Single-frequency ionospheric delay autonomous correction method

Abstract

The application discloses a single-frequency ionospheric delay autonomous correction method and relates to the field of GNSS positioning. In view of a strong ionospheric disturbance scenario caused by magnetic storm, the method adopts a multi-ionospheric piercing point space-time decoupling algorithm, and only single-frequency pseudorange and carrier phase observation can be used to complete autonomous correction of ionospheric delay error of BDSK. The method does not need to depend on a ground reference station network and a double-frequency receiver hardware condition, and only relies on observation data of the receiver itself to autonomously complete ionospheric delay correction calculation, can be applied to a Beidou single-frequency positioning application scenario in a magnetic storm and the like strong ionospheric disturbance environment, effectively solves a technical problem that in the prior art, in a magnetic storm and the like strong ionospheric disturbance environment, ionospheric delay correction precision of a single-frequency receiver is reduced under a condition that a BDS BAS satellite-based augmentation service is invalid, and significantly improves the precision and operation robustness of Beidou single-frequency positioning in a complex space disturbance environment.

Description

Technical Field

[0001] This invention relates to the field of Global Navigation Satellite System (GNSS) positioning, and more particularly to the autonomous correction technology for ionospheric delay of BeiDou single-frequency receivers, specifically to a single-frequency autonomous correction method for ionospheric delay. Background Technology

[0002] The BeiDou Navigation Satellite System (BDS) completed its global network in 2020. It employs a heterogeneous hybrid constellation configuration consisting of geostationary Earth Orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth Orbit (MEO) satellites. The BeiDou Satellite-Based Augmentation System (BDSBAS), built upon BDS, broadcasts ionospheric grid correction information via GEO satellites, providing ionospheric delay correction services to single-frequency users in China and surrounding regions, thereby improving satellite positioning accuracy and navigation service reliability.

[0003] Currently, single-frequency navigation has been widely used in many fields such as transportation, low-cost navigation terminals, and navigation in complex environments due to its advantages of low cost, lightweight terminals, and convenient deployment. However, under complex space weather conditions such as frequent solar activity and geomagnetic storms, the ionosphere will be severely disturbed. How to achieve continuous and high-precision ionospheric delay correction in geomagnetic storm scenarios to ensure the positioning stability and accuracy of single-frequency navigation has become a key technical problem that urgently needs to be solved in this field.

[0004] Currently, the industry typically uses the BeiDou Klobuchar Model (BDSK) to achieve ionospheric delay correction for BDS single-frequency positioning. BDSK analyzes the broadcast ionospheric parameters carried in the navigation message, combines user location information and satellite ionospheric pierce point (IPP) parameters, and relies on an empirical model to calculate ionospheric delay, thereby achieving ionospheric error compensation for single-frequency positioning. This is currently the mainstream single-frequency ionospheric correction technology.

[0005] However, existing BDSK correction techniques still have certain shortcomings and cannot adapt to the high-precision correction requirements under complex disturbance environments. Firstly, BDSK uses fixed broadcast ionospheric parameters for ionospheric delay correction calculations, resulting in long parameter update cycles. When space disturbances such as enhanced solar activity or geomagnetic storms occur, the total electron content (TEC) of the ionosphere undergoes instantaneous and drastic dynamic changes. This model struggles to match the real-time changes in the ionosphere, easily leading to increased ionospheric delay correction errors. Secondly, BDSK is based on ideal conditions of slow and stable ionospheric changes, failing to consider extreme conditions of drastic ionospheric gradient changes during geomagnetic storms. This results in poor adaptability to the spatial variation characteristics of the ionosphere under disturbance conditions, leading to a significant decrease in ionospheric delay correction accuracy in complex space environments. Therefore, existing technologies lack a high-precision ionospheric delay correction method that is compatible with single-frequency receivers and stably applicable even when BDSBAS is unavailable. Summary of the Invention

[0006] In view of at least one of the aforementioned technical problems, this application provides an autonomous correction method for ionospheric delay based on single-frequency pseudorange and carrier phase observations from IGSO and MEO satellites. For scenarios with strong ionospheric disturbances caused by geomagnetic storms, this method employs a multi-ionospheric puncture point spatiotemporal decoupling algorithm to autonomously correct the ionospheric delay error of BDSBAS. This method does not rely on ground-based reference station networks or dual-frequency receiver hardware, and is applicable to BeiDou single-frequency positioning applications in environments with strong ionospheric disturbances such as geomagnetic storms. It effectively solves the technical challenge of decreased ionospheric delay correction accuracy of single-frequency receivers under conditions of BDSBAS satellite-based augmentation service failure and superimposed electromagnetic storm disturbances, significantly improving the accuracy and operational robustness of BeiDou single-frequency positioning in complex space disturbance environments.

[0007] The technical solution of this invention is:

[0008] A single-frequency autonomous correction method for ionospheric delay, comprising the following steps:

[0009] Step 1: Acquire observation data and satellite broadcast ephemeris data from IGSO and MEO satellites, perform carrier phase smoothing pseudorange processing, extract ionospheric delay observations from the smoothed pseudorange, and then calculate the tilted path ionospheric delay and BDSK residual.

[0010] Step 2: Construct the difference observation equation using the BDSK residuals and solve for the time drift correction. ;

[0011] Step 3: Based on the BDSK residuals of all IGSO+MEO satellites at the current epoch, calculate the inter-satellite residual dispersion index ISRD and regard the ISRD index as the geomagnetic storm sensing index.

[0012] Step 4: Determine the state of the ionosphere based on the ISRD index value: if the ISRD index is ≥1.5, the ionosphere is determined to be in a disturbed state; if the ISRD index is <1.5, the ionosphere is determined to be in a calm period.

[0013] Step 5: Solve for the gradient parameters: If the ionosphere is in a quiescent state, set the gradient parameters to zero; if the ionosphere is in a disturbed state, calculate the gradient parameters based on the BDSK residuals and time drift correction. Derive the first-order horizontal gradient observation equation, and solve the gradient parameters using the weighted least squares method.

[0014] Step 6: Adjust according to time drift amount and gradient parameters on ionospheric delay along inclined paths After correction, the single-frequency ionospheric delay correction amount is obtained. .

[0015] The beneficial effects of adopting the above technical solution are as follows:

[0016] (1) This invention utilizes single-frequency pseudorange and carrier phase observations from inclined geosynchronous orbit satellites and medium Earth orbit satellites of the BeiDou Navigation Satellite System to perform real-time estimation and dynamic correction of BDSK residuals. Since this invention overcomes the limitation of traditional BDSK relying solely on fixed broadcast parameters for ionospheric delay modeling, it can promptly capture and adapt to the rapid changes in the total electron content of the ionosphere during geomagnetic storms, thereby reducing the problem of excessive ionospheric delay correction errors caused by parameter update lag in traditional BDSK and significantly improving the correction accuracy under strong disturbance ionospheric environments.

[0017] (2) This invention constructs a spatiotemporal decoupling model based on multiple ionospheric puncture points to separately estimate the ionospheric time drift term and the spatial gradient term. During geomagnetic storm disturbances, the total electron content of the ionosphere exhibits drastic temporal dynamic changes and strong spatial gradient characteristics. Traditional BDSK is constrained by fixed broadcast parameters and cannot accurately characterize the extreme ionospheric change characteristics of this type. However, this invention utilizes the observation residuals of adjacent epochs to dynamically estimate the ionospheric time change rate and horizontal gradient parameters, which can adapt to the non-stationary change characteristics of the ionosphere under geomagnetic storm conditions in real time. This effectively reduces the ionospheric delay correction error caused by model mismatch during geomagnetic storms and improves the BeiDou single-frequency positioning accuracy under strong ionospheric disturbance conditions.

[0018] (3) This invention achieves adaptive sensing of ionospheric disturbance state by constructing the Inter-Satellite Residual Dispersion (ISRD) index. Since ISRD can effectively characterize the degree of dispersion of ionospheric residuals observed by different satellites at the current epoch, it accurately reflects the intensity of real-time ionospheric disturbance. Accordingly, this invention can automatically switch correction strategies according to the strength of ionospheric disturbance, and actively improve the positioning integrity protection level under strong disturbance conditions, thereby enhancing the system's adaptability to abnormal space weather events such as geomagnetic storms, and improving the reliability and robustness of single-frequency navigation and positioning results in complex environments.

[0019] (4) This invention does not rely on BDSBAS satellite-based augmentation broadcast information; it can autonomously complete ionospheric delay correction calculations using only the receiver's own observation data. Therefore, even in the event of BDSBAS service interruption, function degradation, or unreceivable augmentation signals, this invention can still stably provide effective ionospheric delay correction services to single-frequency users, effectively ensuring the continuous output capability of BeiDou single-frequency positioning services and improving the service continuity and availability of the single-frequency BeiDou positioning system in complex space environments.

[0020] (5) This invention can complete autonomous correction of ionospheric delay using only single-frequency pseudorange and carrier phase observations, without the need for dual-frequency receiving hardware. Due to the reduction in receiver hardware complexity and cost, it is more suitable for the large-scale promotion and application of low-cost single-frequency Beidou terminals.

[0021] (6) This invention does not rely on a dense network of continuously operating ground-based reference stations to obtain regional ionospheric modeling parameters. Instead, it directly utilizes local receiver observation data to autonomously complete ionospheric residual estimation and ionospheric gradient correction. Therefore, compared to traditional correction schemes that rely on external regional augmentation networks, this invention avoids the costs of ground-based reference station construction, deployment, and operation and maintenance, overcomes the constraints of regional reference station coverage conditions, and improves the applicability and operational coverage of BeiDou single-frequency positioning technology in remote land, sea, and sparsely populated reference station areas. Attached Figure Description

[0022] Figure 1 This is a flowchart of the single-frequency ionospheric delay autonomous correction method in this embodiment.

[0023] Figure 2 This is a schematic diagram of the ionospheric puncture point.

[0024] Figure 3 Single-frequency ionospheric delay correction amount and tilted path ionospheric delay A schematic diagram showing the change in the root mean square error (RMSE) relative to the baseline. Detailed Implementation

[0025] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0026] A single-frequency autonomous correction method for ionospheric delay, such as Figure 1 As shown, it includes the following steps:

[0027] Step 1: Acquire observation data and satellite broadcast ephemeris data from IGSO and MEO satellites, perform carrier phase smoothing pseudorange processing, and calculate the tilted path ionospheric delay. And extracting BDSK residuals;

[0028] Step 1.1: Obtain BDS single-frequency RINEX observation data and satellite broadcast ephemeris data through the International GNSS Service (IGS) data center, filter out the visible BeiDou on-orbit satellite data within the current epoch, and extract the effective observation data of IGSO satellites and MEO satellites.

[0029] This implementation method downloads the BDS single-frequency RINEX 3.04 format observation file corresponding to the target station from the IGS Data Center CDDIS public data platform (ftp: / / cddis.nasa.gov / gnss / data / daily / ), sets the data sampling interval to 30 seconds, and simultaneously acquires the BDS broadcast ephemeris file for the corresponding date. Basic information and precise site coordinates of the IGS tracking station can be obtained through the official IGS online map platform (https: / / network.igs.org / ).

[0030] All visible BeiDou satellites in orbit at the current epoch are screened, retaining only usable IGSO satellites (BDS numbers C06–C10) and MEO satellites (BDS numbers C19–C46) for the correction term calculation. The cutoff angle for satellite elevation is uniformly set to 15°, and low-elevation angle satellite observations below the cutoff angle are discarded to avoid obstruction and multipath interference affecting calculation accuracy. The visible satellite numbers available for calculation at the current epoch after screening are defined as follows: ,and .

[0031] Step 1.2: Use a hatch filter to process the raw pseudorange data from the selected IGSO and MEO satellite observation data. Carrier phase smoothing is performed to obtain the smoothed pseudorange. .

[0032] Obtain B1I single-frequency pseudorange observations for each visible BDS IGSO and MEO satellite, and use a Hatch filter to refine the raw pseudorange. Carrier phase smoothing processing, filter window length Each epoch is specifically implemented using the following formula:

[0033] (1);

[0034] in, The pseudo-range after smoothing; For the current epoch; For the first The satellite in the The original pseudorange of B1I in the epoch, For the first The satellite in the B1I carrier phase of the epoch, For B1I wavelength, It is the length of the Hatch filter window.

[0035] Step 1.3: From the smoothed pseudo-range Extracting delayed observations of the ionosphere .

[0036] Using BDS broadcast ephemeris data, the ECEF (Earth-Centered Earth-Fixed) coordinates of each satellite at the signal transmission time are calculated, thereby determining the first... Geometric distance between satellites and receiver Satellite clock bias correction and receiver clock difference The tropospheric delay was calculated using the Saastamoinen model. Then, according to equation (2), from the smoothed pseudo-range Extracting delayed observations of the ionosphere :

[0037] (2);

[0038] in, For the first The geometric distance between the satellite and the receiver; It is the speed of light.

[0039] Step 1.4: Based on the selected IGSO and MEO satellite observation data, calculate the... The coordinates of the ionospheric puncture point from the satellite to the receiver.

[0040] The ionospheric penetration point from the satellite to the receiver is the intersection of the satellite navigation signal propagation path and the sphere of a single-layer ionospheric model, specifically as follows: Figure 2As shown. This implementation calculates the first [number] based on the selected IGSO and MEO satellite observation data. The coordinates of the ionospheric puncture point from the satellite to the receiver are determined through the following steps:

[0041] First, calculate the geocentric angle between the receiver and the ionospheric puncture point according to equation (3):

[0042] (3)

[0043] in, This is the epoch corresponding to the ionospheric puncture point; For the first The geocentric angle between the satellite and the receiver's ionospheric puncture point; For the first The elevation angle of each satellite; The average radius of the Earth km; km represents the height of the ionospheric shell.

[0044] Subsequently, the latitude of the ionospheric puncture point is calculated according to equation (4). :

[0045] (4)

[0046] in, The latitude of the receiver's location; The geocentric angle between the receiver and the ionospheric puncture point; For the first The azimuth angle of a satellite.

[0047] Then calculate the longitude of the ionospheric puncture point according to formula (5). :

[0048] (5)

[0049] in, This is the geodetic longitude of the receiver's location.

[0050] Step 1.5: Calculate the tilted path ionospheric delay using the BDSK parameters and ionospheric puncture point coordinates from the acquired broadcast ephemeris data of IGSO and MEO satellites. Thus, based on ionospheric delay observations and tilted path ionospheric delay Calculate the BDSK residuals.

[0051] Based on BDSK parameters parsed from broadcast ephemeris data , The ionospheric delay amplitude corresponding to the ionospheric puncture point is calculated according to equation (6). and cycle :

[0052] (6)

[0053] in, The order of the polynomial is 0, 1, 2, or 3.

[0054] Subsequently, according to the cycle Calculate the ionospheric phase according to equation (7) :

[0055] (7)

[0056] According to the ionospheric phase Calculate the first according to formula (8) Vertical ionospheric delay generated by a satellite :

[0057] (8)

[0058] Then through the mapping function Delaying the vertical ionosphere Converted to ionospheric delay along the tilted path of satellite signal propagation :

[0059] (9)

[0060] (10)

[0061] Finally, based on ionospheric delay observations... and tilted path ionospheric delay Calculate the BDSK residuals according to formula (11) :

[0062] (11)

[0063] in, For the first A satellite in the era BDSK ionospheric delay residual at time 1; It is a delayed observation of the ionosphere.

[0064] Step 2: Construct the difference observation equation using the BDSK residuals and solve for the time drift correction. .

[0065] Step 2.1: Derive the difference observation equation using BDSK residuals.

[0066] Define the residual of the difference between adjacent epochs:

[0067] (12)

[0068] in, For the first A satellite in the era BDSK ionospheric delay residual at time 1; For the first A satellite in the era BDSK ionospheric delay residual at time 1; This represents the differential time step.

[0069] Calculate using broadcast ephemeris data according to the method given in step 1.4. and The coordinates of the ionospheric puncture points of each satellite at each time point are obtained. The displacement within the range is then combined with the gradient parameters to perform a Taylor expansion of equation (12), resulting in equation (13), the difference observation equation:

[0070] (13)

[0071] in, for The rate of change of the ionosphere at each epoch; These are the north-south ionospheric gradient parameters; These are the north-south ionospheric gradient parameters; For the first The satellite's ionospheric puncture point is at The north-south displacement within; For the first The satellite's ionospheric puncture point is at The internal east-west displacement; No. Differential observation noise of satellites.

[0072] Step 2.2: When the total number of visible IGSO satellites and MEO satellites At that time, The differential observation equations of the satellites are combined to construct equation (14). Observation matrix Equation (15) shows Observation vector The formula (16) shows diagonal weight matrix ;

[0073] (14)

[0074] (15)

[0075] Establish diagonal weight matrix :

[0076] (16)

[0077] in, For the first The elevation angle of a satellite.

[0078] Step 2.3: According to Observation matrix of IGSO and MEO satellites Observation vector and diagonal weight matrix The time drift increment is solved using the weighted least squares method. Then, adjust the time drift increment. Sequential integration yields the accumulated time drift correction. .

[0079] With the objective of minimizing the weighted sum of squared residuals, the time drift increment is solved using the weighted least squares method based on the observation matrix, observation vector, and diagonal weight matrix. :

[0080] (17)

[0081] Based on the most recent update time of the BDSK parameter With an initial value of zero, for adjacent epochs Sequential integration yields the accumulated time drift correction. :

[0082] (18)

[0083] Whenever the broadcast ephemeris updates the BDSK parameters, The values ​​are reset to zero, and then the mean of the previous filter window is used as a continuous transition value. This utilizes the statistical continuity of the time drift correction within adjacent time periods before and after the parameter update to smoothly transition the initial value after the parameter update, avoiding excessive time drift correction. The jump.

[0084] Step 3: Based on the BDSK residuals of all IGSO+MEO satellites at the current epoch, calculate the inter-satellite residual dispersion index ISRD and regard the ISRD index as the geomagnetic storm sensing index.

[0085] When the receiver is just starting up and there is insufficient data, the ISRD index cannot be calculated using equation (19) based on historical data. Therefore, the ISRD index during the initial 24-hour learning period uses the latitude-based empirical initial value shown in equation (19). .

[0086] (19)

[0087] in, This refers to the geodetic latitude of the receiver.

[0088] After 24 hours of historical data accumulation, the ISRD index is calculated in real time according to formula (20).

[0089] This implementation method is based on the BDSK residuals of all IGSO+MEO satellites at the current epoch, and calculates the inter-satellite residual dispersion ISRD index according to equation (20). ;

[0090] (20)

[0091] in, This represents the sample standard deviation of the BDSK residuals of N IGSO and MEO satellites at the current epoch. The normalized baseline value is equal to the mean of all numerators of ISRD calculated by equation (19) within a preset sliding window over the past 24 hours.

[0092] Step 4: Determine the ionospheric state based on the ISRD index value: if the ISRD index > 3.0, the ionosphere is determined to be in a strong disturbance state; if 1.5 ≤ ISRD index ≤ 3.0, the ionosphere is determined to be in a moderate disturbance state; if the ISRD index < 1.5, the ionosphere is determined to be in a calm period, and output the value of the ionospheric corrected quality flag ION_FLAG.

[0093] ISRD index > 3.0 strong disturbance Perform step 4, and simultaneously magnify the horizontal protection level of the positioning result by 1.5 times to improve positioning integrity. ION_FLAG=2 1.5 ≤ ISRD index ≤ 3.0 Medium disturbance Perform step 4 ION_FLAG=1 ISRD index <1.5 Calm period Perform step 5 ION_FLAG=0

[0094] ION_FLAG is the ionospheric corrected quality flag, with a value of 0 / 1 / 2.

[0095] Step 5: Solve for the gradient parameters;

[0096] If the ionosphere is in a quiescent period, then let the gradient parameter... ,in The background gradient parameter is used to characterize the background ionospheric bias at the reference ionospheric puncture point. These are the north-south ionospheric gradient parameters; These are the north-south ionospheric gradient parameters;

[0097] If the ionosphere is in a disturbed state, then the correction is based on the BDSK residual and the time drift. Derive the first-order horizontal gradient observation equation and solve the gradient parameters using the weighted least squares method. , and Specifically, it includes the following steps:

[0098] Step 5.1: Subtract the time drift correction from the BDSK residual according to equation (21). The spatial residual of the ionosphere was obtained. ;

[0099] (twenty one)

[0100] Step 5.2: The average coordinates of all ionospheric puncture points above the receiver are obtained. Substituting into equation (21), we obtain the first equation shown in equation (22). The first-order horizontal gradient observation equation for each satellite;

[0101] (twenty two)

[0102] in, The background gradient parameter is used to characterize the background ionospheric bias at the reference ionospheric puncture point. For the first Residual observation noise from satellites.

[0103] Step 5.3: [The sentence is incomplete and requires more context to be translated accurately.] The first-order horizontal gradient observation equations of the IGSO and MEO satellites are combined and written in matrix form as shown in equation (23) to obtain... The simultaneous matrix of the first-order horizontal gradient observation equations of IGSO and MEO satellites;

[0104] (twenty three)

[0105] in, The spatial residual matrix for all satellites; This represents the residual observation noise matrix for all satellites. for The coefficient matrix, The first column is all 1s, corresponding to the bias term. ; Column 2 Behavior Corresponding to the north-south ionospheric gradient ; 3rd column Behavior Corresponding to the east-west ionospheric gradient .

[0106] (twenty four)

[0107] Step 5.4: Based on the matrix Calculate the geometric accuracy factor of ionospheric puncture point distribution according to equation (25). ,like If <10, then proceed to step 5.5. When this occurs, it indicates a poor spatial distribution of ionospheric puncture points and low reliability of gradient parameters, so let .

[0108] (25)

[0109] in, express The smallest eigenvalue of a matrix; express The trace of a matrix, i.e. The sum of the diagonals of a matrix;

[0110] Step 5.5: Combining the matrix The diagonal weight matrix shown in equation (16) Solve for the degree parameter using the weighted least squares method on the simultaneous matrices. , and Specifically, this is achieved through formula (26).

[0111] (26)

[0112] Step 6: Adjust according to time drift amount and gradient parameters , , The tilted path ionospheric delay calculated in step 1.5 After correction, the single-frequency ionospheric delay correction amount is obtained. .

[0113] This implementation method is based on each BDS satellite (including IGSO satellites, MEO satellites, and GEO satellites) visible to the receiver at the current epoch. Delay the ionosphere along the tilted path Time drift correction amount Coordinates of ionospheric puncture point The average of the coordinates of all ionospheric puncture points was obtained. gradient parameters and Superposition to construct enhanced ionospheric delay correction values The calculation formula is as follows:

[0114] (27)

[0115] To verify the effectiveness of the method of this invention, the final Global Ionosphere Map (GIM) published by IGS was used as a benchmark, and the enhanced ionospheric delay correction was obtained. and tilted path ionospheric delay The root mean square error (RMSE) compared to the benchmark. Specific results are as follows: Figure 3 As shown, during the geomagnetic storm, specifically the epoch 600-1200, ionospheric activity significantly increased. and Both the benchmark RMSE and the benchmark RMSE showed a clear upward trend. Among them, The baseline RMSE rises sharply during this stage, reaching over 8m, indicating its limited adaptability to rapid ionospheric changes during strong geomagnetic storms; while The baseline RMSE remained relatively stable within the 3.5–4.5 m range during the geomagnetic storm. After the storm ended, specifically after epoch 1200, Although the RMSE relative to the benchmark has decreased, it has remained at a relatively high level near 6m for a long time. The RMSE relative to the baseline decreased rapidly after epoch 1600, eventually approaching below 0.5m and returning to normal levels. As for the average RMSE over the entire day... The overall RMSE compared to the benchmark is 3.12m, which is higher than... The improvement of approximately 47.9% compared to the baseline of 5.99m demonstrates that the method of this invention has a significant advantage in modeling accuracy of ionospheric delay under both normal and geomagnetic storm conditions.

[0116] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for autonomous correction of single-frequency ionospheric delay, characterized in that, The method includes the following steps: Step 1: Acquire observation data and satellite broadcast ephemeris data from IGSO and MEO satellites, perform carrier phase smoothing pseudorange processing, extract ionospheric delay observations from the smoothed pseudorange, and then calculate the tilted path ionospheric delay and BDSK residual. Step 2: Construct the difference observation equation using the BDSK residuals and solve for the time drift correction. ; Step 3: Based on the BDSK residuals of all IGSO+MEO satellites at the current epoch, calculate the inter-satellite residual dispersion index ISRD and regard the ISRD index as the geomagnetic storm sensing index. Step 4: Determine the state of the ionosphere based on the ISRD index value: if the ISRD index is ≥1.5, the ionosphere is determined to be in a disturbed state; if the ISRD index is <1.5, the ionosphere is determined to be in a calm period. Step 5: Solve for the gradient parameters: If the ionosphere is in a quiescent state, set the gradient parameters to zero; if the ionosphere is in a disturbed state, calculate the gradient parameters based on the BDSK residuals and time drift correction. Derive the first-order horizontal gradient observation equation, and solve the gradient parameters using the weighted least squares method. Step 6: Adjust according to time drift amount and gradient parameters on ionospheric delay along inclined paths After correction, the single-frequency ionospheric delay correction amount is obtained. .

2. The single-frequency ionospheric delay autonomous correction method according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Obtain BDS single-frequency RINEX observation data and satellite broadcast ephemeris data, filter out the visible BeiDou on-orbit satellite data within the current epoch, and extract the effective observation data of IGSO satellites and MEO satellites; Step 1.2: Use a hatch filter to process the raw pseudorange data from the selected IGSO and MEO satellite observation data. Carrier phase smoothing is performed to obtain the smoothed pseudorange. ; Step 1.3: From the smoothed pseudo-range Extracting delayed observations of the ionosphere ; Step 1.4: Based on the observation data from the selected IGSO and MEO satellites, calculate the... Coordinates of the ionospheric puncture point from the satellite to the receiver; Step 1.5: Calculate the tilted path ionospheric delay using the BDSK parameters from the broadcast ephemeris of IGSO and MEO satellites and the coordinates of the ionospheric puncture point. Thus, based on ionospheric delay observations and tilted path ionospheric delay Calculate the BDSK residuals Specifically, this is achieved through the following formula: （11）。 3. The single-frequency ionospheric delay autonomous correction method according to claim 2, characterized in that, Step 1.3 describes the process of obtaining the smoothed pseudorange. Extracting delayed observations of the ionosphere ,include: Calculate the ECEF coordinates of each satellite at the time of signal transmission, and thus calculate the first... Geometric distance between satellites and receiver Satellite clock bias correction and receiver clock difference And the tropospheric delay was calculated using the Saastamoinen model. Then, according to equation (2), from the smoothed pseudo-range Extracting delayed observations of the ionosphere : (2)； in, For the first The geometric distance between the satellite and the receiver; It is the speed of light.

4. The single-frequency ionospheric delay autonomous correction method according to claim 3, characterized in that, Step 2 includes the following steps: Step 2.1: Derive the difference observation equation using BDSK residuals; Step 2.2: When the total number of visible IGSO satellites and MEO satellites At that time, The differential observation equations of the satellites are combined to construct equation (14). Observation matrix Equation (15) shows Observation vector The formula (16) shows diagonal weight matrix ; （14） （15） （16） in, For the first The elevation angle of the satellite; Step 2.3: According to Observation matrix of IGSO and MEO satellites Observation vector and diagonal weight matrix The time drift increment is solved using the weighted least squares method according to equation (17). Then, based on the most recent update time of the BDSK parameter... The initial value is zero, and the time drift increment for adjacent epochs is calculated according to equation (18). The cumulative time drift correction is obtained by performing sequential integration. ; （17） （18）。 5. The single-frequency ionospheric delay autonomous correction method according to claim 4, characterized in that, Step 2.1, which describes deriving the difference observation equation using BDSK residuals, includes: Define the residual of the difference between adjacent epochs: （12） in, For the first A satellite in the era BDSK ionospheric delay residual at time 1; For the first A satellite in the era BDSK ionospheric delay residual at time 1; This is the differential time step; Calculate using broadcast ephemeris data and The coordinates of the ionospheric puncture points of each satellite at each time point are obtained. Displacement within; By performing a Taylor expansion of equation (12) using the gradient parameters, we obtain the difference observation equation (13): （13） in, for The rate of change of the ionosphere at each epoch; These are the north-south ionospheric gradient parameters; These are the north-south ionospheric gradient parameters; For the first The satellite's ionospheric puncture point is at The north-south displacement within, of which express The latitude of the ionospheric puncture point at any given time. express Latitude of the ionospheric puncture point at any given moment; For the first The satellite's ionospheric puncture point is at The east-west displacement within, of which express The longitude of the ionospheric puncture point at any given time. express Longitude of the ionospheric puncture point at any given time; No. Differential observation noise of satellites.

6. The single-frequency ionospheric delay autonomous correction method according to claim 4, characterized in that, The method also includes: accumulating time drift corrections whenever the broadcast ephemeris updates the BDSK parameters. The values ​​are reset to zero, and then the mean of the previous filter window is used as a continuous transition value. This utilizes the statistical continuity of the time drift correction within adjacent time periods before and after the parameter update to smoothly transition the initial value after the parameter update, avoiding... Jump.

7. The single-frequency ionospheric delay autonomous correction method according to claim 5, characterized in that, Step 3, which involves calculating the inter-satellite residual dispersion index (ISRD), includes: The ISRD index during the initial 24-hour learning period adopts the latitude-based empirical initial value shown in equation (19). ; （19） in, The latitude of the receiver; After the initial 24-hour learning period, the ISRD index is calculated in real time according to formula (20); （20） in, This represents the sample standard deviation of the BDSK residuals of N IGSO and MEO satellites at the current epoch. The normalized baseline value is equal to the mean of all numerators of ISRD calculated by equation (19) within a preset sliding window over the past 24 hours.

8. The single-frequency ionospheric delay autonomous correction method according to claim 7, characterized in that, The method also includes: if the ISRD index > 3.0, the ionospheric state is determined to be a strong disturbance; if 1.5 ≤ ISRD index ≤ 3.0, the ionospheric state is determined to be a moderate disturbance.

9. The single-frequency ionospheric delay autonomous correction method according to claim 7, characterized in that, Step 5 describes the correction based on BDSK residuals and time drift. The first-order horizontal gradient observation equation is derived, and the gradient parameters are solved using the weighted least squares method, including the following steps: Step 5.1: Subtract the time drift correction from the BDSK residual according to equation (21). The spatial residual of the ionosphere was obtained. ; （21） Step 5.2: Calculate the average coordinates of all ionospheric puncture points above the receiver. Substituting into equation (21), we obtain the first equation shown in equation (22). The first-order horizontal gradient observation equation for each satellite; （22） in, The background gradient parameter is used to characterize the background ionospheric bias at the reference ionospheric puncture point. For the first Residual observation noise from the satellite; Step 5.3: [The sentence is incomplete and requires more context to be translated accurately.] The first-order horizontal gradient observation equations of the IGSO and MEO satellites are combined and written in matrix form as shown in equation (23) to obtain... The simultaneous matrix of the first-order horizontal gradient observation equations of IGSO and MEO satellites; （23） in, The spatial residual matrix for all satellites; The residual observation noise matrix for all satellites; for The coefficient matrix, The first column is all 1s, corresponding to the bias term. ; Column 2 Behavior Corresponding to the north-south ionospheric gradient ; 3rd column Behavior Corresponding to the east-west ionospheric gradient ; Step 5.4: Based on the matrix Calculate the geometric accuracy factor of ionospheric puncture point distribution according to equation (25). ,like If <10, then proceed to step 5.

5. When this occurs, it indicates a poor spatial distribution of ionospheric puncture points and low reliability of gradient parameters. Therefore, let the gradient parameters... ; （25） in, express The smallest eigenvalue of a matrix; express The trace of a matrix, i.e. The sum of the diagonals of a matrix; Step 5.5: Combining the matrix The diagonal weight matrix shown in equation (16) Solve for the degree parameter using the weighted least squares method on the simultaneous matrices. , and Specifically, this is achieved through formula (26); （26）。

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