Ionized layer delay information estimation method and system based on improved grid

Abstract

The invention discloses an ionosphere delay information estimation method and system based on an improved grid, and belongs to the technical field of GNSS satellite navigation system information estimation. The improved grid-based ionosphere delay information estimation method comprises the following steps: extracting inclined ionosphere delay based on observation data of a foundation GNSS, and converting the inclined ionosphere delay into vertical ionosphere delay of an ionosphere puncture point IPP; calculating original and conservative ionosphere delay process noise standard deviation according to the vertical ionosphere delay; calculating an ionosphere process noise covariance through the original ionosphere delay process noise standard deviation and the longitude and latitude of the puncture point IPP; according to the original ionized layer delay process noise standard deviation, the ionized layer process noise covariance and the vertical ionized layer delay, calculating the vertical ionized layer delay GIVD at the grid point IGP and the vertical ionized layer delay precision GIVA; accurate process noise variance and covariance are established, and the accuracy of ionosphere delay precision evaluation is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of GNSS satellite navigation system information estimation, and in particular to an improved grid-based ionospheric delay information estimation method and system. Background Art

[0002] Global Navigation Satellite System (GNSS) requires high accuracy and reliability in many critical applications. In order to quantify and ensure positioning reliability, the concept of integrity monitoring is proposed to evaluate the credibility of navigation information in civil aviation applications. Since the basic navigation system cannot meet the integrity requirements of users, many countries have gradually developed satellite augmentation systems (SBAS). SBAS plays a key role in enhancing the accuracy and integrity of GNSS positioning, among which ionospheric instability remains one of the main challenges that degrade performance. Currently, SBAS broadcasts ionospheric delay correction information (IDCM), including gridded ionospheric vertical delay (GIVD) and gridded ionospheric vertical error (GIVE). When generating SBAS IDCM, the vertical total electron content (VTEC) at the ionospheric penetration point (IPP) is first extracted and then interpolated to the ionospheric grid point (IGP) to generate the regional GIVD, and then the estimated standard deviation of the GIVD is calculated. However, the estimated standard deviation fails to accurately characterize the modeling accuracy at the IGP and is therefore not provided as an IDCM. Finally, the chi-square statistical method is used to detect faulty IGPs, and GIVE is calculated to define the vertical ionospheric delay error.

[0003] Among the established SBAS, WAAS is a typical representative and has been widely studied and developed. WAAS uses the Kriging method to calculate the GIVD and its estimated standard deviation. Then, the dynamic chi-square factor inflation algorithm is used to detect faulty IGPs and estimate the GIVE. Although WAAS-Kriging performs well in the continental United States, its performance is affected in the low-latitude ionospheric equatorial anomaly region because these regions have strong spatial variability of the ionosphere and frequent anomalies. The availability and optimization of WAAS-Kriging in low-latitude regions have been widely studied, but there are still some challenges. For example, due to the strong spatial variability of the ionosphere and frequent anomalies, the performance of the WAAS-Kriging method in these regions may be further limited. To overcome this problem, more accurate models and algorithms are needed to improve the ionospheric delay correction effect in low-latitude regions. Summary of the invention

[0004] In view of the above problems existing in the prior art, the present invention is proposed.

[0005] To achieve the above object, the present invention provides the following technical solution: a method and system for estimating ionospheric delay information based on an improved grid, comprising:

[0006] The inclined ionospheric delay is extracted based on the observation data of ground-based GNSS and converted into the vertical ionospheric delay of the ionospheric piercing point IPP;

[0007] Calculate the original and conservative ionospheric delay process noise standard deviations based on the vertical ionospheric delay;

[0008] The ionospheric process noise covariance is calculated by the standard deviation of the original ionospheric delay process noise and the longitude and latitude of the puncture point IPP;

[0009] According to the standard deviation of the original ionospheric delay process noise, the ionospheric process noise covariance and the vertical ionospheric delay, the vertical ionospheric delay GIVD at the grid point IGP and the vertical ionospheric delay accuracy GIVA are calculated;

[0010] The vertical ionospheric delay integrity parameter GIVE at the grid points is calculated using the conservative ionospheric delay process noise standard deviation and ionospheric process noise covariance.

[0011] As a further solution of the present invention: the inclined ionospheric delay utilizes a mapping function to transform the vertical ionospheric delay of the ionospheric puncture point IPP.

[0012] 3. The improved grid ionospheric delay information estimation method according to claim 3, characterized in that: the mapping function formula is:

[0013]

[0014] Where STEC is the slant ionospheric delay, VTEC is the vertical ionospheric delay, is the mapping function, is the zenith distance in the direction of the signal path at the measuring station; R is the radius of the earth; H is the approximate single-layer height; α is a constant.

[0015] As a further solution of the present invention: the step of calculating the original and conservative ionospheric delay process noise standard deviations according to the vertical ionospheric delay comprises:

[0016] Using historical ionospheric delay data, the plane fitting method is used to estimate the ionospheric delay at each puncture point, and the ionospheric delay modeling error is calculated. At the same time, the local ionospheric spatial activity index LISAI is calculated at each puncture point.

[0017] Analyze the statistical relationship between the ionospheric modeling error and the local ionospheric spatial activity index, and calculate the original standard deviation and envelope standard deviation of each set of errors;

[0018] Two exponential functions are used to fit the original standard deviation and envelope standard deviation scatter points respectively, and the empirical formula of the local ionospheric spatial activity index LISAI and the original standard deviation and envelope standard deviation is obtained;

[0019] By calculating the ionospheric activity index LISAI at any spatial point and substituting it into the empirical formula, the original standard deviation of the process noise and the envelope standard deviation of the point can be calculated.

[0020] As a further solution of the present invention: the steps of estimating the ionospheric delay of each puncture point by plane fitting method and calculating the local ionospheric spatial activity index LISAI of each puncture point include:

[0021] Using the ionospheric piercing point IPP search method, a spatial point is selected as the center and a radius of R is fit Search for the ionospheric puncture point IPP around it and set the initial R fit Set to R min ;

[0022] If the number of ionospheric piercing points (IPPs) is less than N target , then increase the search radius R fit When the number of IPPs reaches N, target t or R fit t reaches R min until;

[0023] The standard deviation of the vertical ionospheric delay of the ionospheric piercing point IPP within the search range is calculated and used as the local ionospheric spatial activity index LISAI.

[0024] As a further solution of the present invention: analyzing the statistical relationship between the ionospheric modeling error and the local ionospheric space activity index, calculating the original standard deviation and envelope standard deviation of each group of errors, specifically grouping the modeling errors according to the size of the local ionospheric space activity index, calculating the original standard deviation and envelope standard deviation of each group of errors, and further fitting them with two exponential functions;

[0025] The fitting formula is:

[0026] σ orig =0.70·σ LISAI 0.80

[0027] σ ovbd =0.78·σ LISAI 0.75

[0028] Among them, σ orig and σ ovbd are the standard deviation of the original ionospheric delay process noise and the standard deviation of the envelope process noise, σ LISAI is the calculated LISAI index.

[0029] As a further solution of the present invention: the step of calculating the ionospheric process noise covariance by using the original ionospheric delay process noise standard deviation and the longitude and latitude of the puncture point IPP includes:

[0030] Using historical ionospheric delay data, the ionospheric delay modeling error is divided by the standard deviation of the original ionospheric delay process noise to standardize the modeling error;

[0031] The relationship between the correlation and distance between standardized modeling errors was analyzed, and the calculation formula for covariance was established.

[0032] As a further solution of the present invention: the calculation formula of covariance is,

[0033]

[0034] Among them, C i，j is the position x i and x j The covariance of i，j is the position x i and x j The distance, d decorr is the decorrelation distance, σ norm is the decorrelation parameter, σ(x i ) and σ(x j ) is the position x i and x j The standard deviation of the process noise at .

[0035] As a further solution of the present invention: the formula for calculating the vertical ionospheric delay GIVD at the grid point IGP is,

[0036]

[0037] w=[W-WG(G T WWG -1 G T W]c+WG(G T WG) -1 s

[0038] in, is the distance between the i-th puncture point and the grid point; I meas (x i ) is the ionospheric delay at the puncture point; w i is the weight of the i-th ionospheric delay; w is the weight element w i The matrix is ​​composed of , G and s are the design matrix and design vector, W is the variance-covariance matrix, and the symbol T represents matrix transpose.

[0039] As a further solution of the present invention: an improved grid-based ionospheric delay information estimation system, applied to the estimation method, comprises:

[0040] A data processing module, used to extract the tilted total ionospheric delay data from the ground-based GNSS observation data and convert it into the vertical ionospheric delay of the ionospheric piercing point;

[0041] A model building module, connected to the data processing module, is used to calculate the local ionospheric spatial activity index LISAI, the standard deviation and covariance of the ionospheric process noise, and the least squares parameter estimation, and to build the GIVD and GIVE models;

[0042] The output module is used to output the obtained ionospheric delay GIVD, ionospheric delay accuracy GIVA and ionospheric delay integrity parameter GIVE of the grid point, and the output module is connected to the model building module.

[0043] As a further solution of the present invention:.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention establishes accurate process noise variance and covariance based on the improved grid ionospheric delay information estimation method and system, improves the accuracy of ionospheric delay precision assessment, and the estimated grid ionospheric delay error GIVE can more tightly and effectively envelope the ionospheric modeling error, thereby improving the calculation accuracy of the grid ionospheric delay standard deviation and integrity parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. Among them:

[0046] Figure 1 This is a schematic diagram of the overall process described in the embodiment provided by the present invention.

[0047] Figure 2 A graph showing the response of GIVA to errors during a quiet moment according to an embodiment of the present invention.

[0048] Figure 3 This is a diagram showing the response of GIVA to errors at the jump moment of an embodiment provided by the present invention.

[0049] Figure 4 A graph showing the response of GIVE to errors during a quiet moment according to an embodiment of the present invention.

[0050] Figure 5A graph showing the response of GIVE to errors during active moments of an embodiment provided by the present invention.

[0051] Figure 6 The envelope diagram of the GIVE error for all epochs of the embodiment provided by the present invention. DETAILED DESCRIPTION

[0052] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0053] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0054] Secondly, the present invention is described in detail with reference to the schematic diagram. When describing the embodiments of the present invention in detail, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0055] Furthermore, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor is it a separate or selective embodiment that is mutually exclusive with other embodiments.

[0056] Example 1

[0057] like Figure 1 As shown, the present invention provides a technical solution: a method for estimating ionospheric delay information based on an improved grid, comprising:

[0058] S1: Extract the inclined ionospheric delay based on the observation data of ground-based GNSS and convert it into the vertical ionospheric delay of the ionospheric piercing point IPP;

[0059] It should be noted that the tilted ionospheric delay is extracted using the non-differenced non-combined precise point positioning method; the tilted ionospheric delay is converted into the vertical ionospheric delay of the ionospheric piercing point IPP using a mapping function; the mapping function formula is:

[0060]

[0061] Where STEC is the slant ionospheric delay, VTEC is the vertical ionospheric delay, is the mapping function, is the zenith distance in the direction of the signal path at the measuring station; R is the radius of the earth, which is 6371 km; H is the approximate single-layer height, which is 506.7 km; α is a constant, which is 0.9782.

[0062] Preferably, satellite observation data from the China Regional Landform Network base station are used, and external high-precision satellite orbit and clock products are introduced, such as the post-precision satellite orbit and clock products provided by the International GPS Service (IGS) organization, and non-differenced and non-combined precise single points are used to extract the slant-path ionospheric delay, and based on the spherical thin shell, the slant-path ionospheric delay is converted into the vertical ionospheric delay at the puncture point.

[0063] S2: original and conservative ionospheric delay process noise standard deviation calculated based on vertical ionospheric delay;

[0064] S3: Calculate the ionospheric process noise covariance through the original ionospheric delay process noise standard deviation and the longitude and latitude of the puncture point IPP;

[0065] The calculation formula of noise covariance is:

[0066]

[0067] Among them, C i，j is the position x i and x j The covariance of i，j is the position x i and x j The distance, d decorr is the decorrelation distance, σ norm is the decorrelation parameter, σ(x i ) and σ(x j ) is the position x i and x j The standard deviation of the process noise at .

[0068] S4: Calculate the vertical ionospheric delay GIVD at the grid point IGP and the vertical ionospheric delay accuracy GIVA based on the original ionospheric delay process noise standard deviation, ionospheric process noise covariance and vertical ionospheric delay;

[0069] The formula for calculating the vertical ionospheric delay GIVD at the grid point IGP is:

[0070]

[0071] w=[W-WG(G T WG) -1 G T W]c+WG(G T WG) -1 s

[0072] in, is the distance between the i-th puncture point and the grid point; I meas (x i ) is the ionospheric delay at the puncture point; w i is the weight of the i-th ionospheric delay; w is the weight element w i The matrix is ​​composed of , G and s are the design matrix and design vector, W is the variance-covariance matrix, and the symbol T represents matrix transpose.

[0073] It should be noted that G and s are the calculation formulas for the design matrix and design vector:

[0074]

[0075] s=[1 0 0] T

[0076] in, and are the direction vectors for the east and north directions; is the distance between the i-th puncture point and the grid point; T represents the matrix transpose.

[0077] Specifically, and The calculation formula is:

[0078]

[0079] Among them, λ IGP is the grid point longitude, φ IGP is the grid point latitude.

[0080] It should be noted that the vertical ionospheric delay accuracy GIVA formula is:

[0081]

[0082] Among them, W orig is the original variance-cosquare matrix; c orig is the original covariance vector between the grid points and the puncture points, is the original process noise variance of the grid points.

[0083] Furthermore, the original variance-covariance matrix W orig The formula is:

[0084]

[0085] Among them, σ orig is the original process noise standard deviation; C i，j is the position x i and x jThe noise covariance of represents the original process noise variance at the first puncture point, and N represents the Nth puncture point.

[0086] It should be noted that the original variance-covariance matrix W is constructed using the established original standard deviation and covariance empirical formula orig

[0087] S5: Calculate the vertical ionospheric delay integrity parameter GIVE at the grid point using the conservative ionospheric delay process noise standard deviation and ionospheric process noise covariance.

[0088] It should be noted that the vertical ionospheric delay integrity parameter GIVE formula is:

[0089]

[0090] Among them, W ovbd is the envelope variance-cosquare matrix; c ovbd is the envelope covariance vector between the grid points and the puncture points; is the original process noise variance of the grid points; w is the weight element w i The matrix is ​​composed of; W is the variance-covariance matrix, and the symbol T represents the matrix transpose.

[0091] Furthermore, the envelope variance-cosquare matrix W ovbd The formula is:

[0092]

[0093] Among them, σ ovbd is the standard deviation of the process noise of the envelope; C i，j is the position x i and x j The noise covariance of represents the envelope process noise variance at the first puncture point, and N represents the Nth puncture point.

[0094] It should be noted that the envelope standard deviation and covariance empirical formulas are established to construct the envelope variance-covariance matrix W ovbd .

[0095] Further, the step of calculating the original and conservative ionospheric delay process noise standard deviations according to the vertical ionospheric delay includes:

[0096] S21: Using historical ionospheric delay data, the plane fitting method is used to estimate the ionospheric delay at each puncture point, and the ionospheric delay modeling error is calculated. At the same time, the local ionospheric spatial activity index LISAI is calculated for each puncture point.

[0097] S22: Analyze the statistical relationship between the ionospheric modeling error and the local ionospheric spatial activity index, and calculate the original standard deviation and envelope standard deviation of each set of errors;

[0098] S23: Use two exponential functions to fit the original standard deviation and envelope standard deviation scatter points respectively, and obtain the empirical formula of the local ionospheric spatial activity index LISAI and the original standard deviation and envelope standard deviation;

[0099] S24: Calculate the ionospheric activity index LISAI at any spatial point and substitute it into the empirical formula to calculate the original standard deviation of the process noise and the envelope standard deviation of the point.

[0100] Specifically, the statistical relationship between the ionospheric modeling error and the local ionospheric space activity index is analyzed, and the original standard deviation and envelope standard deviation of each group of errors are calculated. Specifically, the modeling errors are grouped according to the size of the local ionospheric space activity index, and the original standard deviation and envelope standard deviation of each group of errors are calculated. Then, two exponential functions are used for fitting, and the resulting formula is:

[0101] σ orig =0.70·σ UISAI 0.80

[0102] σ ovbd =0.78·σ LISAI 0.75

[0103] Among them, σ orig and σ ovbd They are the original ionospheric delay process noise standard deviation and the envelope process noise standard deviation, which are also empirical formulas and exponential functions, σ LISAI is the calculated LISAI index.

[0104] Furthermore, using the original standard deviation, the standard modeling error is calculated as follows:

[0105]

[0106] Among them, r(x) is the modeling error at the puncture point x, σ(x) is the original standard deviation at the puncture point x, and r norm (x) is the normalized error.

[0107] Furthermore, the variance function of the variable variance is calculated using the standardized error, and the formula is as follows:

[0108]

[0109] Among them, γ norm (x i , x j) is the position x i and x j The variogram value at i ), r(x j )) is the position x i and x j The covariance of the modeling error at r norm (x i ) is the position x i The standard modeling error at r norm (x j ) is the position x j The standard modeling error at σ(x i ) and σ(x j ) is the position x i and x j The standard deviation of the process noise at .

[0110] It should be noted that the steps of estimating the ionospheric delay of each puncture point by plane fitting method and calculating the local ionospheric spatial activity index LISAI of each puncture point include:

[0111] S211: Using the ionospheric puncture point IPP search method, select a spatial point as the center and search for the ionospheric puncture point with a radius of R. fit Search for the ionospheric puncture point IPP around it and set the initial R fit Set to R min .

[0112] S212: If the number of ionospheric puncture points IPP is less than N target , then increase the search radius R fit When the number of IPPs reaches N, target t or R fit t reaches R min until.

[0113] S213: Calculate the standard deviation of the vertical ionospheric delay of the ionospheric piercing point IPP within the search range and use it as the local ionospheric spatial activity index LISAI.

[0114] Further, the step of calculating the ionospheric process noise covariance by using the original ionospheric delay process noise standard deviation and the longitude and latitude of the puncture point IPP includes:

[0115] S31: Using historical ionospheric delay data, the ionospheric delay modeling error is divided by the standard deviation of the original ionospheric delay process noise to standardize the modeling error;

[0116] S32: Analyze the relationship between the correlation and distance between standardized modeling errors and establish a formula for calculating covariance.

[0117] This embodiment establishes accurate process noise variance and covariance, improves the accuracy of ionospheric delay precision assessment, and the estimated grid ionospheric delay error GIVE can more tightly and effectively envelope the ionospheric modeling error, thereby improving the calculation accuracy of the grid ionospheric delay standard deviation and integrity parameters.

[0118] Example 2

[0119] The following is a second embodiment of the present invention. The difference between this embodiment and the first embodiment is that this embodiment further provides a system based on an improved grid ionospheric delay information estimation method, including:

[0120] A data processing module, used to extract the tilted total ionospheric delay data from the ground-based GNSS observation data and convert it into the vertical ionospheric delay of the ionospheric piercing point;

[0121] The model building module is connected to the data processing module to calculate the local ionospheric spatial activity index LISAI, the standard deviation and covariance of the ionospheric process noise, and the least squares parameter estimation for building the GIVD and GIVE models;

[0122] The output module is used to output the obtained ionospheric delay GIVD, ionospheric delay accuracy GIVA and ionospheric delay integrity parameter GIVE of the grid points. The output module is connected to the model building module.

[0123] Specifically, the data processing module is used to receive and pre-process data, and then send the processed data to the model building module; the configuration building module further builds the model and sends the results obtained by the model to the output module; the output module outputs the results to the user.

[0124] This embodiment also provides a computer device, which is applicable to the case of an improved grid ionospheric delay information estimation method, including: a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute computer executable instructions to implement the improved grid ionospheric delay information estimation method proposed in the above embodiment.

[0125] The computer device may be a terminal, and the computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, NFC (near field communication) or other technologies. The display screen of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball or touchpad provided on the housing of the computer device, or an external keyboard, touchpad or mouse, etc.

[0126] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, the improved grid ionospheric delay information estimation method proposed in the above embodiment is implemented; the storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (Static Random Access Memory, referred to as SRAM), electrically erasable programmable read-only memory (Electrically Erasable Programmable Read-Only Memory, referred to as EEPROM), erasable programmable read-only memory (Erasable Programmable Read Only Memory, referred to as EPROM), programmable read-only memory (Programmable Red-Only Memory, referred to as PROM), read-only memory (Read-Only Memory, referred to as ROM), magnetic storage, flash memory, magnetic disk or optical disk.

[0127] In summary, this study introduces an improved Kriging method in which the spatiotemporal variogram is re-established so that the covariance is estimated using a variable variance, while the standard deviation of the process noise is adaptively modeled using a LISAI-based approach. Then, two sets of process noise are established: an accurate set of noise is used to estimate the additional IDCM, defined as the gridded ionospheric delay accuracy GIVA, to accurately characterize the GIVD modeling accuracy; and a conservative set of noise is used for GIVE modeling to ensure integrity. Overall, this study provides a complete process on how to generate and utilize this ionospheric information from the server to the user.

[0128] Example 3

[0129] Reference Figure 2 to Figure 6 , which is the third embodiment of the present invention. This embodiment is different from the first embodiment in that, in order to verify its beneficial effects, the experimental results of the present invention are provided. In this example, the experiment uses the China Land State Network observation data of DOY 277 in 2021, and the selected research area ranges from longitude 70°E to 140°E and latitude 10°N to 55°N°.

[0130] like Figure 2 and Figure 3 The response of GIVA calculated by the present invention to the error is shown as follows, where Figure 2 is the result of a quiet period in the ionosphere. Figure 3 Results for periods of ionospheric activity. As can be seen from the figure, the optimized Kriging GIVAs respond very quickly to errors. During quiet moments, the error changes are relatively small, resulting in small changes in GIVAs, mostly below 0.3m. However, during active periods, the errors increase and fluctuate significantly, highlighting the impact of ionospheric disturbances on modeling accuracy. GIVAs show large changes in these periods, often exceeding 0.5 meters and up to 1.5 meters, indicating that they are very sensitive to ionospheric disturbances.

[0131] like Figure 4 and Figure 5 The response of GIVE to the error calculated by the present invention is shown as follows, where Figure 3 is the result of a quiet period in the ionosphere. Figure 4 The results are for the period of active ionosphere. It can be seen from the figure that the calculated GIVE can respond to the error in time and can successfully envelop the result.

[0132] like Figure 6 The figure shows the envelope results of GIVE calculated by the present invention under different integrity risks. The left sub-figure is the envelope result of the mid-latitude region, and the right sub-figure is the envelope result of the low-latitude region. In the mid-latitude region, the average GIVE value of the optimized Kriging is 0.64m; in the low-latitude region, the average GIVE value of the optimized Kriging is 1.14m. In addition, under different integrity risks, the GIVE value can envelop the error.

[0133] The experimental results based on measured data in China show that the grid ionospheric vertical accuracy GIVA estimated by the present invention can accurately express the error accuracy and can be used to accelerate the convergence of static PPP positioning; the estimated grid ionospheric vertical error GIVE can tightly and effectively envelope the ionospheric modeling error.

[0134] Importantly, it should be noted that the construction and arrangement of the present application shown in a number of different exemplary embodiments are only exemplary. Although only a few embodiments are described in detail in this disclosure, it should be readily understood by those who refer to this disclosure that many modifications are possible, for example, the size, scale, structure, shape and proportion of various elements, and parameter values ​​such as temperature, pressure, etc., mounting arrangements, use of materials, color, directional changes, etc., without substantially departing from the novel teachings and advantages of the subject matter described in the application. For example, the element shown as integrally formed can be composed of multiple parts or elements, the position of the element can be inverted or otherwise changed, and the nature or number or position of the discrete element can be changed or changed. Therefore, all such modifications are intended to be included in the scope of the present invention. The order or sequence of any process or method steps can be changed or reordered according to alternative embodiments. In the claims, any "device plus function" clause is intended to cover the structure of the execution function described herein, and is not only structurally equivalent but also equivalent structure. Without departing from the scope of the present invention, other substitutions, modifications, changes and omissions can be made in the design, operating conditions and arrangement of the exemplary embodiments. Therefore, the invention is not limited to a specific embodiment, but extends to numerous modifications still falling within the scope of the appended claims.

[0135] Furthermore, in order to provide a concise description of exemplary embodiments, all features of an actual embodiment may not be described, i.e., those features that are not relevant to the best mode presently contemplated for carrying out the invention or those features that are not relevant to implementing the invention.

[0136] It should be understood that in the development of any actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort may be complex and time-consuming, but for those of ordinary skill having the benefit of this disclosure, the development effort will be a routine task of design, fabrication, and production without undue experimentation.

[0137] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for estimating ionospheric delay information based on an improved grid, characterized in that: include, The inclined ionospheric delay is extracted based on the observation data of ground-based GNSS and converted into the vertical ionospheric delay of the ionospheric piercing point IPP; Calculate the original and conservative ionospheric delay process noise standard deviations based on the vertical ionospheric delay; The ionospheric process noise covariance is calculated by the standard deviation of the original ionospheric delay process noise and the longitude and latitude of the puncture point IPP; According to the standard deviation of the original ionospheric delay process noise, the ionospheric process noise covariance and the vertical ionospheric delay, the vertical ionospheric delay GIVD at the grid point IGP and the vertical ionospheric delay accuracy GIVA are calculated; The vertical ionospheric delay integrity parameter GIVE at the grid points is calculated using the conservative ionospheric delay process noise standard deviation and ionospheric process noise covariance.

2. The method for estimating ionospheric delay information based on improved grid as claimed in claim 1, characterized in that: The inclined ionospheric delay utilizes a mapping function to transform the vertical ionospheric delay of the ionospheric piercing point IPP.

3. The method for estimating ionospheric delay information based on improved grid as claimed in claim 2, characterized in that: The mapping function formula is: Where STEC is the slant ionospheric delay, VTEC is the vertical ionospheric delay, is the mapping function, is the zenith distance in the direction of the signal path at the measuring station; R is the radius of the earth; H is the approximate single-layer height; α is a constant.

4. The method for estimating ionospheric delay information based on improved grid as claimed in claim 3, characterized in that: The steps of calculating the original and conservative ionospheric delay process noise standard deviations based on the vertical ionospheric delay include: Using historical ionospheric delay data, the plane fitting method is used to estimate the ionospheric delay at each puncture point, and the ionospheric delay modeling error is calculated. At the same time, the local ionospheric spatial activity index LISAI is calculated at each puncture point. Analyze the statistical relationship between the ionospheric modeling error and the local ionospheric spatial activity index, and calculate the original standard deviation and envelope standard deviation of each set of errors; Two exponential functions are used to fit the original standard deviation and envelope standard deviation scatter points respectively, and the empirical formula of the local ionospheric spatial activity index LISAI and the original standard deviation and envelope standard deviation is obtained; By calculating the ionospheric activity index LISAI at any spatial point and substituting it into the empirical formula, the original standard deviation of the process noise and the envelope standard deviation of the point can be calculated.

5. The method for estimating ionospheric delay information based on improved grid as claimed in claim 4, characterized in that: The steps of estimating the ionospheric delay of each puncture point by plane fitting method and calculating the local ionospheric spatial activity index LISAI of each puncture point include: Using the ionospheric piercing point IPP search method, a spatial point is selected as the center and a radius of R is fit Search for the ionospheric puncture point IPP around it and set the initial R fit Set to R min ; If the number of ionospheric piercing points (IPPs) is less than N target , then increase the search radius R fit When the number of IPPs reaches N, targett or R fit t reaches R min until; The standard deviation of the vertical ionospheric delay of the ionospheric piercing point IPP within the search range is calculated and used as the local ionospheric spatial activity index LISAI.

6. The method for estimating ionospheric delay information based on improved grid as claimed in claim 4 or 5, characterized in that: The statistical relationship between the ionospheric modeling error and the local ionospheric space activity index is analyzed, and the original standard deviation and envelope standard deviation of each group of errors are calculated. Specifically, the modeling errors are grouped according to the size of the local ionospheric space activity index, the original standard deviation and envelope standard deviation of each group of errors are calculated, and then two exponential functions are used for fitting. The fitting formula is: s orig =0.70·s LISAI 0.80 s ovbd =0.78·s LISAI 0.75 Among them, σ orig and σ ovbd are the standard deviation of the original ionospheric delay process noise and the standard deviation of the envelope process noise, σ LISAI is the calculated LISAI index.

7. The method for estimating ionospheric delay information based on improved grid as claimed in claim 6, characterized in that: The steps of calculating the ionospheric process noise covariance by using the original ionospheric delay process noise standard deviation and the latitude and longitude of the puncture point IPP include: Using historical ionospheric delay data, the ionospheric delay modeling error is divided by the standard deviation of the original ionospheric delay process noise to standardize the modeling error; The relationship between the correlation and distance between standardized modeling errors was analyzed, and the calculation formula for covariance was established.

8. The method for estimating ionospheric delay information based on improved grid as claimed in claim 7, characterized in that: The formula for calculating covariance is, Among them, C i，j is the position x i and x j The covariance of i，j is the position x i and x j The distance, d decorr is the decorrelation distance, σ norm is the decorrelation parameter, σ(x i ) and σ(x j ) is the position x i and x j The standard deviation of the process noise at .

9. The method for estimating ionospheric delay information based on improved grid as claimed in claim 8, characterized in that: The formula for calculating the vertical ionospheric delay GIVD at the grid point IGP is: w=[W-WG(G T WG) -1 G T W]c+WG(G T WG) -1 s in, is the distance between the i-th puncture point and the grid point; I meas (x i ) is the ionospheric delay at the puncture point; w i is the weight of the i-th ionospheric delay; w is the weight element w i The matrix is ​​composed of , G and s are the design matrix and design vector, W is the variance-covariance matrix, and the symbol T represents matrix transpose.

10. An improved grid-based ionospheric delay information estimation system, characterized in that: Applicable to the estimation method according to any one of claims 1 to 9, comprising: A data processing module, used to extract the tilted total ionospheric delay data from the ground-based GNSS observation data and convert it into the vertical ionospheric delay of the ionospheric piercing point; A model building module, connected to the data processing module, is used to calculate the local ionospheric spatial activity index LISAI, the standard deviation and covariance of the ionospheric process noise, and the least squares parameter estimation, and to build the GIVD and GIVE models; The output module is used to output the obtained ionospheric delay GIVD, ionospheric delay accuracy GIVA and ionospheric delay integrity parameter GIVE of the grid point, and the output module is connected to the model building module.

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