectively reflect the anisotropic change characteristics of the ionosphere. The projection function value calculated by the APMF projection function model can greatly approximate the true value of the projection function at different azimuths and times, and can ensure a high projection conversion accuracy. Therefore, the ionospheric delay correction error obtained by the projection conversion at a low altitude angle of the present invention is small.

[0022] 2. In the GNSS-TEC projection function APMF estimation method with additional azimuth parameters of the present invention, the influence of satellite azimuth, local time at IPP point and satellite altitude angle at IPP point on the ionospheric projection function is taken into account, and the relationship between the ionospheric projection function and the satellite azimuth, local time at IPP point and satellite altitude angle at IPP point is analyzed to establish a high-precision GNSS TEC projection function. Then, the APMF projection function can be used to accurately calculate the STEC in the station-satellite direction, thereby shortening the positioning convergence time in precise positioning.

[0023] 3. In the GNSS-TEC projection function estimation method with additional azimuth parameters of the present invention, APMF takes into account the spatial azimuth change of the ionosphere in the north-south direction where the ionosphere gradient difference is large, and ensures that it is consistent with SLM in the east-west direction where the ionosphere gradient difference is small, effectively ensuring the projection conversion accuracy. The APMF projection function can take into account the changes of the ionosphere at different azimuths and places on the basis of the classic SLM projection function. Therefore, the present invention has accurate calculation and high conversion accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart of the present invention.

[0025] Figure 2 It is a diagram showing the variation of MFV with azimuth in the present invention. DETAILED DESCRIPTION

[0026] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0027] See also Figure 1 to Figure 2 , a GNSS-TEC projection function estimation method with additional azimuth parameters, the GNSS-TEC projection function estimation method with additional azimuth parameters comprising the following steps:

[0028] The first step is to use GNSS observation data to extract clean STEC information without satellite and receiver differential code bias DCB;

[0029] The second step is to obtain the ionospheric intersection point IPP positions with satellite elevation angles greater than 70° and the IPP point positions with satellite elevation angles less than 40° for each satellite at multiple times, and then match the satellites with satellite elevation angles greater than 70° and less than 40° at the same IPP point position at the same time to obtain multiple groups of high-low matching "conjugate" IPP point groups;

[0030] Step 3: Project the STEC with satellite elevation angle greater than 70° in each high-low conjugate IPP point group to the zenith direction to obtain VTEC, and then calculate the projection function value MFV at low satellite elevation angle based on the STEC with satellite elevation angle less than 40°;

[0031] Step 4: Combine the projection function value MFV to build the GNSS-TEC ionospheric projection function model with additional azimuth parameters;

[0032] The fifth step is to solve the estimated coefficients of the GNSS-TEC ionospheric projection function model with additional azimuth parameters based on the least squares method in the latitude band, and then substituted the altitude angle, azimuth angle and local time of the IPP point into the GNSS-TEC ionospheric projection function model with additional azimuth parameters to obtain the APMF projection function values ​​at different low altitude angles.

[0033] The meaning of the APMF projection function value is an additional AzimuthParameter Mapping Function.

[0034] In the first step, GNSS observation data is used to extract clean STEC information without satellite and receiver differential code bias DCB, wherein the GNSS observation data sampling epoch interval is selected to be 30s and the satellite cutoff elevation angle is 10°.

[0035] In the second step, the satellites with a satellite elevation angle greater than 70° and the satellites with a satellite elevation angle less than 40° at the same IPP point position at the same time are matched to obtain multiple sets of high-low matching "conjugate" IPP point groups. Specifically, it is assumed that the longitude and latitude of the two GNSS station-satellite lines of sight at the ionospheric piercing point at the same time are If the distance relationship between two points meets the following conditions, then these two puncture points are "conjugate" puncture points, and the "conjugate" puncture points are the high-low matching IPP point group, and the conditions are as follows:

[0036]

[0037] In the third step, the STEC with a satellite elevation angle greater than 70° in each high-low "conjugate" IPP point group is projected to the zenith direction to obtain VTEC, and then the projection function value MFV at a low satellite elevation angle is calculated based on the STEC with a satellite elevation angle less than 40°. The specific calculation formula is as follows:

[0038]

[0039] In the fourth step, a GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, including local time, altitude, azimuth, longitude, and latitude as parameters, as follows:

[0040]

[0041] Where E′ is the satellite altitude angle at the IPP point in the ionosphere, ω is the GNSS satellite azimuth, t is the local time at the IPP point, E0, E 1，n , E 2，n , E 3，m , E 4，m is the estimated coefficient of the APMF projection function, n and m are the APMF coefficient orders, n max With m max is the maximum order of coefficients.

[0042] In the fifth step, the APMF projection function values ​​at different low altitude angles are calculated by using the least square method in different latitude bands.

[0043] The supplementary description of the present invention is as follows:

[0044] When the satellite elevation angle decreases, the larger the value of the additional azimuth constraint term, the greater the difference between it and the traditional projection function. It can be seen that APMF will effectively take into account the ionospheric characteristics with large differences in TEC projections in different azimuths under low altitude conditions. APMF and verification analysis are determined based on GNSS TEC simulation and measured data. The results show that the projection function value calculated by the APMF projection function model can guarantee a high GNSS TEC projection conversion accuracy to a great extent at different azimuths and times.

[0045] Embodiment 1:

[0046] A GNSS-TEC projection function estimation method with additional azimuth parameters, the GNSS-TEC projection function estimation method with additional azimuth parameters comprising the following steps:

[0047] The first step is to use GNSS observation data to extract clean STEC information without satellite and receiver differential code bias DCB;

[0048] The second step is to obtain the ionospheric intersection point IPP positions with satellite elevation angles greater than 70° and the IPP point positions with satellite elevation angles less than 40° for each satellite at multiple times, and then match the satellites with satellite elevation angles greater than 70° and less than 40° at the same IPP point position at the same time to obtain multiple groups of high-low matching "conjugate" IPP point groups;

[0049] Step 3: Project the STEC with satellite elevation angle greater than 70° in each high-low conjugate IPP point group to the zenith direction to obtain VTEC, and then calculate the projection function value MFV at low satellite elevation angle based on the STEC with satellite elevation angle less than 40°;

[0050] Step 4: Combine the projection function value MFV to build the GNSS-TEC ionospheric projection function model with additional azimuth parameters;

[0051] The fifth step is to solve the estimated coefficients of the GNSS-TEC ionospheric projection function model with additional azimuth parameters based on the least squares method in the latitude band, and then substituted the altitude angle, azimuth angle and local time of the IPP point into the GNSS-TEC ionospheric projection function model with additional azimuth parameters to obtain the APMF projection function values ​​at different low altitude angles.

[0052] Embodiment 2:

[0053] Embodiment 2 is substantially the same as Embodiment 1, except that:

[0054] Assume that at the same time, the longitude and latitude of the two GNSS station-satellite lines of sight at the ionospheric piercing point are If the distance relationship between two points satisfies the following conditions, then these two puncture points are conjugate puncture points, and the conjugate puncture points are the high-low matching IPP point group, and the conditions are as follows:

[0055]

[0056] Embodiment 3:

[0057] Embodiment 3 is substantially the same as Embodiment 1, except that:

[0058] The VTEC1 obtained by projecting the STEC1 of the IPP point position with a satellite altitude angle greater than 70° in each high-low matching IPP point group to the zenith direction is obtained, and then the STEC2 projection function MFV of the IPP point position with a satellite altitude angle less than 40° is calculated according to VTEC1. The VTEC1 projected to the zenith direction with a high satellite altitude angle (satellite altitude angle greater than 70°) is selected as the reference value, which is a comprehensive consideration of the factors of accuracy and quantity. Accuracy means that when the satellite altitude angle is high, the VTEC obtained by projecting STEC to the zenith direction is relatively accurate, and the quantity means that the amount of data at the high satellite altitude angle is relatively small. Therefore, the VTEC1 projected to the zenith direction with a satellite altitude angle greater than 70° is selected as the reference value after comprehensive consideration. The specific calculation formula is as follows:

[0059]

[0060] Embodiment 4:

[0061] Embodiment 4 is substantially the same as Embodiment 1, except that:

[0062] The GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, as follows:

[0063]

[0064] Where E′ is the satellite altitude angle at the IPP point in the ionosphere, ω is the GNSS satellite azimuth, t is the local time at the IPP point, E0, E 1，n , E 2，n , E 3，m , E 4，m is the estimated coefficient of the APMF projection function, n and m are the APMF coefficient orders, n max With m max is the maximum order of coefficients;

[0065] The GNSS-TEC ionospheric projection function with additional azimuth parameters includes local time, altitude and azimuth as parameters; the APMF projection function is divided into different latitude bands at intervals of 5° to calculate the projection function coefficients; due to the lack of observation distribution within the azimuth range of [-45°, 45°] of GNSS satellites, it is recommended to impose a thin layer projection function MSLM value constraint within the azimuth range of [-45°, 45°] when using this method in practice.

[0066] Embodiment 5:

[0067] Embodiment 5 is substantially the same as Embodiment 1, except that:

[0068] Considering that the ionosphere has certain differences in different latitudes, in order to effectively compare the effects of different latitudes, the data in China are divided into low-latitude areas (latitude <30°) and mid-latitude areas (latitude >30°) for analysis. Based on the measured data, the mean absolute error (MAE), mean absolute correction rate (P) and root mean square error (RMSE) between the STEC converted by different projection functions and the measured STEC true value are calculated. The calculation results of each statistic are shown in the table:

[0069] Statistics of STEC conversion accuracy of projection functions in China

[0070]

[0071]

[0072] According to the statistical data analysis in the table, it is found that the correction of each projection function is different in different latitudes in China: in the low-latitude area, in January 2014, the MSLM projection function has the highest conversion accuracy, with a MAE of 6.26TECu, a correction rate of 75.93%, and a RMSE of 7.79TECu; the Klobuchar projection function has the lowest conversion accuracy, with a MAE of 8.77TECu, a correction rate of 67.71%, and a RMSE of 10.64TECu; in January 2022, the projection conversion accuracy of MSLM is the highest among several projection functions, with a MAE of 4.33TECu, an average correction rate of 81.24%, and a RMSE of 6.30TECu, but the difference between the MAE and RMSE of each projection function is within 1TECu, and the maximum difference in correction rate is 4%.

[0073] In the mid-latitude region, in January 2014, the projection conversion accuracy of MSLM was the highest, with a MAE of 3.25TECu, a correction rate of 83.43%, and a RMSE of 4.24TECu. The differences in MAE and RMSE of several projection functions were less than 1TECu. In January 2022, the differences between several projection functions were very small, with MAE within 3TECu, and the difference was less than 0.1TECu. The average correction rate difference was less than 2%, the RMSE was around 4TECu, and the difference was less than 0.15TECu.

[0074] Embodiment 6:

[0075] Embodiment 6 is substantially the same as Embodiment 1, except that:

[0076] See also Figure 2 Considering that there are certain differences in ionospheric STEC at different azimuths, the true values ​​of the projection function at different azimuths will also be different. In order to systematically analyze the influence of azimuth on the true value of the projection function and STEC, Figure 2 The variation of the projection function true value and STEC with azimuth at different altitudes at GXNN, WUHN, BJFS and XJDS stations at UT=6:00 on January 1, 2014 is shown. From the variation results of the projection function true value, it can be seen that the projection function true value decreases with the increase of the altitude angle, and the variation amplitude with the azimuth angle is also decreasing. When the altitude angle is greater than 40°, the variation of the projection function true value with azimuth angle at different stations is almost negligible. In addition, there are certain differences in the variation of the projection true value with azimuth angle at different stations. At an altitude angle of 10°, at the low-latitude GXNN station, the difference of the projection true value at different azimuth angles reaches 0.79, and the corresponding maximum variation of STEC is 53. .9TECu; at the mid-latitude WUHN station, the maximum difference in projection true values ​​at different azimuths is 0.21, and the corresponding maximum STEC change is 9.7TECu; at the mid-latitude BJFS station, the difference in projection true values ​​at different azimuths reaches 0.14, and the corresponding maximum STEC change is 4.3TECu; at the mid-latitude XJDS station, the difference in projection true values ​​at different azimuths reaches 0.05, and the corresponding maximum STEC change is 1.9TECu; the lower the latitude, the greater the change in the true value of the projection function with the azimuth. It can be seen that in the low-latitude region, if a projection function that is independent of the azimuth is used, it will cause a huge projection error, and there will also be certain errors in the mid- and high-latitude regions.

[0077] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A GNSS-TEC projection function estimation method with additional azimuth parameters, characterized in that: The GNSS-TEC projection function estimation method with additional azimuth parameters comprises the following steps: The first step is to use GNSS observation data to extract clean STEC information without satellite and receiver differential code bias DCB; The second step is to obtain the ionospheric intersection point IPP positions of each satellite with a satellite elevation angle greater than 70° and the IPP point positions of the satellite elevation angle less than 40° at multiple times, and then match the satellites with a satellite elevation angle greater than 70° and the satellites with a satellite elevation angle less than 40° at the same IPP point position at the same time to obtain multiple groups of high-low matching "conjugate" IPP point groups; Step 3: Project the STEC with satellite elevation angle greater than 70° in each high-low conjugate IPP point group to the zenith direction to obtain VTEC, and then calculate the projection function value MFV at low satellite elevation angle based on the STEC with satellite elevation angle less than 40°; Step 4: Combine the projection function value MFV to build the GNSS-TEC ionospheric projection function model with additional azimuth parameters; The fifth step is to solve the estimated coefficients of the GNSS-TEC ionospheric projection function model with additional azimuth parameters based on the least squares method in the latitude band, and then substituted the altitude angle, azimuth angle and local time of the IPP point into the GNSS-TEC ionospheric projection function model with additional azimuth parameters to obtain the APMF projection function values ​​at different low altitude angles.

2. The GNSS-TEC projection function estimation method with additional azimuth parameters according to claim 1, characterized in that: In the first step, GNSS observation data is used to extract clean STEC information without satellite and receiver differential code bias DCB, wherein the GNSS observation data sampling epoch interval is selected to be 30s and the satellite cutoff elevation angle is 10°.

3. The GNSS-TEC projection function estimation method with additional azimuth parameters according to claim 1, characterized in that: In the second step, the satellites with a satellite elevation angle greater than 70° and the satellites with a satellite elevation angle less than 40° at the same IPP point position at the same time are matched to obtain multiple sets of high-low matching "conjugate" IPP point groups. Specifically, it is assumed that the longitude and latitude of the two GNSS station-satellite lines of sight at the ionospheric piercing point at the same time are If the distance relationship between two points meets the following conditions, then these two puncture points are "conjugate" puncture points. "Conjugate" puncture points are high-low IPP point groups. The conditions are as follows:

4. The GNSS-TEC projection function estimation method with additional azimuth parameters according to claim 1, characterized in that: In the third step, the STEC with a satellite elevation angle greater than 70° in each high-low "conjugate" IPP point group is projected to the zenith direction to obtain VTEC, and then the projection function value MFV at a low satellite elevation angle is calculated based on the STEC with a satellite elevation angle less than 40°. The specific calculation formula is as follows:

5. The GNSS-TEC projection function estimation method with additional azimuth parameters according to claim 1, characterized in that: In the fourth step, a GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, as follows: Where E′ is the satellite altitude angle at the IPP point in the ionosphere, ω is the GNSS satellite azimuth, t is the local time at the IPP point, E0, E 1，n , E 2，n , E 3，m , E 4，m is the estimated coefficient of the APMF projection function, n and m are the APMF coefficient orders, n max With m max is the maximum order of coefficients.

6. The GNSS-TEC projection function estimation method with additional azimuth parameters according to claim 5, characterized in that: In the fourth step, a GNSS-TEC ionospheric projection function model with additional azimuth parameters is constructed in combination with the projection function value MFV, including local time, altitude angle, and azimuth angle as parameters.

Images