Network RTK ionosphere delay calculation method and device and storage medium

Abstract

The invention discloses a network RTK ionosphere delay calculation method and device and a storage medium. The method comprises the steps that the ionosphere activeness of a network RTK is determined; under the condition that the obtained ionosphere activeness is smaller than a first activeness threshold value, a curved surface function model is adopted to calculate delay; under the condition that the obtained ionospheric activeness is not smaller than a first activeness threshold value and not larger than a second activeness threshold value, delay is calculated in the mode that a curved surface function model and a Gaussian process regression model are combined; under the condition that the obtained ionospheric activeness is greater than a second activeness threshold value, calculating delay by adopting a Gaussian process regression model; wherein the first activeness threshold value is smaller than the second activeness threshold value. Due to the fact that different ionosphere activeness is calculated in a targeted and adaptive mode, advantage complementation of the two models is achieved, and errors are reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to high-precision positioning technology, in particular to a network RTK ionospheric delay calculation method, device and storage medium. BACKGROUND

[0002] As the core solution of modern Global Navigation Satellite System (GNSS) high-precision real-time kinematic positioning, network RTK (Real-Time Kinematic) technology effectively overcomes the precision decline problem caused by the baseline length limitation in traditional single base station RTK technology by constructing a distributed reference station network and combining with a cloud computing processing architecture, and significantly improves the service coverage range and positioning reliability.

[0003] In the related art, linear interpolation, surface function interpolation and other modeling methods are usually used to estimate and correct ionospheric delay, thereby generating Virtual Reference Station (VRS) observation data.

[0004] However, during the active period of the ionosphere, the ionospheric electron density distribution presents a highly nonlinear characteristic, and it is difficult to accurately reflect the actual ionospheric delay trend by using the interpolation model, and this modeling error is directly reflected in the ionospheric correction number broadcast by the VRS, which causes a large deviation between the real ionospheric delay of the user's location and the VRS broadcast ionospheric delay, thereby causing the user end RTK ambiguity to be unable to be quickly fixed, and seriously affecting the positioning accuracy and convergence speed. SUMMARY

[0005] The embodiments of the present application provide a network RTK ionospheric delay calculation method, device and storage medium, which can effectively and significantly reduce the VRS ionospheric delay error, thereby improving the user end RTK fixing rate and positioning reliability.

[0006] The embodiments of the present application provide a network RTK ionospheric delay calculation method, which comprises:

[0007] determining the ionospheric activity of the network RTK;

[0008] in the case that the obtained ionospheric activity is less than the first activity threshold, calculating the delay of the ionosphere of the network RTK by using a surface function model; in the case that the obtained ionospheric activity is not less than the first activity threshold and not greater than the second activity threshold, calculating the delay of the ionosphere of the network RTK by using a combination of a surface function model and a Gaussian process regression model; in the case that the obtained ionospheric activity is greater than the second activity threshold, calculating the ionospheric delay of the network RTK by using a Gaussian process regression model;

[0009] wherein the first activity threshold is less than the second activity threshold.

[0010] The embodiments of the present application also provide an electronic device, comprising a memory and a processor.

[0011] The memory is connected with the processor, and is configured to store a program.

[0012] The processor is configured to realize the network RTK ionospheric delay calculation method by running the program in the memory.

[0013] The embodiments of the present application also provide a storage medium, which has a computer program stored thereon, and the computer program is run by a processor to realize the network RTK ionospheric delay calculation method.

[0014] In the case that the obtained ionospheric activity is less than the first activity threshold, the embodiments of the present application calculate the ionospheric delay by using a surface function model, the surface function model provides a globally stable ionospheric delay trend, and is suitable for large-scale spatial smoothing, in the case that the obtained ionospheric activity is greater than the second activity threshold, the network RTK ionospheric delay is calculated by using a Gaussian process regression model, the Gaussian process regression model can finely capture local ionospheric disturbance characteristics, and in the case that the obtained ionospheric activity is not less than the first activity threshold and not greater than the second activity threshold, the ionospheric delay is calculated by using a combination of the surface function model and the Gaussian process regression model, therefore, the adaptive calculation is performed by using the surface function model and the Gaussian process regression model in different ionospheric activities, the advantages of the surface function model and the Gaussian process regression model are complementary, the ionospheric delay error of the calculated network RTK is significantly reduced, and the user end RTK fixing rate and the positioning reliability are improved.

[0015] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the present application. Other advantages of the present application can be realized and attained by means of the instrumentalities and combinations particularly pointed out in the description and appended claims. BRIEF DESCRIPTION OF DRAWINGS

[0016] The accompanying drawings are included to provide an understanding of the present application, and constitute a part of the specification, and together with the embodiments of the present application serve to explain the technical solutions of the present application, and do not constitute a limitation on the technical solutions of the present application.

[0017] Figure 1 FIG. 1 is a flowchart of a network RTK ionospheric delay calculation method according to an embodiment of the present application;

[0018] Figure 2A structural schematic diagram of a network RTK ionospheric delay calculation device according to an embodiment of the present application;

[0019] Figure 3 A structural schematic diagram of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0020] The present application describes a number of embodiments, but the description is exemplary rather than limiting and it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the embodiments described in the present application. Although a number of possible combinations of features have been set forth in the appended figures and discussed in the detailed description, many other combinations of features are possible. Unless specifically intended otherwise, any feature or element of any embodiment can be used in combination with any other feature or element of any other embodiment, or in combination with any other feature or element of the same embodiment.

[0021] The present application includes and contemplates combinations of features and elements known to those of ordinary skill in the art. The embodiments, features and elements disclosed in the present application can also be combined with any conventional features or elements to form unique invention solutions. Any feature or element of any embodiment can also be combined with features or elements from other invention solutions to form another unique invention solution. Therefore, it should be understood that any feature shown and / or discussed in the present application can be implemented alone or in any appropriate combination. Accordingly, the embodiments are not to be restricted, except as by the appended claims and their equivalents. Furthermore, various modifications and changes can be made within the scope of the claims.

[0022] Furthermore, in describing representative embodiments, the specification can have presented the method and / or process as a particular sequence of steps. However, to the extent that the method or process depends on more than one step, the method or process should not be limited to the particular sequence of steps described. Other sequences of steps can be possible, depending on the implementation, without departing from the spirit and scope of the present application. Thus, the particular sequence of steps set forth in the specification is not a limitation of the application. Further, the claims should not be limited to the steps in accordance with the written order of execution, unless the claim language explicitly states otherwise.

[0023] As the core means of modern Global Navigation Satellite System (GNSS) high-precision real-time kinematic positioning, network RTK (Real-Time Kinematic) technology effectively overcomes the inherent limitations of traditional single-base station RTK technology, which is restricted by baseline length, by constructing a distributed reference station network and cloud computing processing architecture. The implementation process of this technology can be systematically divided into the following three key technical links:

[0024] 1. Reference station networking and data collection: At least three reference stations are arranged within a radius of about 70 kilometers to form an observation network with the user's approximate position as the center. Each reference station synchronously collects GNSS raw observation data (such as pseudorange, carrier phase, and multi-frequency observation values) and forms multiple independent baseline observation combinations.

[0025] 2. Baseline solution: A double-difference observation model is used to precisely solve each baseline, extracting double-difference ionospheric delay and tropospheric delay parameters between stations and satellites, providing high-precision input data for subsequent spatial modeling.

[0026] 3. Atmospheric delay spatial modeling: Based on the atmospheric delay parameters obtained from the reference station network solution, a regional atmospheric delay field is constructed through spatial interpolation algorithms (such as linear interpolation, least squares collocation, etc.), calculating the atmospheric correction information near the user and generating the observation data of the user's virtual reference station (VRS).

[0027] In the field of network RTK spatial modeling, existing technologies mainly use linear interpolation model (Linear Interpolation Model, LIM), low-order surface model (Low-order Surface Model, LSM), and least squares collocation (Least Squares Collocation, LSC) modeling methods. These traditional models are based on specific ionospheric simplification assumptions. Among them, the LIM model is based on the assumption that ionospheric delay is distributed in a plane; the low-order surface model relies on the assumption that ionospheric spatial changes are smooth; and the LSC model uses the prior assumption that ionospheric correlation is inversely proportional to distance. However, during active ionospheric periods (such as geomagnetic storms, equatorial anomalies, etc.), the ionospheric electron density distribution exhibits significant nonlinear characteristics and spatial heterogeneity, leading to large deviations in the ionospheric corrections generated by the above models based on a single assumption. This not only affects the accuracy of the user's dual-frequency carrier phase observation values, but also further hinders the rapid fixing of RTK ambiguities, causing the positioning solution to converge slowly, reducing the initialization success rate, and even leading to distorted positioning results, thereby affecting the stability and usability of high-precision positioning services.

[0028] To this end, the embodiments of the present disclosure provide a network RTK ionospheric delay calculation method, as shown in the following formula (1): Figure 1

[0029] Step 100, determine the ionospheric activity of the network RTK.

[0030] Step 110, in the case that the obtained ionospheric activity is less than the first activity threshold, calculate the delay of the network RTK ionosphere by using a curved surface function model; in the case that the obtained ionospheric activity is not less than the first activity threshold and not greater than the second activity threshold, calculate the delay of the network RTK ionosphere by using a combination of a curved surface function model and a Gaussian process regression model; in the case that the obtained ionospheric activity is greater than the second activity threshold, calculate the ionospheric delay of the network RTK by using a Gaussian process regression model; wherein the first activity threshold is less than the second activity threshold.

[0031] Step 100 can be implemented in the following way:

[0032] 1. Use the reference station network data: Network RTK system relies on a distributed reference station network, each reference station will collect GNSS raw observation data, including pseudorange and carrier phase information, etc. By processing these data, ionospheric delay parameters can be extracted. For example, the total electron content of the ionosphere can be calculated by the data measured by a dual-frequency GNSS receiver, which is an important indicator of ionospheric activity.

[0033] 2. Use GNSS data service: Some GNSS data services provide information on ionospheric activity or ionospheric disturbance. These data are usually monitored by satellite observation and real-time RTK system. Therefore, service providers providing real-time GNSS data can be found, and ionosphere-related indicators can be obtained from the services provided by the service providers, and then the ionospheric activity can be analyzed and processed.

[0034] 3. Access international or local GNSS monitoring station network: Many countries and regions have services that provide GNSS real-time monitoring data, such as China's reference station network. These sites usually publish real-time information about the ionosphere, including ionospheric delay, total electron content (TEC), etc. The ionospheric activity can be obtained by using these information.

[0035] 4. Use ionospheric model: Some ionospheric models, such as ITU model, NeQuick model, etc., can be used to predict the activity of the ionosphere.

[0036] ​5. Professional RTK hardware: Some RTK receivers and software support real-time monitoring of ionospheric effects, and ionospheric activity information can be viewed directly from hardware devices or software.

[0037] The network RTK ionospheric delay calculation method provided by the embodiments of the present application, in the case of obtaining ionospheric activity less than the first activity threshold, uses a curved surface function (i.e. Spline) model to calculate the delay of the ionosphere, the curved surface function model provides a globally stable ionospheric delay trend, suitable for large-scale spatial smoothing, in the case of obtaining ionospheric activity greater than the second activity threshold, uses a Gaussian process regression model to calculate the network RTK ionospheric delay, the Gaussian process regression (Gaussian Process Regression, i.e. GPR) model can finely capture the local ionospheric disturbance characteristics, and in the case of obtaining ionospheric activity not less than the first activity threshold and not greater than the second activity threshold, the curved surface function model and the Gaussian process regression model are combined to calculate the delay of the ionosphere, so that the adaptive calculation is performed in different ionospheric activities, the advantages of the curved surface function model and the Gaussian process regression model are complementary, the error of the calculated network RTK ionospheric delay is significantly reduced, and the user end RTK fixing rate and positioning reliability are improved.

[0038] In an exemplary example, the determination of the ionospheric activity of the network RTK comprises:

[0039] The standard deviation of the ionosphere IonoStd of the network RTK is calculated by the following method, and the calculated IonoStd is taken as the ionospheric activity of the network RTK:

[0040]

[0041] Where ΔI i is the double-difference ionospheric delay of the ith baseline, is the average double-difference ionospheric delay of the double-difference ionospheric delay of all baselines, and N is the total number of baselines.

[0042] IonoStd is calculated based on real-time GNSS observation data, providing a real-time error estimate that directly reflects the changes in the ionosphere and the current state of the ionosphere. In contrast, prediction methods based on geographic latitude or time are calculated based on historical data or models and are static estimates that cannot directly capture the specific changes in the ionosphere at a certain time, are prone to delay, and cannot respond immediately to irregular changes in the ionosphere, especially under the influence of solar activity or sudden events. Therefore, using IonoStd for real-time monitoring is more reliable than using prediction methods based on geographic latitude or time, especially in situations where high-precision positioning information is required, which can better demonstrate its advantages.

[0043] In an exemplary example, the network RTK ionosphere delay is calculated using a combination of a curved function model and a Gaussian process regression model, including:

[0044] According to the obtained ionospheric activity, the network RTK ionosphere delay is calculated using a smooth transition between the curved function model and the Gaussian process regression model.

[0045] The curved function model is typically used to construct the spatial variation trend of regional ionosphere delay, such as polynomials, spherical harmonics, or thin plate splines, with good analytical properties and computational efficiency; the Gaussian process regression model is a non-parametric regression method based on statistical learning, which can capture local nonlinear characteristics and random disturbances in ionosphere delay, and is suitable for complex spatio-temporal variation scenarios.

[0046] In the spatial modeling process, a hybrid weighted function model can be introduced, in which the weights of the curved function model and the Gaussian process regression model are dynamically adjusted according to the changes in ionospheric activity. This method allows smooth transition between the curved function model and the Gaussian process regression model, thereby calculating the network RTK ionosphere delay. In this way, when the ionospheric activity is relatively stable, the system can rely more on the curved function model with high computational efficiency and strong global fitting ability; while in the case of intense ionospheric activity, the weight of the Gaussian process regression model that can capture local nonlinear characteristics is increased to improve the estimation accuracy.

[0047] In an exemplary example, the network RTK ionosphere delay is calculated using a combination of a curved function model and a Gaussian process regression model, including:

[0048] The network RTK ionosphere delay VRSlono is calculated using the following method:

[0049]

[0050] In the formula, Splinelono is the first delay result of the network RTK ionosphere calculated by using the curved surface function model, GPRlono is the second delay result of the network RTK ionosphere calculated by using the Gaussian process regression model, IonoStd is the ionosphere activity of the network RTK, Th1 is the first activity threshold, and Th2 is the second activity threshold.

[0051] Because the curved surface function model and the Gaussian process regression model will calculate different ionosphere delay values for the same baseline data, if the ionosphere delay calculated by using the curved surface function model is directly switched to the ionosphere delay calculated by using the Gaussian process regression model, it is easy to cause a large jump of the VRS ionosphere of adjacent epochs. The smoothing interval and the linear weighting make the ionosphere activity of adjacent epochs not change too much, and thus the ionosphere jump caused by the model switching can be effectively avoided.

[0052] In an example, in the case of calculating the network RTK ionosphere delay by using the Gaussian process regression model, or in the case of calculating the network RTK ionosphere delay by using the combination of the curved surface function model and the Gaussian process regression model, the ionosphere delay E[f * |y] of the virtual reference station VRS is calculated according to the following manner, and the calculated E[f * |y] is taken as the second delay result GPRlono:

[0053]

[0054] In the formula, y is the known baseline ionosphere delay, K * is the covariance vector of each baseline and the VRS, K is the kernel function, is the observation noise variance of the baseline, and I is the unit matrix.

[0055] The Gaussian process regression is a machine learning method, which realizes prediction by modeling the spatial correlation of observation data. The core idea is to use the covariance function (i.e. the kernel function) to describe the spatial correlation of the ionosphere delay, and to learn the optimal hyperparameter (the hyperparameter is the distance attenuation factor L in the radial basis rbf kernel) through the historical observation data. The observation data can be expressed as:

[0056] y = f(x) + ∈

[0057] where f(x) is ionospheric delay, f(x) ~ GP(m(x), k(x, x’)); m(x) is mean function, usually set to 0 in double difference of ionospheric delay; k(x, x’) is covariance function (i.e. kernel function) to measure the correlation between x and x’, x and x’ represent spatial position coordinates. The joint distribution of baseline ionospheric delay (i.e. ionospheric delay between secondary station and primary station) vector y = f(x) and VRS ionospheric delay f(x * ) can be expressed as:

[0058]

[0059] where K is the covariance matrix of each baseline, K ij = k(x i ,x j ) is the covariance of i, j two baselines, x i ,x j is the plane vector of baseline; K * is the covariance vector of each baseline and VRS, is the observation noise variance of baseline; σ * is the variance of VRS modeling; A is the covariance matrix of each baseline plus noise, B is the covariance vector of each baseline and VRS.

[0060] Through the conditional probability formula of Gaussian distribution:

[0061]

[0062] Calculate the ionospheric delay E[f * |y] of VRS using the known baseline ionospheric delay y:

[0063]

[0064] In an exemplary instance, the kernel function K of the Gaussian process regression model is obtained according to a radial basis kernel K rbf and a linear dot product kernel K dot ;

[0065] where,

[0066] x1, x2 are the positions of two observation points respectively; σ0 is the default observation noise; L is the distance attenuation factor in K rbf .

[0067] Based on the analysis of GNSS base station network long-period ionospheric data, the embodiments of the present application find that the ionospheric delay presents double characteristics in the active period, i.e. large-scale quasi-planar feature (1) and small-scale local disturbance (2), so the radial basis kernel K rbfK(x1,x2) = K dot The kernel function K of the Gaussian process regression model is obtained as follows:

[0068] Iono(x,y) ~ ax+by+c (1)

[0069] Cov(x1,x2) ~ exp(-‖x1-x2‖ 2 )(2)

[0070] In an exemplary instance, the kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot by the following way:

[0071] According to the radial basis kernel K rbf and the linear dot product kernel K dot , the kernel function K of the Gaussian process regression model is obtained by adding them together.

[0072] Alternatively,

[0073] According to the radial basis kernel K rbf and the linear dot product kernel K dot , the kernel function K of the Gaussian process regression model is obtained by adding them together and adding the origin constraint.

[0074] In the case where the kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot , the obtained kernel function K is directly added, i.e., K(x1,x2) = K rbf (x1,x2) + K dot (x1,x2)

[0075] In the case where the kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot , and the origin constraint is added, it can be obtained by the following formula:

[0076] K'(x1,x2) = K(x1,x2) - K(x1,0) - K(0,x2)

[0077] In actual tests, the unconstrained Gaussian model does not perform well. In order to improve the performance of the ionospheric model (better than the traditional model), the origin fixed constraint can be added, which can make the ionosphere of the master station position zero. After the origin fixed constraint is added, the new kernel function (i.e., K'(x1,x2)) is substituted into the E[f * |y] calculation formula in the above embodiments to calculate the VRS ionospheric delay.

[0078] In the embodiments of the present application, the linear component (i.e., K dot ) is used to generate a plane function fitting data, which is similar to the least square plane interpolation, and can be approximated as a linear function for the ionospheric model of 100 kilometers scale in the actual application scenario. In the embodiments of the present application, a curved surface function based on a radial basis function (RBF) is obtained through K rbf , which can adjust the local shape and its influence decays with the increase of the distance. Relative to the addition of the origin fixed constraint, the systematic deviation of the area near the master station (the deviation of the master station is not 0) is eliminated, and when the baseline is added or deleted, the ionospheric model near the master station will not change significantly, thereby ensuring the unity and stability of the model.

[0079] In an example, the first activity threshold is 0.1, and the second activity threshold is 0.4.

[0080] The network RTK ionospheric delay calculation method provided by the embodiments of the present application dynamically combines Gaussian process regression (GPR) and a spline function model (Spline) to optimize the ionospheric delay correction accuracy of network RTK. Compared with related technologies, the following advantages are obtained:

[0081] Hybrid kernel function design: in the Gaussian process regression, the radial basis function (RBF) kernel and the dot product (Dot) kernel are combined, the local spatial correlation of the ionospheric delay is captured by using the RBF kernel, and the fitting ability of the model to the long baseline ionospheric trend is enhanced by using the Dot kernel, thereby improving the overall adaptability of the model.

[0082] Master station ionospheric zero adjustment method: through the ionospheric delay zeroization processing of the master reference station, the systematic deviation is eliminated, and the unity and stability of the hybrid model in the region are ensured.

[0083] Dynamic evaluation of ionospheric activity and model switching: based on the root mean square value (IonoStd) of the ionospheric delay of all satellites / baselines, the ionospheric activity is quantified in real time, and the hybrid weight of GPR and Spline is dynamically adjusted according to the preset threshold. When the activity is low, the globally stable Spline model is preferred, and when the activity is high, the locally high-precision GPR model is switched to. The linear weighting in the transition interval can effectively avoid the ionospheric jump caused by model switching, thereby realizing smooth transition.

[0084] Corresponding to the network RTK ionospheric delay calculation method described above, the embodiments of the present application also provide a network RTK ionospheric delay calculation device. Figure 2 is a structural schematic diagram of a network RTK ionospheric delay calculation device provided by the embodiments of the present application, as shown in Figure 2 , the network RTK ionospheric delay calculation device comprises:

[0085] The activity determination unit 200 is configured to determine the ionospheric activity of the network RTK.

[0086] The delay calculation unit 210 is configured to, in a case where the obtained ionospheric activity is less than the first activity threshold, calculate the delay of the ionosphere of the network RTK by using a curved surface function model; in a case where the obtained ionospheric activity is not less than the first activity threshold and not greater than the second activity threshold, calculate the delay of the ionosphere of the network RTK by using a combination of the curved surface function model and a Gaussian process regression model; and in a case where the obtained ionospheric activity is greater than the second activity threshold, calculate the delay of the ionosphere of the network RTK by using the Gaussian process regression model; wherein the first activity threshold is less than the second activity threshold.

[0087] In an exemplary example, the activity determination unit 200 calculates the ionospheric standard deviation IonoStd of the network RTK by the following manner, and takes the calculated IonoStd as the ionospheric activity of the network RTK:

[0088]

[0089] wherein ΔI i is the double-difference ionospheric delay of the ith baseline, is the average double-difference ionospheric delay of the double-difference ionospheric delays of all baselines, and N is the total number of baselines.

[0090] In an exemplary example, when the delay of the ionosphere of the network RTK is calculated by using a combination of the curved surface function model and the Gaussian process regression model, the delay calculation unit 210 is configured to:

[0091] According to the obtained ionospheric activity, the delay of the ionosphere of the network RTK is calculated by using a smooth transition between the curved surface function model and the Gaussian process regression model.

[0092] In an exemplary example, the delay calculation unit 210 is configured to:

[0093] The delay of the ionosphere of the network RTK is calculated by using the following manner:

[0094]

[0095] In the formula, Splinelono is the first delay result of the network RTK ionosphere calculated by using the curved surface function model, GPRlono is the second delay result of the network RTK ionosphere calculated by using the Gaussian process regression model, IonoStd is the ionosphere activity of the network RTK, Th1 is the first activity threshold, and Th2 is the second activity threshold.

[0096] In an exemplary example,

[0097] In the case of calculating the delay of the network RTK ionosphere by using the Gaussian process regression model, or in the case of calculating the delay of the network RTK ionosphere by using the combination of the curved surface function model and the Gaussian process regression model, the ionosphere delay E[f * |y] of the virtual reference station VRS is calculated according to the following manner: * |y] is taken as the second delay result GPRlono:

[0098]

[0099] In the formula, y is the known baseline ionosphere delay, K * is the covariance vector of each baseline and the VRS, K is the kernel function, is the observation noise variance of the baseline, and I is the unit matrix.

[0100] In an exemplary example, the kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot .

[0101] In the formula, x1 and x2 are the positions of two observation points, σ0 is the default observation noise, L is the distance attenuation factor in K rbf .

[0102] x1, x2 are the positions of two observation points, σ0 is the default observation noise, L is the distance attenuation factor in K rbf .

[0103] In an exemplary example, the kernel function construction unit 220 is further configured to:

[0104] The kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot .

[0105] Alternatively,

[0106] The kernel function K of the Gaussian process regression model is obtained according to the radial basis kernel K rbf and the linear dot product kernel K dot , and adding the origin constraint.

[0107] In an example, the first activity threshold is 0.1, and the second activity threshold is 0.4.

[0108] The network RTK ionospheric delay calculation device provided by the embodiment belongs to the same application concept as the network RTK ionospheric delay calculation method provided by the above-mentioned embodiments of the application, can execute the network RTK ionospheric delay calculation method provided by any of the above-mentioned embodiments of the application, and has the corresponding function modules and beneficial effects of executing the network RTK ionospheric delay calculation method. Technical details not described in detail in the embodiment can be referred to the specific processing content of the network RTK ionospheric delay calculation method provided by the above-mentioned embodiments of the application, which will not be described here.

[0109] The embodiment of the application further provides an electronic device, such as Figure 3 as shown, comprising a memory 300 and a processor 310;

[0110] The memory 300 is connected with the processor 310, and is used for storing programs;

[0111] The processor 310 is used for realizing the network RTK ionospheric delay calculation method described in any of the above-mentioned embodiments by running the programs in the memory 300.

[0112] Specifically, the above-mentioned electronic device can further include a bus, a communication interface 320, an input device 330 and an output device 340.

[0113] The processor 310, the memory 300, the communication interface 320, the input device 330 and the output device 340 are connected with each other through the bus. Among them:

[0114] The bus can include a channel for transmitting information between various components of the computer system.

[0115] The processor 310 can be a general-purpose processor, such as a general-purpose central processing unit (CPU), a microprocessor, etc., or can be an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the program execution of the application scheme. It can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a ready-to-use programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components.

[0116] The processor 310 can include a main processor, and can also include a baseband chip, a modem, etc.

[0117] The memory 300 stores programs for implementing the technical solutions of the present application, and can also store operating systems and other key services. Specifically, the programs can include program codes, which include computer operation instructions. More specifically, the memory 300 can include read-only memory (ROM), other types of static storage devices that can store static information and instructions, random access memory (RAM), other types of dynamic storage devices that can store information and instructions, disk storage, flash memory, and the like.

[0118] The input device 330 can include devices that receive data and information input by a user, such as a keyboard, a mouse, a camera, a scanner, a light pen, a voice input device, a touch screen, a pedometer, or a gravity sensor, and the like.

[0119] The output device 340 can include devices that allow information to be output to a user, such as a display screen, a printer, a speaker, and the like.

[0120] The communication interface 320 can include devices such as transceivers that are used to communicate with other devices or communication networks, such as Ethernet, a radio access network (RAN), a wireless local area network (WLAN), and the like.

[0121] The processor 310 executes programs stored in the memory 300 and invokes other devices, which can be used to implement each step of any network RTK ionospheric delay calculation method provided by the above-described embodiments of the present application.

[0122] In addition to the above-described methods and devices, the embodiments of the present application can also be computer program products that include computer program instructions that, when executed by a processor, cause the processor to perform the steps of the network RTK ionospheric delay calculation method according to various embodiments of the present application described in any of the above-described embodiments of the present application.

[0123] The computer program product can be written in any combination of one or more programming languages to perform the operations of the embodiments of the present application, including object-oriented programming languages such as Java, C++, and the like, and conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on a user computing device, partially on a user device, as a standalone software package, partially on a user computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0124] In addition, the embodiment of the present application further provides a storage medium, wherein the storage medium stores a computer program, and the computer program is run by a processor to implement the network RTK ionospheric delay calculation method described in any of the above embodiments.

[0125] Those of ordinary skill in the art understand that all or some of the steps in the above disclosed method, the functions of the modules / units in the system and the device can be implemented as software, firmware, hardware and appropriate combinations thereof. In the hardware implementation, the division between the functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, one physical component can have multiple functions, or one function or step can be performed by several physical components in cooperation. Some or all of the components can be implemented as software executed by a processor, such as a digital signal processor or a microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer readable medium, which can include computer storage media (or non-transitory media) and communication media (or transitory media). As known to those of ordinary skill in the art, the term "computer storage media" includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. Furthermore, as known to those of ordinary skill in the art, communication media typically includes computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism, and can include any information delivery medium.

Claims

1. A network RTK ionospheric delay calculation method, characterized in that: include: Determine ionospheric activity for network RTK; When the obtained ionospheric activity is less than the first activity threshold, calculating the network RTK ionospheric delay using a surface function model; When the obtained ionospheric activity is not less than the first activity threshold and not greater than the second activity threshold, calculating the network RTK ionospheric delay by combining a surface function model and a Gaussian process regression model; When the obtained ionospheric activity is greater than the second activity threshold, a Gaussian process regression model is used to calculate the ionospheric delay of the network RTK; wherein the first activity threshold is less than the second activity threshold.

2. The method according to claim 1, characterized in that The determining of the ionospheric activity of the network RTK includes: The ionospheric standard deviation IonoStd of the network RTK is calculated by the following method, and the calculated IonoStd is used as the ionospheric activity of the network RTK: Among them, ΔI i is the double-difference ionospheric delay of the ith baseline, is the average double-difference ionospheric delay of all baselines, and N is the total number of baselines.

3. The method according to claim 1, characterized in that The method of calculating the network RTK ionospheric delay by combining a surface function model and a Gaussian process regression model includes: According to the obtained ionospheric activity, the network RTK ionospheric delay is calculated by smoothly transitioning between a surface function model and a Gaussian process regression model.

4. The method according to claim 3, characterized in that The method of calculating the network RTK ionospheric delay by smoothly transitioning between a surface function model and a Gaussian process regression model based on the obtained ionospheric activity includes: The network RTK ionospheric delay VRSlono is calculated as follows: Among them, Splinelono is the first delay result of the network RTK ionosphere calculated using the surface function model, GPRlono is the second delay result of the network RTK ionosphere calculated using the Gaussian process regression model, IonoStd is the ionospheric activity of the network RTK, Th1 is the first activity threshold, and Th2 is the second activity threshold.

5. The method according to claim 4, characterized in that When the network RTK ionospheric delay is calculated using a Gaussian process regression model, or when the network RTK ionospheric delay is calculated using a combination of a surface function model and a Gaussian process regression model, the ionospheric delay E[f * |y], and calculate the E[f * |y] as the second delay result GPRlono: Where y is the known baseline ionospheric delay, K * is the covariance vector of each baseline and VRS, K is the kernel function, is the observation noise variance of the baseline, and I is the identity matrix.

6. The method according to claim 5, characterized in that The kernel function K of the Gaussian process regression model is based on the radial basis kernel K rbf With the linear dot product kernel K dot get; in, x1 and x2 are the positions of the two observation points respectively; σ0 is the default observation noise; L is K rbf Mid-range attenuation factor.

7. The method according to claim 6, characterized in that The kernel function K of the Gaussian process regression model is based on the radial basis kernel K rbf With the linear dot product kernel K dot Obtained by: According to the radial basis kernel K rbf With the linear dot product kernel K dot Adding them together to obtain the kernel function K of the Gaussian process regression model; or, According to the radial basis kernel K rbf With the linear dot product kernel K dot The kernel function K of the Gaussian process regression model is obtained by adding the origin constraint.

8. The method according to claim 1 or 4, characterized in that The first activity threshold is 0.1, and the second activity threshold is 0.

4.

9. An electronic device, characterized in that: include: memory and processor; The memory is connected to the processor and is used to store programs; The processor is used to implement the network RTK ionospheric delay calculation method according to any one of claims 1 to 8 by running the program in the memory.

10. A storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the network RTK ionospheric delay calculation method according to any one of claims 1 to 8 is implemented.

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