A method for generating regional ionospheric delay based on spatio-temporal constraint enhancement

Abstract

The application relates to a regional ionospheric delay generation method based on space-time constraint enhancement, which comprises the following steps: obtaining original data of reference stations in a target region and completing preprocessing; based on the preprocessed data, adopting an M-W combination model and an ionosphere-free combination algorithm to solve and fix double-difference integer ambiguity between a main reference station and an auxiliary reference station; based on the obtained double-difference integer ambiguity, solving carrier phase double-difference ionospheric delay between the main reference station and the auxiliary reference station through a carrier phase double-difference equation; adopting a linear combination model to perform spatial interpolation on the carrier phase double-difference ionospheric delay, obtaining regional ionospheric delay correction based on spatial interpolation; constructing a regional ionospheric delay short-term change prediction model, obtaining regional ionospheric delay correction based on time series prediction; combining the obtained regional ionospheric delay correction and the regional ionospheric delay correction, weighting with a weight coefficient to generate a final regional ionospheric delay.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation technology, specifically relating to a method for generating regional ionospheric delay based on spatiotemporal constraints. Background Technology

[0002] The Global Navigation Satellite System (GNSS) has powerful functions such as navigation, positioning, and timing. It is an important means to help realize the informatization and modernization of transportation. It covers multiple typical application scenarios such as sea, land, and air, and is widely used in transportation, military, agriculture and other fields. Examples include fully automatic aircraft landing, fully automatic carrier landing, vehicle navigation systems, unmanned driving, intelligent traffic control, intelligent marine operations, and intelligent agricultural machinery collaborative operations.

[0003] With the rapid development of Global Navigation Satellite Systems (GNSS) and the increasing number of GNSS users, the demands for GNSS navigation and positioning are constantly rising. The requirement for positioning accuracy has increased from meter-level to centimeter-level and even millimeter-level, making high-precision positioning the development trend of GNSS navigation and positioning. Ionospheric delay, as one of the main error sources in satellite signal propagation, exhibits significant distance attenuation characteristics in its spatial correlation. As the baseline distance between the reference station and the user terminal increases, the spatial consistency of ionospheric errors gradually weakens, leading to a significant decrease in the accuracy of traditional pure space-domain ionospheric interpolation modeling methods. This inherent characteristic fundamentally restricts the service range and application scenario expansion of regional high-precision positioning technology.

[0004] Traditional pure spatial domain ionospheric modeling methods have significant limitations under sparse baseline conditions. Traditional methods rely on dense spatial sampling to fit the ionospheric distribution characteristics, but long baselines lead to a significant decrease in ionospheric spatial correlation, and sparse baselines cannot supplement sufficient sampling points. In addition, the spatiotemporal characteristics of the ionosphere are complex and susceptible to anomalous activity, making pure spatial domain modeling under long baseline conditions difficult to adapt to the error evolution of the ionosphere. This results in a significant reduction in the accuracy of ionospheric delay modeling under sparse baseline conditions, directly causing an increase in the failure rate of user-end ambiguity fixation and a decrease in the stability of positioning results. This fails to meet the core requirements of large-scale, high-precision, and high-reliability ionospheric error compensation in scenarios such as intelligent transportation, precision agriculture, and drone swarm operations. Summary of the Invention

[0005] To ensure centimeter-level accuracy and service continuity for high-precision positioning within a large, sparsely populated area covered by reference stations, and to meet the stringent requirements of various industries for high-precision positioning, this invention proposes a regional ionospheric delay generation method based on spatiotemporal constraint enhancement, which includes:

[0006] S1) Obtain the raw data of the base stations in the target area and complete the preprocessing;

[0007] S2) Based on the preprocessed data, the double-difference integer ambiguity between the main reference station and the auxiliary reference station is solved and fixed using the MW combined model and the ionosphere-free combined algorithm.

[0008] S3) Based on the obtained double-difference integer ambiguity, the carrier phase double-difference ionospheric delay between the main reference station and the auxiliary reference station is calculated by the carrier phase double-difference equation;

[0009] S4) Spatial interpolation is performed on the carrier phase double-difference ionospheric delay, and a linear combination model is used to obtain the regional ionospheric delay correction based on spatial interpolation.

[0010] S5) Based on the time characteristics of the ionosphere, a prediction model for short-term changes in regional ionospheric delay is constructed to obtain the regional ionospheric delay correction amount based on time series prediction;

[0011] S6) The obtained regional ionospheric delay correction amount based on spatial interpolation and the regional ionospheric delay correction amount based on time series prediction are weighted by dynamic weighting coefficients to generate the final regional ionospheric delay.

[0012] The beneficial effects of this invention are as follows:

[0013] To address the issue of decreased compensation accuracy due to the gradual attenuation of spatial correlation of ionospheric delay with increasing distance under long baseline conditions, this invention proposes a regional ionospheric delay generation method based on spatiotemporal constraint enhancement. It deeply analyzes the temporal evolution of ionospheric delay, constructs a high-precision regional ionospheric delay generation model that combines spatial correlation and temporal continuity, and generates high-precision regional ionospheric delay through a spatiotemporal joint correction algorithm using dynamic weighting coefficients. This effectively solves the problem of insufficient accuracy in ionospheric delay modeling under long baseline conditions, meeting the centimeter-level accuracy and service continuity requirements for high-precision regional positioning within a large area covered by sparse reference stations. It can be applied to application scenarios requiring centimeter-level real-time positioning services, such as surveying, intelligent transportation, precision agriculture, and UAV swarm operations, ensuring the accuracy and reliability of high-precision positioning in user areas, which is of great significance. Attached Figure Description

[0014] Figure 1 This is a flowchart of a method for delayed generation of regional ionosphere based on spatiotemporal constraints. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] Combined with appendix Figure 1 Taking the Global Navigation Satellite System (GNSS) as an example, the technical solution of the present invention will be further described in detail.

[0017] As attached Figure 1 As shown, this invention provides a method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement, which includes:

[0018] Step S1) Obtain the raw data of the base stations in the target area and complete the preprocessing.

[0019] The preprocessing includes: 1) conducting integrity verification, including verifying data format, number of visible satellites, etc.; 2) using the ionospheric residual method combined with MW combination to detect and repair cycle slips; and 3) using weighted least squares method to identify and remove gross errors, thereby ensuring data reliability and laying the foundation for subsequent modeling.

[0020] Step S2) Based on the preprocessed data, the double-difference integer ambiguity between the main reference station and the auxiliary reference station is solved and fixed using the MW combined model and the ionosphere-free combined algorithm.

[0021] When using observations transmitted from a base station for positioning, one base station is typically designated as the primary base station among multiple base stations within the target area, while the others are designated as secondary base stations. The primary base station is generally the base station within the target area that is closest to the user's location (also known as the target location). It is usually determined based on the spatial relationship between the base station and the user's location, and it serves as the core base station for reference in the fusion of observation information or the generation of correction information.

[0022] Fixing the baseline ambiguity between two reference stations is a prerequisite for the operation of multi-reference station positioning technology. This invention first uses the Melbourne-Wübbena (MW) combined model to fix the double-difference wide-lane integer ambiguity. After correctly fixing the double-difference wide-lane integer ambiguity, the double-difference integer ambiguity is obtained through an ionospherically-free combined algorithm, as detailed below:

[0023] (1)

[0024] In formula (1) These are double-difference carrier phase observations without ionosphere. The satellite signal is observed as a double-difference carrier phase in frequency band 1. f1 represents the double-difference carrier phase observation of the satellite signal in frequency band 2, where f1 is the carrier frequency of the satellite signal in frequency band 1, and f2 is the carrier frequency of the satellite signal in frequency band 2. Let c be the double-difference geometric distance, and c be the speed of light. The double-difference integer ambiguity of the satellite signal in frequency band 1. The double-difference integer ambiguity of the satellite signal in frequency band 2. This is the double-difference tropospheric delay error. These are double-difference wide-lane carrier phase observations. For double-difference, ionosphere-free combined ambiguity, λ IF For ionosphere-free combination wavelengths, ε IF This is to eliminate ionospheric observation noise.

[0025] The value of the double-difference tropospheric delay error can be determined using the Saastamoinen model.

[0026] The double-difference integer ambiguity can be obtained by solving formula (1). and The floating-point solution is obtained by fixing the double-difference integer ambiguity using the LAMBDA algorithm, thus obtaining the correct double-difference integer ambiguity.

[0027] Step S3) Based on the obtained double-difference integer ambiguity, the carrier phase double-difference ionospheric delay between the main reference station and the auxiliary reference station is calculated by the carrier phase double-difference equation.

[0028] Based on step S2, the double-difference integer ambiguity between the primary and secondary reference stations is obtained. and Then, the double-difference ionospheric delay on the carrier phase observation is calculated using the carrier phase double-difference equation. The calculation formula is as follows:

[0029] (2)

[0030] In equation (2), λ1 is the double-difference ionospheric delay of the carrier phase of the satellite signal in frequency band 1, λ2 is the wavelength of the satellite signal in frequency band 1, and λ3 is the wavelength of the satellite signal in frequency band 2; the meanings of the other parameters are the same as those in equation (2).

[0031] Based on the known relationship between ionospheric delay error and frequency in this field, namely that the magnitude of the ionospheric delay error is inversely proportional to the square of the frequency, the carrier phase double-difference ionospheric delay of the satellite signal in frequency band 2 and other frequency bands can be calculated, which will not be elaborated here.

[0032] Step S4) Spatial interpolation is performed on the carrier phase double-difference ionospheric delay, and the regional ionospheric delay correction amount based on spatial interpolation is obtained by using a linear combination model.

[0033] The modeling accuracy of regional ionospheric delay directly affects the positioning accuracy of regional positioning. The modeling accuracy of regional ionospheric delay is highly correlated with the spatial distribution of the base station. Based on the spatial correlation characteristics of the ionosphere, this invention employs a linear combination model to model the regional ionospheric delay. The specific description of the established linear combination model, based on the regional ionospheric delay correction obtained through spatial interpolation, is as follows:

[0034] (3)

[0035] In equation (3), the subscript r represents the primary reference station, the subscript m represents the interpolation point, and the subscript n represents the number of reference stations (i.e., the total number of primary and secondary reference stations). mr This represents the regional ionospheric delay between the baseline of the main reference station and the point to be interpolated. This represents the carrier phase double-difference ionospheric delay between the primary reference station and the (n-1)th auxiliary reference station. All are linear combination coefficients. (i=1,2,……n) must satisfy the following condition:

[0036] (4)

[0037] In equation (4), n is the number of reference stations. X is the coefficient of the linear combination. m Let X be the plane coordinate vector of the point to be interpolated. i Let be the plane coordinate vector of the i-th reference station, and Min represents the minimum value.

[0038] To explain further, since the number of reference stations is n, the set of linear combination coefficients will also include the coefficients of the main reference station. Therefore, the linear combination coefficients in formulas 4, 5, and 6 are... The linear combination coefficients appearing in Equation 3, which represents the linear combination model, are... The reason for this is that this paper uses a double-difference model to construct the ionospheric delay, with the main reference station serving as the reference station. Its ionospheric term is eliminated during the double-difference process, therefore, only n-1 independent ionospheric parameters actually participate in the linear combination. In other words, although equations 4, 5, and 6 formally contain n coefficients, due to the reference station constraint of the double-difference model, its effective degrees of freedom are n-1, among which the term corresponding to the main reference station does not have independent physical meaning in the double-difference model.

[0039] Regarding the selection of the value of n, a specific value can be set according to the network density of the deployed base stations, the positioning area range, and the algorithm requirements. Typically, n is selected as at least three. For base station networks within different target areas, the number of base stations n may vary because the positioning area ranges may differ. However, for a base station network within the same target area, the number of base stations n is fixed, and the number of base stations n is the same for different interpolation points m. In this invention, the interpolation point is selected from the obtained approximate user location coordinates.

[0040] Formula (4) above can be rewritten as:

[0041] (5)

[0042] in:

[0043] (6)

[0044] In equation (6), and (i=1,2,……n-1) represent the coordinate differences between the i-th auxiliary reference station and the main reference station; and These represent the coordinate differences between the point to be interpolated and the main reference station; It is a linear combination coefficient matrix.

[0045] Solving equation (6) using the least squares algorithm yields the linear combination coefficient matrix. :

[0046]

[0047] The obtained linear combination coefficient matrix contains all the linear combination coefficient values. .

[0048] Step 3 yields the carrier phase double-difference ionospheric delay between the main reference station and the first auxiliary reference station, the carrier phase double-difference ionospheric delay between the main reference station and the second auxiliary reference station, ..., the carrier phase double-difference ionospheric delay between the main reference station and each auxiliary reference station.

[0049] Therefore, according to formula (3), the regional ionospheric delay V between the baseline of the main reference station and the interpolation point can be obtained. mr The ionosphere in this region is delayed by V mr It is the regional ionospheric delay correction amount obtained based on spatial interpolation, using To express.

[0050] Step S5) Based on the time characteristics of the ionosphere, construct a prediction model for short-term changes in regional ionospheric delay and obtain the correction amount of regional ionospheric delay based on time series prediction.

[0051] Regarding ionospheric time prediction, since ionospheric changes have a strong temporal correlation, establishing ionospheric time models and predicting ionospheric times is feasible. This invention uses a linear fitting model to construct a prediction model for delayed short-term changes in the regional ionosphere. The linear fitting model is shown below:

[0052] (7)

[0053] In equation (7), x represents the systematic bias. The rate of change of the systematic deviation, For time intervals, A sequence of random variables with zero mean. Let covariance matrix be the variance matrix. A sequence of random variables with zero mean. Let k be the Dirac function, and t be discrete-time indices. This represents the variance of the acceleration noise.

[0054] The zero-mean random variable sequence and Let x represent the process noise of the system deviation, and k and t represent different epoch times.

[0055] Based on epoch-by-epoch and satellite-by-satellite data, system bias can be predicted using Kalman filtering. Specifically, by using Kalman filtering, the observation sequence of user ionospheric delay corrections up to the current epoch (t) within the sliding time window is used as the input x of the linear fitting model (Formula (7)). This allows for real-time estimation of the system bias at the next epoch (t+1), thus predicting the regional ionospheric delay correction for the next epoch. This process can be repeated to achieve dynamic evolution modeling of regional ionospheric delay in the time dimension, obtaining the regional ionospheric delay correction based on time series prediction. The sliding time window width is selected according to actual needs. A larger time window width helps extract long-term trends and is suitable for predictions over large latitudes; a smaller time window width is more suitable for short-term predictions and can more accurately reflect the instantaneous changes in the ionosphere.

[0056] The observation sequence for user ionospheric delay correction can be obtained using existing techniques. It originates from epochs in historical observation data where ambiguity was successfully fixed. The corresponding epoch's user ionospheric delay estimate is obtained through inversion using dual-frequency GNSS observations. Since epochs with fixed ambiguity have high solution reliability, the inverted ionospheric delay can serve as a highly reliable reference value for the ionospheric delay at the user's location. Arranging these inversion results from multiple consecutive epochs in chronological order forms the observation sequence for user ionospheric delay correction.

[0057] As can be seen from the above, the user ionospheric delay correction amount within the sliding time window up to the current epoch (t) is used as the system bias at time t and input into formula (7). The resulting system bias at time t+1 is the regional ionospheric delay correction amount obtained based on time series prediction. To express.

[0058] Step S6) The obtained regional ionospheric delay correction amount based on spatial interpolation and the regional ionospheric delay correction amount based on time series prediction are weighted by dynamic weighting coefficients to generate the final regional ionospheric delay.

[0059] For the regional ionospheric delay correction obtained based on spatial interpolation and the regional ionospheric delay correction obtained based on time series prediction, a spatiotemporal joint correction algorithm is designed. Dynamic weighting is performed using dynamic weight coefficients to generate the final regional ionospheric delay, which integrates the spatial correlation and temporal continuity of the regional ionospheric delay.

[0060] The method for generating the final regional ionospheric delay is as follows:

[0061] (8)

[0062] In formula (8) For the final regional ionospheric delay, This is the regional ionospheric delay correction amount obtained based on time series prediction, which reflects temporal continuity. This is the regional ionospheric delay correction obtained based on spatial interpolation, which reflects spatial correlation. t w represents the first weighting coefficient for the regional ionospheric delay correction obtained from time series predictions. s This represents the second weighting coefficient for the regional ionospheric delay correction obtained based on spatial interpolation. The first weighting coefficient is w. t Second weighting coefficient w s The expressions are as follows:

[0063] (9)

[0064] In equation (9), p is the current epoch number. The regional ionospheric delay correction amount obtained from the time series prediction of the previous epoch. The error between the true value and the regional ionospheric delay. The regional ionospheric delay correction obtained from spatial interpolation in the previous epoch. The error between the actual value and the regional ionospheric delay.

[0065] The true value of the regional ionospheric delay of the previous epoch can be obtained after the ambiguity is fixed.

[0066] As can be seen from formula (9), the first and second weighting coefficients w t and w s It is dynamic and changing.

[0067] This invention proposes a spatiotemporal constraint-enhanced regional ionospheric delay generation method. Addressing the technical challenge of insufficient error compensation accuracy caused by the attenuation of ionospheric delay with increasing distance due to spatial correlation in long-baseline scenarios, this invention constructs a short-term ionospheric delay prediction model based on the temporal evolution characteristics of the ionosphere. It also designs a spatiotemporal joint correction algorithm that integrates spatial correlation and temporal continuity to generate high-precision regional ionospheric delay, ensuring the high accuracy and reliability of regional high-precision positioning technology.

[0068] The above description, in conjunction with specific embodiments, provides a more detailed explanation of the present invention. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions are considered to be within the scope of protection claimed by the present invention.

Claims

1. A method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement, comprising: S1) Obtain the raw data of the base stations in the target area and complete the preprocessing; S2) Based on the preprocessed data, the double-difference integer ambiguity between the main reference station and the auxiliary reference station is solved and fixed using the MW combined model and the ionosphere-free combined algorithm. S3) Based on the obtained double-difference integer ambiguity, the carrier phase double-difference ionospheric delay between the main reference station and the auxiliary reference station is calculated by the carrier phase double-difference equation; S4) Spatial interpolation is performed on the carrier phase double-difference ionospheric delay, and a linear combination model is used to obtain the regional ionospheric delay correction based on spatial interpolation. S5) Based on the time characteristics of the ionosphere, a prediction model for short-term changes in regional ionospheric delay is constructed to obtain the regional ionospheric delay correction amount based on time series prediction; S6) The obtained regional ionospheric delay correction amount based on spatial interpolation and the regional ionospheric delay correction amount based on time series prediction are weighted by dynamic weighting coefficients to generate the final regional ionospheric delay.

2. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 1, wherein: In step S1, the preprocessing includes: performing integrity verification, using the ionospheric residual method combined with MW combination to detect and repair cycle slips, and using weighted least squares method to identify and remove gross errors.

3. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 1, wherein: Step S2 further includes: first, using the MW combination model to fix the double-difference wide-lane integer ambiguity, then obtaining the double-difference integer ambiguity through the ionosphere-free combination algorithm, and finally fixing the double-difference integer ambiguity through the LAMBDA algorithm to obtain the correct double-difference integer ambiguity.

4. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 3, wherein: Step S2 further includes: the method for obtaining double-difference integer ambiguity through the ionosphere-free combination algorithm is as follows: ； in These are double-difference carrier phase observations without ionosphere. The satellite signal is observed as a double-difference carrier phase in frequency band 1. f1 represents the double-difference carrier phase observation of the satellite signal in frequency band 2, where f1 is the carrier frequency of the satellite signal in frequency band 1, and f2 is the carrier frequency of the satellite signal in frequency band 2. Let c be the double-difference geometric distance, and c be the speed of light. The double-difference integer ambiguity of the satellite signal in frequency band 1. The double-difference integer ambiguity of the satellite signal in frequency band 2. This is the double-difference tropospheric delay error. These are double-difference wide-lane carrier phase observations. For double-difference, ionosphere-free combined ambiguity, λ IF For ionosphere-free combination wavelengths, ε IF This is to eliminate ionospheric observation noise.

5. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 4, wherein: In step S3, the method for calculating the carrier phase double-difference ionospheric delay between the primary and secondary reference stations using the carrier phase double-difference equation is as follows: ； in: λ1 is the carrier phase double-difference ionospheric delay of the satellite signal in frequency band 1, λ2 is the wavelength of the satellite signal in frequency band 1, and λ3 is the wavelength of the satellite signal in frequency band 2. By recognizing that the magnitude of the ionospheric delay error is inversely proportional to the square of the frequency, the double-difference ionospheric delay of the satellite signal in other frequency bands can be obtained.

6. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 1, wherein: In step S4, the method for obtaining the regional ionospheric delay correction based on spatial interpolation using a linear combination model is as follows: ； Where the subscript r represents the main reference station, the subscript m represents the interpolation point, and the subscript n represents the number of reference stations, V mr This represents the regional ionospheric delay between the baseline of the main reference station and the point to be interpolated. This represents the carrier phase double-difference ionospheric delay between the primary reference station and the (n-1)th auxiliary reference station. All are linear combination coefficients. The following conditions must be met: ； Where n is the number of base stations, X m Let X be the plane coordinate vector of the point to be interpolated. i Let be the plane coordinate vector of the i-th reference station, and Min represent the minimum value; Regional ionospheric delay V between the baseline of the main reference station and the interpolation point mr This is the regional ionospheric delay correction amount obtained based on spatial interpolation.

7. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 6, wherein: linear combination coefficients The condition to be satisfied can be replaced with the following expression: ； in: ； in and Let i and n represent the coordinate difference between the i-th auxiliary reference station and the main reference station, respectively, i=1,2,……n-1; and These represent the coordinate differences between the point to be interpolated and the main reference station; It is a linear combination coefficient matrix; The least squares algorithm is used to solve for the linear combination coefficient matrix: .

8. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 1, wherein: In step S5, a linear fitting model is used to construct a prediction model for delayed short-term changes in the regional ionosphere. The linear fitting model is shown below: ； Where x is the systematic bias. The rate of change of the systematic deviation, For time intervals, A sequence of random variables with zero mean. Let covariance matrix be the variance matrix. A sequence of random variables with zero mean. Let k be the Dirac function, and t be discrete-time indices. The variance of the acceleration noise; Using the observation sequence of user ionospheric delay correction up to the current epoch within the sliding time window as input to the linear fitting model, the regional ionospheric delay correction for the next epoch is predicted by estimating the system bias in real time. This process is repeated to obtain the regional ionospheric delay correction based on time series prediction.

9. The method for delayed generation of regional ionosphere based on spatiotemporal constraint enhancement according to claim 1, wherein: In step S6, the method for generating the final regional ionospheric delay is as follows: ； in Indicates the final regional ionospheric delay, This represents the regional ionospheric delay correction amount obtained based on time series prediction. w represents the regional ionospheric delay correction obtained based on spatial interpolation. t w represents the first weighting coefficient for the regional ionospheric delay correction obtained from time series predictions. s w represents the second weighting coefficient for the regional ionospheric delay correction obtained based on spatial interpolation. t and w s The expressions are as follows: ； Where p is the current epoch number. The regional ionospheric delay correction amount obtained from the time series prediction of the previous epoch. The error between the true value and the regional ionospheric delay. The regional ionospheric delay correction obtained from spatial interpolation in the previous epoch. The error between the actual value and the regional ionospheric delay.

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