Atmospheric delay modeling method suitable for banded region and considering median error

Abstract

The invention discloses an atmospheric delay modeling method suitable for a banded area and considering a median error, and belongs to the technical field of satellite positioning, and the method comprises the steps: generating a server atmospheric delay, and processing the server atmospheric delay through employing a polynomial fitting method; the atmospheric delay variance of the user side is calculated, and the ionosphere delay variance and the troposphere delay variance in the random model are calculated through an empirical constant model and a prior variance model; and the user side establishes an atmospheric delay random model, fuses an empirical constant and a prior variance, and performs adjustment in a normalization processing mode. According to the atmospheric delay modeling method suitable for the banded region and considering the median error, the random model is established by fusing the empirical constants and the prior variance, the convergence speed of PPP-RTK is remarkably improved, continuous and stable positioning capacity is achieved, and reliable technical support is provided for practical application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite positioning, and particularly relates to an atmospheric delay modeling method considering mean errors suitable for a strip-shaped area. BACKGROUND

[0002] Before the rise of PPP-RTK technology, many scholars have shown interest in modeling regional ionospheric delay and tropospheric delay, and on this basis, atmospheric enhanced PPP technology has emerged. A large number of studies have shown that a fast-converging, high-reliability atmospheric correction model is the key to PPP-RTK high-precision service.

[0003] Since the tropospheric dry delay model correction accuracy can reach 90-95%, the wet component is difficult to correct, but the error value is very small, and real-time estimation can generally meet the positioning requirements, so the research on ionosphere in atmospheric delay modeling is more common. At present, many studies have shown that ionospheric slant delay products have higher precision and can significantly improve the performance of PPP RTK, but such products have the disadvantage of large data broadcast.

[0004] At present, regional ionospheric slant delay modeling can be divided into interpolation and modeling. Here, interpolation refers to using ionospheric slant delay corrections obtained by different base stations to interpolate grid products and provide them to users for use, and modeling refers to solving model coefficients through regional ionospheric slant delay corrections and providing them to users for use. In the article: Hong J, Tu R, Zhang S, et al. Inter-Satellite Single-Difference Ionospheric Delay Interpolation Model for PPP-RTK and Its Positioning Performance Verification. Remote Sensing, 2022, 14(17):4153, several ionospheric interpolation methods are systematically compared, and a DSM interpolation model is proposed, which has achieved good positioning results in various scenarios, especially in the case of only 3 reference stations. The service performance of PPP-RTK does not decrease significantly. When the user coordinates are known, the user's upper ionospheric delay can be calculated through the interpolation model, but providing all ionospheric delays at the network end to the user is not conducive to network data transmission. Therefore, grid products are generally generated at the server end for broadcast. The modeling method compresses a large number of ionospheric delay corrections into several or several groups of model coefficients, and the user end calculates according to the specified model, which can greatly reduce the data transmission amount. Common ionospheric slant delay modeling methods include spherical harmonic function modeling, spherical cap harmonic function modeling, and polynomial model, among which the polynomial model is most widely used in regional atmospheric modeling.

[0005] Atmosphere delay correction is always the focus of GNSS research. In the application of PPP-RTK, the real-time performance and data broadcast volume should also be considered. At present, some commercial services have analyzed the atmosphere correction model. However, these studies mainly focus on verifying the effect of atmosphere correction from the accuracy and convergence speed of the final positioning result, and the selection of modeling strategy and the construction of random model are relatively insufficient. The good operation of sparse reference network is an advantage of PPP-RTK, but in related researches, the number of reference stations is sufficient and the distribution is uniform. However, in engineering applications, the reference station network is sparse and unevenly distributed (such as a strip-shaped road), and the research on such actual situations is relatively less. SUMMARY

[0006] The purpose of the present application is to provide an atmosphere delay modeling method considering the mean error suitable for a strip-shaped area, so as to solve the current model for high-precision estimation of atmosphere delay in a strip-shaped area.

[0007] To achieve the above purpose, the present application provides the following technical scheme:

[0008] An atmosphere delay modeling method considering the mean error suitable for a strip-shaped area, comprising:

[0009] The server uses a polynomial model method to fit and generate an atmosphere delay model in the target strip-shaped area;

[0010] The user end establishes an atmosphere delay random model, and adjusts the weight of the observation equation in combination with the empirical constant and the prior variance.

[0011] As a further optimization scheme of the present application, the server uses a polynomial model method to fit and generate a troposphere delay model in the target area:

[0012] T r =A0+A1·(lat r -lat0)+A2·(lon r -lon0),

[0013] In the formula, T r represents the zenith troposphere delay of the station r, A i is the coefficient, i=0,1,2, lat0 and lon0 are the latitude and longitude of the reference point, lat r and lon r are the latitude and longitude of the station r.

[0014] As a further optimization scheme of the present application, the server uses a polynomial model method to fit and generate an ionosphere delay model in the target area:

[0015] ΔI s=A0+A1·(lat s -lat0)+A2·(lon s -lon0),

[0016] In the formula, ΔI s For satellite s, inter-satellite single-difference ionospheric delay, A i The coefficients are i = 0, 1, 2, where lat0 and lon0 are the latitude and longitude of the reference point, respectively. s and lon s Let be the latitude and longitude of the puncture point of satellite s.

[0017] As a further optimization of the present invention, the coefficients of the tropospheric delay model are calculated using the least squares method, resulting in:

[0018] x=(B T B) -1 B T l

[0019] Where x = [A0 A1 A2], l = [T1 … T] n ],

[0020] T r For the zenith tropospheric delay of station r, lat r and lon r Let r be the longitude and latitude of the station r, where r = 1, ..., m, and m is the number of stations involved in the calculation.

[0021] As a further optimization of the present invention, considering the error in atmospheric delay, the coefficients of the tropospheric delay model are calculated using the least squares method, resulting in:

[0022] x=(B T PB) -1 B T l

[0023] in, σ r This represents the mean square error of atmospheric delay obtained by station r after PPP is fixed.

[0024] As a further optimization of the present invention, the coefficients of the ionospheric delay model are calculated using the least squares method, resulting in:

[0025] x=(B T B) -1 B T l

[0026] Where x = [A0 A1 A2], l=[ΔI 1 … ΔI n ],

[0027] lat s and lon s Let ΔI be the latitude and longitude of the puncture point of satellite s. s Let be the inter-satellite single-difference ionospheric delay of satellite s, where s = 1, 2, ..., n, and n is the number of satellites involved in the solution.

[0028] As a further optimization of the present invention, considering the error in atmospheric delay, the coefficients of the ionospheric delay model are calculated using the least squares method, resulting in:

[0029] x=(B T PB) -1 B T l

[0030] in, σ s This represents the mean square error of atmospheric delay obtained by satellite s after PPP is fixed.

[0031] As a further optimization of the present invention, during the process of generating the atmospheric delay model on the server side, the internal consistency accuracy is evaluated simultaneously, and the internal consistency accuracy and atmospheric delay data are broadcast to the user side together.

[0032] As a further optimization of the present invention, the weights of the observation equations are adjusted by combining empirical constants and prior variances. The weights of the adjusted observation equations are the reciprocals of the corresponding final ionospheric / tropospheric delay variances.

[0033]

[0034] Where a and b are empirical constants, and n is the number of satellites involved in the solution. This represents the final ionospheric delay variance of satellite s. This represents the final tropospheric delay variance at station r. This represents the prior variance of the ionospheric delay data broadcast from the server to the user.

[0035] As a further optimization of the present invention, the empirical constant a is set to 0.05 and b is set to 0.04.

[0036] The technical effects and advantages of this invention are as follows: This atmospheric delay modeling method, which considers mean square errors and is applicable to zonal regions, exhibits strong adaptability when combined with a stochastic model. The improvement in convergence speed is particularly significant. Finally, positioning experiments switching between different regions fully verify that the proposed atmospheric delay stochastic model possesses continuous and stable positioning capabilities, providing reliable technical support for practical applications. Attached Figure Description

[0037] Figure 1This is a schematic diagram of the process of the present invention. Detailed Implementation

[0038] 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.

[0039] This invention provides, for example Figure 1 The atmospheric delay modeling method shown, which considers the mean square error and is suitable for zonal regions, includes:

[0040] Step 1: Atmospheric delay generation on the server side. The atmospheric delay model in the target zonal region is generated by fitting the model using a polynomial model method.

[0041] The polynomial model method uses data from multiple base stations to fit an atmospheric delay model within a region and ultimately expresses it as a mathematical function related to latitude and longitude.

[0042] (1) Tropospheric delay modeling

[0043] The handling of tropospheric delay is relatively simple. A model is created for the zenith tropospheric delay, and the user end uses a projection function to convert it into a slant delay. The specific function model is as follows:

[0044] T r =A0+A1·(lat r -lat0)+A2·(lon r -lon0) (1)

[0045] In the formula, T r Indicates the zenith tropospheric delay at station r, A i Let lat0 and lon0 be the coefficients, i = 0, 1, 2, and lat0 and lon0 be the latitude and longitude of the reference point, respectively. r and lon r Let r be the latitude and longitude of the station.

[0046] (2) Ionospheric delay modeling

[0047] Ionospheric delay modeling and tropospheric delay modeling are mathematically consistent, but the ionosphere has two characteristics that require special handling:

[0048] First, the ionosphere is located in the upper atmosphere, and directly using ground station locations for modeling cannot accurately reflect its spatial distribution characteristics. This invention adopts the classic thin ionospheric assumption, which assumes that the ionospheric delay occurs on a sphere 350 km above the ground, and fits the model based on the coordinates of the puncture point.

[0049] Second, the hardware delay at the receiver cannot be separated from ionospheric parameters. In PPP-AR, direct calculation of hardware delay is avoided by using inter-satellite single-difference, resulting in the ionospheric delay extracted from a single base station including the hardware delay at the receiver, which cannot be used for regional ionospheric modeling.

[0050] Therefore, the extracted ionospheric delay is also subjected to inter-satellite single-difference processing, and the equivalent ionospheric delay after single-difference is used for modeling.

[0051] The satellite with the highest elevation angle is selected as the reference satellite for inter-satellite single-difference calculation, and its expression is as follows:

[0052] ΔI s =I s -I ref =(I s +DCB s )-(I ref +DCB ref (2)

[0053] In the formula, ΔI s The inter-satellite single-difference ionospheric delay is represented by ref, which indicates the reference satellite, and DCB is the receiver-side hardware delay. It is generally assumed that the receiver-side DCB is only related to the satellite system; therefore, by selecting a reference satellite for each satellite system, the receiver-side hardware delay can be considered eliminated.

[0054] For ionospheric slant delay, a separate model is built for each satellite:

[0055] ΔI s =A0+A1·(lat s -lat0)+A2·(lon s -lon0) (3)

[0056] In the formula, ΔI s For satellite s, inter-satellite single-difference ionospheric delay, A i The coefficients are i = 0, 1, 2, where lat0 and lon0 are the latitude and longitude of the reference point, respectively. s and lon s Let be the latitude and longitude of the puncture point of satellite s.

[0057] (3) Solving for model coefficients

[0058] The server utilizes the atmospheric delay model of the atmospheric delay generation region extracted from a single-station PPP-AR. Taking tropospheric delay as an example, the coefficients in equation (1) are calculated using the least squares method, and the observation equation can be written as:

[0059] l=Bx+ε (4)

[0060] In the formula, T r For the zenith tropospheric delay of station r, lat r and lon r Let r be the longitude and latitude of the station, r = 1, ..., m, where m is the number of stations involved in the calculation.

[0061]

[0062] x = [A0 A1 A2]

[0063] l = [T1 … T] n ]

[0064] For the equal-weight model, the coefficient calculation formula is as follows:

[0065] x=(B T B) -1 B T l (5)

[0066] In fact, after the base station completes the PPP fixed solution, in addition to outputting the atmospheric delay value, it also outputs the mean square error information of the atmospheric delay. This error information reflects the accuracy of the atmospheric delay estimation and should be taken into account when constructing the fitting model.

[0067] By setting the weights using the mean square error of atmospheric delay, the following weight matrix can be obtained:

[0068]

[0069] In the formula, σ r This represents the mean square error of atmospheric delay obtained by station r after PPP is fixed.

[0070] Therefore, the coefficient calculation formula is adjusted as follows:

[0071] x=(B T PB) -1 B T Pl (7)

[0072] The processing of ionospheric delay is largely the same as that of tropospheric delay, except that the equivalent ionospheric delay and its error need to be obtained using inter-satellite single differences:

[0073] x=(B T B) -1 B T l

[0074] Where x = [A0 A1 A2], l=[ΔI 1 … ΔI n ], lat s and lon sLet ΔI be the latitude and longitude of the puncture point of satellite s. s Let be the inter-satellite single-difference ionospheric delay of satellite s, where s = 1, 2, ..., n, and n is the number of satellites involved in the solution.

[0075] Furthermore, considering the error in atmospheric delay, the coefficients of the ionospheric delay model are calculated using the least squares method, yielding:

[0076] x=(B T PB) -1 B T l

[0077] in, σ s This represents the mean square error of atmospheric delay obtained by satellite s after PPP is fixed.

[0078] Step 2: Calculate the atmospheric delay variance at the user end. Use the empirical constant model and the prior variance model to calculate the ionospheric delay and tropospheric delay variance in the stochastic model.

[0079] Atmospheric delay variance is calculated at the user end, and ionospheric delay variance in the stochastic model is calculated using empirical constant model and prior variance model.

[0080] (1) Empirical constant model

[0081] Because the accuracy of atmospheric delay error at the server end is constrained by multiple complex factors such as network structure and observation data quality, and is difficult to accurately measure through post-event evaluation, empirical constants are commonly used in the stochastic models of atmospheric constraint equations at the user end. Based on existing research and positioning experiment results, the empirical constants are set as follows:

[0082]

[0083] In the formula, σ ion σ is the variance of the equivalent ionospheric delay. trop The variance of tropospheric delay is expressed in meters. 2 .

[0084] (2) Prior variance model

[0085] During the generation of atmospheric delay products on the server side, the internal compliance accuracy is evaluated simultaneously. Subsequently, the internal compliance accuracy and atmospheric delay data are broadcast to the user. After receiving this data, the user terminal uses it as the prior variance to construct a stochastic model with atmospheric constraints. The specific weighting scheme is as follows:

[0086]

[0087] In the formula, and This represents the variance of ionospheric delay and tropospheric delay in the final stochastic model used; This indicates the prior variance provided by the ionospheric product. This represents the prior variance provided by the tropospheric product.

[0088] Step 3: Establish an atmospheric delay stochastic model on the user end, and adjust it by integrating empirical constants and prior variances and normalizing them.

[0089] By adjusting the weights of the observation equation using the prior variance provided by the server, differences between different satellites can be effectively distinguished. However, during the setup of the stochastic model, there is a phenomenon of artificially high internal consistency accuracy. This may adversely affect the positioning results.

[0090] Therefore, a fusion stochastic model that simultaneously considers empirical constants and prior variance is proposed. For ionospheric delay, a normalization method is used to adjust the prior variance to ensure that the overall variance approaches the pre-set empirical constant. For tropospheric delay, since different satellites use the same tropospheric parameters in the solution process, its weights directly use the empirical constants. The final weights of the virtual observation equation are as follows:

[0091]

[0092] In the formula, a and b are empirical constants, and n is the number of satellites involved in the solution. This represents the final ionospheric delay variance of satellite s. This represents the final tropospheric delay variance at station r. This represents the prior variance of the ionospheric delay data broadcast from the server to the user.

[0093] Based on this atmospheric delay model, setting the atmospheric delay accuracy too low leads to slow filtering convergence, while setting it too high results in fixing errors. The fused stochastic model, however, exhibits strong adaptability, with a particularly significant improvement in convergence speed. Finally, positioning experiments across different regions fully validated the continuous and stable positioning capabilities of the proposed atmospheric delay stochastic model, providing reliable technical support for practical applications.

[0094] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An atmospheric delay modeling method considering mean square errors applicable to zonal regions, characterized in that: include: The server uses a multinomial modeling method to fit and generate an atmospheric delay model within the target zonal region; The user-side establishes an atmospheric delay stochastic model and adjusts the weights of the observation equation by combining empirical constants and prior variance.

2. The method according to claim 1, characterized in that: On the server side, a tropospheric delay model within the target region is generated using a polynomial modeling method. T r =A0+A1·(lat r -lat0)+A2·(lon r -lon0), In the formula, T r Indicates the zenith tropospheric delay at station r, A i Let lat0 and lon0 be the coefficients, i = 0, 1, 2, and lat0 and lon0 be the latitude and longitude of the reference point, respectively. r and lon r Let r be the latitude and longitude of the station.

3. The method according to claim 1, characterized in that: On the server side, a polynomial model method is used to fit and generate an ionospheric delay model within the target region: ΔI s =A0+A1·(lat s -lat0)+A2·(lon s -lon0), In the formula, ΔI s For satellite s, inter-satellite single-difference ionospheric delay, A i The coefficients are i = 0, 1, 2, where lat0 and lon0 are the latitude and longitude of the reference point, respectively. s and lon s Let be the latitude and longitude of the puncture point of satellite s.

4. The method according to claim 3, characterized in that: The coefficients of the tropospheric delay model were calculated using the least squares method, yielding the following results: x=(B T B) -1 B T l Where x = [A0 A1 A2], l = [T1 … T] n ], T r For the zenith tropospheric delay of station r, lat r and lon r Let r be the longitude and latitude of the station r, where r = 1, ..., m, and m is the number of stations involved in the calculation.

5. The method according to claim 4, characterized in that: Considering the errors in atmospheric delay, the coefficients of the tropospheric delay model are calculated using the least squares method, yielding: x=(B T PB) -1 B T l in, σ r This represents the mean square error of atmospheric delay obtained by station r after PPP is fixed.

6. The method according to claim 3, characterized in that: The coefficients of the ionospheric delay model were calculated using the least squares method, yielding the following results: x=(B T B) -1 B T l Where x = [A0 A1 A2], l=[ΔI 1 … ΔI n ], lat s and lon s Let ΔI be the latitude and longitude of the puncture point of satellite s. s Let be the inter-satellite single-difference ionospheric delay of satellite s, where s = 1, 2, ..., n, and n is the number of satellites involved in the solution.

7. The method according to claim 6, characterized in that: Considering the error in atmospheric delay, the coefficients of the ionospheric delay model are calculated using the least squares method, yielding: x=(B T PB) -1 B T l in, φ s This represents the mean square error of atmospheric delay obtained by satellite s after PPP is fixed.

8. The method according to claim 1, characterized in that: During the generation of the atmospheric delay model on the server side, the internal consistency accuracy is evaluated simultaneously, and the internal consistency accuracy and atmospheric delay data are broadcast to the user terminal together.

9. The method according to claim 8, characterized in that: The weights of the observation equations are adjusted by combining empirical constants and prior variances. The adjusted weights of the observation equations are the reciprocals of the corresponding final ionospheric / tropospheric delay variances. Where a and b are empirical constants, and n is the number of satellites involved in the solution. This represents the final ionospheric delay variance of satellite s. This represents the final tropospheric delay variance at station r. This represents the prior variance of the ionospheric delay data broadcast from the server to the user.

10. The method according to claim 9, characterized in that: The empirical constants a and b are set to 0.05 and 0.04 respectively.

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