Ionized layer weighted modeling method for Beidou ground-based enhancement

Abstract

The invention discloses a Beidou ground-based enhancement-oriented ionized layer weighted modeling method, which comprises the following steps of: proposing a weight function which takes an included angle between a connecting line from an interpolation point to a main reference station and each baseline as an independent variable according to the correlation of ionized layer delay of a to-be-interpolated point and a baseline and the characteristic related to the included angle between the to-be-interpolated point and the baseline; according to the correlation of ionosphere delay of a point to be interpolated and a baseline and the characteristic related to the distance ratio between the point to be interpolated and the baseline, proposing a weight function which takes the ratio of the distance from the interpolation point to a main reference station to the length of each baseline as an independent variable; the normalized ionosphere delay sample weight can be obtained by integrating the two weight functions, and the value of the point to be interpolated is obtained by using the weight according to the interpolation model of the BLUP framework. High interpolation precision can be achieved in each area in a large and medium-sized network with an active ionized layer, and the service quality of network RTK (Real-Time Kinematic) is improved.

Description

Technical Field

[0001] The invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and specifically relates to an ionospheric weighted modeling method for Beidou ground-based enhancement. Background Art

[0002] The Global Positioning System (GNSS) aims to provide high-precision positioning information to users around the world. Single-point positioning technology was first proposed, which can obtain positioning results using only satellite observation data. However, due to the neglect of a large number of errors in the solution process and the influence of pseudo-range noise, its positioning accuracy is not high. To solve this problem, the PPP and RTK methods proposed later respectively use the single-station error modeling correction and inter-station differential elimination of common errors to achieve decimeter-level and centimeter-level positioning accuracy. For the PPP method, since more error parameters need to be estimated, its convergence time is longer than that of RTK. Among these error parameters that need to be estimated, atmospheric delay is difficult to accurately model due to its strong uncertainty, which is the main factor that makes it difficult to shorten the convergence time of PPP. In recent years, the Beidou Satellite Navigation System (BDS) has provided new ideas for solving the above problems with its unique advantages of multi-frequency and multi-satellite. Compared with other GNSS systems, the BeiDou system can simultaneously provide signals in multiple frequency bands, such as B1I, B1C, B2a, and B3I, and has more satellites, which provides a richer data basis for the fusion of multi-frequency observation data and the optimization of satellite spatial geometry.

[0003] For the RTK method, most of the errors can be eliminated by the double difference between stations and satellites, while the remaining errors related to the propagation path (i.e., atmospheric delay, including ionospheric delay and tropospheric delay) cannot be completely eliminated, but can only be weakened. As the distance between stations increases, the spatial correlation of the errors weakens, making these errors impossible to ignore. Some scholars' research points out that tropospheric delay has a significant correlation with height difference, altitude angle, and baseline distance, and changes slowly over time. Due to its good spatial correlation, it can be effectively solved. In comparison, ionospheric delay is related to complex factors such as geomagnetism, solar activity, and day and night seasons, and has higher uncertainty. It is a very difficult problem that must be considered. Some scholars use the frequency-related characteristics of the ionosphere and adopt non-combined ionospheric estimation models or multi-frequency combination models to weaken and eliminate the influence of the ionosphere.

[0004] The NRTK method solves the problem that RTK accuracy is limited by the distance between stations from a new perspective. It does not require the user terminal to deploy complex algorithms, but provides enhanced information in the form of services. This method continuously solves the double-difference atmospheric delay value of the baseline between each reference station in the region through the base station network. Therefore, the problem is turned to how to design an accurate interpolation method to characterize the ionospheric activity in the region. It mainly includes: distance-based linear interpolation (DIM); linear combination model (LCM); linear interpolation model (LIM); least squares registration model (LSC); low-order trend surface model (LSM); Kriging model (KRG). In summary, whether it is RTK, NRTK or PPP-RTK, atmospheric delay, especially the influence of ionospheric delay, must be considered. Among the methods for dealing with ionospheric delay, regional modeling and interpolation methods are important solutions for a large number of users over a large area. However, current modeling interpolation methods all attempt to establish an overall model to describe the atmospheric conditions in the area, but fail to adjust the model according to the different locations of users, resulting in large differences in the accuracy of atmospheric corrections obtained by users in the modeling area due to their different locations. Summary of the invention

[0005] To solve the above problems, the present invention discloses an ionospheric weighted modeling method for Beidou ground-based enhancement. According to the correlation between the ionospheric delay of the interpolation point and the baseline, a new ionospheric delay modeling interpolation method is designed. Through this method, high interpolation accuracy can be achieved in all areas of large and medium-sized networks with active ionosphere, and the accuracy is better than the existing main interpolation methods.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] The ionospheric weighted modeling method for Beidou ground-based enhancement includes the following steps:

[0008] Step 1: According to the characteristics of the correlation between the ionospheric delay of the interpolation point and the baseline and the angle between them, a weight function is proposed with the angle between the line from the interpolation point to the main reference station and each baseline as the independent variable;

[0009] Step 2: According to the characteristics that the correlation between the ionospheric delay of the interpolation point and the baseline is related to the distance ratio between the two, a weight function is proposed with the ratio of the distance between the interpolation point and the main reference station and the length of each baseline as the independent variable;

[0010] Step 3: Combining the weight functions in steps 1 and 2, the normalized ionospheric delay sample weights are obtained, and the values ​​of the points to be interpolated are obtained according to the interpolation model of the BLUP framework.

[0011] The specific steps are:

[0012] Step 1. Define a weight function with the angle between the line from the interpolation point to the main reference station and each baseline as the independent variable.

[0013] for and The angle between , we can define the weight function:

[0014]

[0015] In the formula, w a,i is the weight function calculated between the interpolation point and the baseline i when only the angle factor is considered; a π is the value of the function at π; a π2 is the value of the function at π / 2; θ is and Angle.

[0016] Formula (1) fully considers the relationship between the angle and the ionospheric delay correlation: when the angle is equal to π / 2, the correlation is weakest and the weight function reaches the minimum value; in the interval [0, π / 2], the weight drops rapidly from 1 to a π2 , in the interval [π / 2,π], the weight slowly rises to a π .

[0017] Step 2. Define a weight function with the ratio of the distance between the interpolation point and the main reference station to the length of each baseline as the independent variable.

[0018] for and The length ratio of can be used to define the weight function:

[0019]

[0020] In the formula, w d,i is the weight function calculated between the interpolation point and the baseline i when only the length ratio factor is considered; d is and The ratio of the modulus length; k1 and k2 are two adjustment parameters, so that the function passes through (0,0) and (1,0).

[0021] Formula (2) considers the relationship between the length ratio and the ionospheric delay correlation at a fixed angle. Obviously, when the length ratio is 1, the correlation is the strongest and the weight reaches the maximum value; in the interval [0,1], the function value is monotonically increasing and bounded, and in the interval [1,+∞), the function value is monotonically decreasing and infinitely approaches 0.

[0022] The weight function of the comprehensive angle and distance ratio described in step 3 is used to obtain the normalized ionospheric delay sample weight, and the value of the point to be interpolated is obtained according to the interpolation model of the BLUP framework; combining the two weights w a,i and wd,i , where the angle weight is dominant and the length ratio weight is used as an adjustment factor. The integrated weights are normalized to obtain the sample weights:

[0023]

[0024] The BLUP framework takes into account fixed effects, random effects, and the correlation between the interpolation points and the sample points. The interpolation expression is shown in equation (4), which represents the two steps of fitting the atmospheric modeling parameters and solving the ionospheric delay value at the unknown point. The solution of this equation is shown in equation (5):

[0025]

[0026] Wherein, the subscripts r and u represent the part used to fit the atmospheric modeling parameters and the part used for interpolation back-substitution solution, respectively; Δ▽I r is the double difference ionosphere extracted from the baseline; Δ▽I u is the double difference ionospheric value at the user position to be found; A represents the design matrix; X is the atmospheric modeling parameter to be fitted; the variance of the double difference ionospheric

[0027]

[0028] In the formula, is the least squares estimate of the model parameters; is the estimated value at the interpolation point u, which includes the linear prediction term considering the fixed effect and the residual correction term considering the random effect; is the conditional expectation coefficient of the joint normal distribution.

[0029] Note that the interpolation method is defined by the A and Q matrices in equation (5), and the weighted interpolation method matrix of the present invention is defined as follows:

[0030]

[0031] Where ΔX and ΔY represent the column vectors composed of the three-dimensional coordinate differences from each reference station to the main reference station, and the subscripts m and i represent the main reference station and other reference stations, respectively.

[0032] The beneficial effects of the present invention are:

[0033] The ionospheric weighted modeling method for Beidou ground-based enhancement proposed in the present invention can adaptively adjust the modeling parameters of ionospheric delay according to the user's location. Based on the influencing factors of the correlation between the ionospheric delay of the interpolation point and the baseline, a fixed weight function with the angle and distance ratio as independent variables is designed, so that the sample weight of the regional ionospheric interpolation is more reasonable, so that the atmospheric correction accuracy of users in the region is uniformly improved, the regional application range of network RTK is expanded, and the service quality of network RTK is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is an implementation flow chart of the present invention;

[0035] Figure 2 It is a weight function curve diagram defined by the angle according to the present invention;

[0036] Figure 3 A weight function curve graph defined by distance ratio according to the present invention is used;

[0037] Figure 4 It is a comparison diagram of the ionospheric delay interpolation error calculated by the method of the present invention and the conventional method. DETAILED DESCRIPTION

[0038] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0039] like Figure 1 As shown, this embodiment discloses an ionospheric weighted modeling method for Beidou ground-based enhancement, and the specific steps are as follows:

[0040] Step 1. Define a weight function with the angle between the line from the interpolation point to the main reference station and each baseline as the independent variable

[0041] for and The angle between , we can define the weight function:

[0042]

[0043] In the formula, w a,i is the weight function calculated between the interpolation point and the baseline i when only the angle factor is considered; a π is the value of the function at π; a π2 is the value of the function at π / 2; θ is and Angle.

[0044] Formula (1) fully considers the relationship between the angle and the ionospheric delay correlation: when the angle is equal to π / 2, the correlation is weakest and the weight function reaches the minimum value; in the interval [0, π / 2], the weight drops rapidly from 1 to a π2 , in the interval [π / 2,π], the weight slowly rises to a π The specific function graph is as follows: Figure 2 shown.

[0045] Step 2. Define a weight function with the ratio of the distance between the interpolation point and the main reference station to the length of each baseline as the independent variable

[0046] for and The length ratio of can be used to define the weight function:

[0047]

[0048] In the formula, w d,i is the weight function calculated between the interpolation point and the baseline i when only the length ratio factor is considered; d is and The ratio of the modulus length; k1 and k2 are two adjustment parameters, so that the function passes through (0,0) and (1,0).

[0049] Formula (2) considers the relationship between the length ratio and the ionospheric delay correlation under a fixed angle. Obviously, when the length ratio is 1, the correlation is the strongest and the weight reaches the maximum value; in the interval [0,1], the function value is monotonically increasing and bounded, and in the interval [1,+∞), the function value is monotonically decreasing and infinitely approaches 0. The specific function graph is as follows Figure 3 shown.

[0050] The weight function of the comprehensive angle and distance ratio described in step 3 is used to obtain the normalized ionospheric delay sample weight, and the value of the point to be interpolated is obtained according to the interpolation model of the BLUP framework; combining the two weights w a,i and w d,i , where the angle weight is dominant and the length ratio weight is used as an adjustment factor. The integrated weights are normalized to obtain the sample weights:

[0051]

[0052] The BLUP framework takes into account fixed effects, random effects, and the correlation between the interpolation points and the sample points. The interpolation expression is shown in equation (4), which represents the two steps of fitting the atmospheric modeling parameters and solving the ionospheric delay value at the unknown point. The solution of this equation is shown in equation (5):

[0053]

[0054] Wherein, the subscripts r and u represent the part used to fit the atmospheric modeling parameters and the part used for interpolation back-substitution solution, respectively; Δ▽I r is the double difference ionosphere extracted by equation (1); Δ▽I u is the double difference ionospheric value at the user position to be found; A represents the design matrix; X is the atmospheric modeling parameter to be fitted; the variance of the double difference ionospheric

[0055]

[0056] In the formula, is the least squares estimate of the model parameters; is the estimated value at the interpolation point u, which includes the linear prediction term considering the fixed effect and the residual correction term considering the random effect; is the conditional expectation coefficient of the joint normal distribution.

[0057] Note that the interpolation method is defined by the A and Q matrices in equation (5), and the weighted interpolation method matrix of the present invention is defined as follows:

[0058]

[0059] Where ΔX and ΔY represent the column vectors composed of the three-dimensional coordinate differences between each reference station and the main reference station, and the subscripts m and i represent the main reference station and other reference stations, respectively.

[0060] Before implementing ionospheric interpolation, it is necessary to first obtain the double-difference ionospheric delay between reference stations as sample data. The carrier observations are combined into geometry-free combined observations, and after the ambiguity is fixed, the double-difference ionospheric delay with centimeter-level accuracy is extracted by back-substituting the fixed ambiguity:

[0061]

[0062] In the formula, is a double difference operator; subscripts 1 and 2 represent two different frequency points; f and λ represent frequency and wavelength respectively; and N represent the carrier observation value and its corresponding integer ambiguity respectively.

[0063] On this basis, it is also necessary to obtain the Gaussian projection coordinates of the interpolation position and the reference station position to obtain ΔX and ΔY defined in equation (6). Finally, substitute equation (6) and equation (7) into equation (5) to obtain the modeling parameters: and the ionospheric delay value at the point to be interpolated.

[0064] Figure 4The ionospheric delay interpolation error curves at two different monitoring station locations are shown. The upper and lower sub-figures are comparisons between the method proposed in the present invention and the conventional LIM method.

[0065] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. An ionospheric weighted modeling method for BeiDou ground-based enhancement is characterized by: include: Step 1: According to the characteristics of the correlation between the ionospheric delay of the interpolation point and the baseline and the angle between them, a weight function is proposed with the angle between the line from the interpolation point to the main reference station and each baseline as the independent variable; Step 2: According to the characteristics that the correlation between the ionospheric delay of the interpolation point and the baseline is related to the distance ratio between the two, a weight function is proposed with the ratio of the distance between the interpolation point and the main reference station and the length of each baseline as the independent variable; Step 3: Combining the weight functions in steps 1 and 2, the normalized ionospheric delay sample weights are obtained, and the values ​​of the points to be interpolated are obtained according to the interpolation model of the BLUP framework.

2. The ionospheric weighted modeling method for Beidou ground-based enhancement according to claim 1, characterized in that: The weight function defined in step 1 takes the angle between the line from the interpolation point to the main reference station and each baseline as the independent variable. and The angle between , first define the weight function: In the formula, w a,i is the weight function calculated between the interpolation point and the baseline i when only the angle factor is considered; a π is the value of the function at π; a π2 is the value of the function at π / 2; θ is and The angle of Formula (1) fully considers the relationship between the angle and the ionospheric delay correlation: when the angle is equal to π / 2, the correlation is the weakest and the weight function reaches the minimum value; In the interval [0,π / 2], the weight drops rapidly from 1 to a π2 , in the interval [π / 2,π], the weight slowly rises to a π .

3. The ionospheric weighted modeling method for Beidou ground-based enhancement according to claim 1, characterized in that: Step 2 defines a weight function with the ratio of the distance between the interpolation point and the main reference station to the length of each baseline as the independent variable; and The length ratio of , first define the weight function: In the formula, w d,i is the weight function calculated between the interpolation point and the baseline i when only the length ratio factor is considered; d is and The ratio of the modulus length; k1 and k2 are two adjustment parameters, so that the function passes through (0,0) and (1,0). Formula (2) considers the relationship between the length ratio and the ionospheric delay correlation at a fixed angle. Obviously, when the length ratio is 1, the correlation is the strongest and the weight reaches the maximum value. In the interval [0,1], the function value is monotonically increasing and bounded. In the interval [1,+∞), the function value is monotonically decreasing and infinitely approaches 0.

4. The ionospheric weighted modeling method for Beidou ground-based enhancement according to claim 1, characterized in that: The weight function of the comprehensive angle and distance ratio described in step 3 is used to obtain the normalized ionospheric delay sample weight, and the value of the point to be interpolated is obtained according to the interpolation model of the BLUP framework; combining the two weights w a,i and w d,i , where the angle weight is dominant and the length ratio weight is used as an adjustment factor. The integrated weights are normalized to obtain the sample weights: The BLUP framework takes into account fixed effects, random effects, and the correlation between the interpolation points and the sample points. The interpolation expression is shown in equation (4), which represents the two steps of fitting the atmospheric modeling parameters and solving the ionospheric delay value at the unknown point position. The solution of this equation is shown in equation (5): The subscripts r and u represent the part used to fit the atmospheric modeling parameters and the part used to interpolate the solution, respectively; The double-difference ionosphere extracted for the baseline; is the double difference ionospheric value at the user position to be found; A represents the design matrix; X is the atmospheric modeling parameter to be fitted; the variance of the double difference ionospheric In the formula, is the least squares estimate of the model parameters; is the estimated value at the interpolation point u, which includes the linear prediction term considering the fixed effect and the residual correction term considering the random effect; is the conditional expectation coefficient of the joint normal distribution; The interpolation method is defined by the A and Q matrices in equation (5), and the weighted interpolation method matrix is ​​defined as follows: Where ΔX and ΔY represent the column vectors composed of the three-dimensional coordinate differences from each reference station to the main reference station, and the subscripts m and i represent the main reference station and other reference stations, respectively.

Images