Ionospheric delay determination method, device, equipment, storage medium and product

Abstract

The present application provides a method, device, equipment, storage medium and product for determining ionospheric delay. The method includes: determining the current electron information and current ion information of the ionosphere based on the observation data obtained by the observation station for the ionosphere; performing inversion based on the current electron information and the current ion information to obtain the first electron information and the first ion information of the ionosphere at the first moment; performing ionosphere simulation based on the first electron information and the first ion information to obtain the ionosphere simulation result; determining the electron number density and the electron content change rate corresponding to the ionosphere based on the ionosphere simulation result; determining the ionosphere delay based on the electron number density and the electron content change rate.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a method, device, equipment, storage medium and product for determining ionospheric delay. Background Art

[0002] The Global Navigation Satellite System (GNSS) has the characteristics of global coverage, all-weather and high precision, and is widely used in automobile navigation, surveying and mapping, aerospace and other fields. However, in the positioning process, the electromagnetic wave signal emitted by the satellite needs to pass through the earth's ionosphere. The free electrons in the ionosphere will affect the propagation speed and direction of the signal, resulting in ionospheric delay error in the signal. Therefore, the corresponding ionospheric delay needs to be calculated to compensate for the error.

[0003] In the prior art, the ionospheric data calculated by the external measuring station is generally interpolated to obtain the ionospheric delay at the required position. Alternatively, the ionospheric delay is calculated using the ionospheric model preset in the global satellite navigation system interface control file. However, these methods have limited simulation capabilities, and the ionospheric data obtained using these methods are of low accuracy. Summary of the invention

[0004] The embodiments of the present application provide a method, apparatus, device, storage medium and product for determining ionospheric delay, which can accurately calculate the delay caused by the ionosphere to the signal.

[0005] In a first aspect, the present application provides a method for determining ionospheric delay, comprising:

[0006] Based on the observation data of the ionosphere obtained by the observation station, the current electron information and the current ion information of the ionosphere are determined;

[0007] Perform inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at a first moment;

[0008] Performing ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result;

[0009] Determining the electron number density and electron content change rate corresponding to the ionosphere based on the ionosphere simulation result;

[0010] The ionospheric delay is determined based on the electron number density and the electron content change rate.

[0011] In some possible implementations, the performing inversion based on the current electron information and the current ion information to obtain initial electron information and initial ion information includes:

[0012] According to the inversion model, based on the current electron information and the current ion information, the initial value of the ionospheric electron and ion distribution is determined, wherein the inversion model represents the changing relationship between the ionospheric electron information and the ion information;

[0013] Iteratively perform the following steps until the initial value meets the preset convergence condition;

[0014] Calculating the error between the initial value and the actual observed data;

[0015] Using a preset gradient descent algorithm, adjusting the initial value according to the error;

[0016] In the case where the initial value satisfies a preset convergence condition, initial electron information and initial ion information are obtained according to the initial value.

[0017] In some possible implementations, performing ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result includes:

[0018] Iteratively perform the following steps until physical parameters at multiple moments within a preset time period are obtained;

[0019] Calculate and obtain a first physical parameter of the ionosphere corresponding to a first moment according to the first electron information and the first ion information;

[0020] Using the first physical quantity as a parameter, solving the corresponding momentum equation and continuity equation using a preset differential equation solving algorithm to obtain a second physical parameter at a second moment, where the second moment is after the first moment;

[0021] Updating the first moment to the second moment, and updating the first physical parameter to the second physical parameter;

[0022] When the physical parameters at multiple moments within a preset time period are obtained, the ionosphere simulation is performed according to the physical parameters corresponding to the preset time period to obtain the ionosphere simulation result.

[0023] In some possible implementations, calculating a first physical parameter of the ionosphere corresponding to a first moment according to the first electron information and the first ion information includes:

[0024] Calculating a corresponding electronic physical quantity according to the first electronic information;

[0025] Calculating corresponding ion physical quantities according to the first ion information;

[0026] Based on the electron physical quantity and the ion physical quantity, a first physical parameter of the ionosphere corresponding to a first moment is determined.

[0027] In some possible implementations, the first physical quantity is used as a parameter, and a preset differential equation solving algorithm is used to solve the corresponding momentum equation and continuity equation to obtain a second physical parameter at a second moment, where the second moment is after the first moment, including:

[0028] Substituting the first physical quantity as a parameter into the corresponding momentum equation and continuity equation;

[0029] Using a preset differential equation solving algorithm, solving the target derivative of the momentum equation, and obtaining velocity change information of electrons and ions in the ionosphere;

[0030] Using a preset differential equation solving algorithm, the target derivative of the continuity equation is solved to obtain density change information of electrons and ions in the ionosphere;

[0031] Based on the speed change information and the density change information, a second physical parameter at a second moment is calculated.

[0032] In some possible implementations, the momentum equation includes:

[0033]

[0034] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, P represents pressure, μ represents the dynamic viscosity coefficient, λ represents the volume viscosity coefficient, f(t,x) represents the external force exerted on electrons and ions at time t and spatial position x, q represents the charge of electrons and ions, E represents the electric field strength, u represents the velocity vector of electrons and ions, and B represents the magnetic field strength.

[0035] In some possible implementations, the continuity equation includes:

[0036]

[0037] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, and S represents the predefined source term.

[0038] In some possible implementations, determining the electron number density and electron content change rate corresponding to the ionosphere based on the ionosphere simulation result includes:

[0039] Integrate based on the change to obtain the electron number density within a preset time period;

[0040] The electron content change rate within a preset time period is calculated according to the electron number density.

[0041] In a second aspect, the present application provides an ionospheric delay determination device, the device comprising:

[0042] A determination module, used to determine current electron information and current ion information of the ionosphere based on observation data obtained by the observation station for the ionosphere;

[0043] An inversion module, used for performing inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at a first moment;

[0044] A simulation module, used for performing ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result;

[0045] The determination module is further used to determine the electron number density and electron content change rate corresponding to the ionosphere based on the ionosphere simulation result;

[0046] The determination module is also used to determine the ionospheric delay according to the electron number density and the electron content change rate.

[0047] In a third aspect, the present application provides an ionospheric delay determination device, the device comprising: a processor, and a memory storing computer program instructions; the processor reads and executes the computer program instructions to implement the ionospheric delay determination method as described above.

[0048] In a fourth aspect, the present application provides a computer-readable storage medium having computer program instructions stored thereon, and when the computer program instructions are executed by a processor, the ionospheric delay determination method as described above is implemented.

[0049] In a fifth aspect, the present application provides a computer program product. When the instructions in the computer program product are executed by a processor of an electronic device, the electronic device performs the ionospheric delay determination method described above.

[0050] The ionospheric delay determination method, apparatus, device, storage medium and product provided in the embodiments of the present application determine the current electron information and current ion information of the ionosphere based on the observation data obtained by the observation station for the ionosphere, and then perform inversion based on the current electron information and the current ion information to obtain the first electron information and the first ion information of the ionosphere at the first moment, perform ionosphere simulation based on the first electron information and the first ion information to obtain ionosphere simulation results, and then determine the electron number density and the electron content change rate corresponding to the ionosphere based on the ionosphere simulation results, and finally determine the ionospheric delay based on the electron number density and the electron content change rate, and simulate the movement of ionospheric clouds from a physical perspective based on the ionospheric dynamics physical quantities, so that the simulation is closer to the actual situation and can accurately calculate the delay caused by the ionosphere to the signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The present application can be better understood from the following description of the specific embodiments of the present application in conjunction with the accompanying drawings, in which:

[0052] Other features, objects and advantages of the present application will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings, in which the same or similar reference numerals represent the same or similar features.

[0053] Figure 1 is a flow chart of a method for determining ionospheric delay provided by an embodiment of the present application;

[0054] Figure 2 is a flowchart of an iterative process in a method for determining ionospheric delay provided by another embodiment of the present application;

[0055] Figure 3 is a flow chart of a loop process in a method for determining ionospheric delay provided by another embodiment of the present application;

[0056] Figure 4 is a schematic structural diagram of an ionospheric delay determination device provided by an embodiment of the present application;

[0057] Figure 5 It is a schematic diagram of the hardware structure of the ionospheric delay determination device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0058] The features and exemplary embodiments of various aspects of the present application will be described in detail below. In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present application, rather than to limit the present application. For those skilled in the art, the present application can be implemented without the need for some of these specific details. The following description of the embodiments is only to provide a better understanding of the present application by illustrating the examples of the present application.

[0059] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "include..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0060] In order to solve the problems of the prior art, the embodiments of the present application provide a method, device, equipment, storage medium and product for determining ionospheric delay. The following first introduces the method for determining ionospheric delay provided by the embodiments of the present application.

[0061] The electron density in the vertical direction of the ionosphere (Total Electron Content Unit, TEC) refers to the total number of electrons per unit area along the signal path, which has important application value in satellite communications, navigation, remote sensing and other fields.

[0062] Vertical Total Electron Content (VETC) refers to the total electron content in the vertical direction of the ionosphere between the ground and the satellite receiver position: it refers to the total electron content in the vertical direction of the ionosphere along the signal path.

[0063] Slant Total Electron Content (STEC) on the path from the ground to the satellite: refers to the total electron content of the ionosphere along the signal path.

[0064] The rate of change of the vertical total electron content of the ionosphere per unit time (Rate of Total Electron Content Index, ROTI): the rate of change of the total electron content in the ionosphere.

[0065] Figure 1 FIG. 2 is a flow chart of a method for determining ionospheric delay provided by an embodiment of the present application. Figure 1 As shown, the method includes the following steps: S101 to S105.

[0066] S101: Based on the observation data of the ionosphere obtained by the observation station, determine the current electron information and current ion information of the ionosphere.

[0067] In a specific implementation, ionospheric data is usually collected by ground observation stations. The observation data may include the total electron density of the ionosphere, the vertical electron density distribution, the plasma frequency, etc. During the execution process, these observation data are received and analyzed to determine the current electron information and current ion information of the ionosphere.

[0068] As another implementation method, the observed data may be affected by noise or interference, so correction and filtering are needed. For example, standardized mathematical methods (such as filters, interpolation methods, etc.) are used to correct the data to obtain the electron number density and ion information of the ionosphere at the current moment.

[0069] S102: Perform inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at the first moment.

[0070] Inversion can be used to infer the state of the ionosphere from known observational data. Common inversion methods include inversion based on integral equations, least squares method, Bayesian inference, etc.

[0071] In a specific implementation, based on the observed current electron information and ion information, the inversion algorithm uses a physical model to infer a more detailed electron and ion distribution, and obtains the first electron information and the first ion information of the ionosphere at the first moment.

[0072] S103: Perform ionosphere simulation according to the first electron information and the first ion information to obtain ionosphere simulation results.

[0073] Ionosphere simulation is based on physical models and numerical simulation to describe the behavior of electrons and ions in the ionosphere. Based on numerical simulation methods such as finite element method and finite difference method, the electromagnetic field equations of the ionosphere and the motion equations of ions and electrons are solved.

[0074] In a specific implementation, the simulation process usually depends on the initial state of the ionosphere obtained in step S102 and is simulated according to existing physical rules. According to the first electron information and ion information, the evolution of the ionosphere is simulated, and the ionosphere state at a future time is obtained to determine the ionosphere simulation result.

[0075] S104: Determine the electron number density and electron content change rate corresponding to the ionosphere based on the above ionosphere simulation results.

[0076] In the specific implementation, the electron density at each moment is estimated through the simulation model, and the electron number density at different height levels is extracted from the simulation results. The rate of change of the electron content reflects the fluctuation of the ionosphere on different time scales. By differentiating the simulation results, the rate of change of the electron number density over time can be calculated, indicating the dynamic changes of the ionosphere.

[0077] S105: Determine the ionospheric delay based on the electron number density and the electron content change rate.

[0078] In the specific implementation, the change of electron number density directly affects the change of TEC, which in turn affects the speed of electromagnetic wave propagation in the ionosphere. Therefore, by calculating the electron number density and the rate of change, it is possible to predict the impact of the ionosphere on signal propagation. High-density electrons will have a strong impact on electromagnetic waves passing through the ionosphere. Based on the electron number density and the rate of change of electron content, the ionospheric delay is calculated.

[0079] The ionospheric delay determination method provided in the embodiment of the present application determines the current electron information and the current ion information of the ionosphere based on the observation data obtained by the observation station for the ionosphere, and then performs inversion based on the above current electron information and the above current ion information to obtain the first electron information and the first ion information of the ionosphere at the first moment, performs ionosphere simulation based on the above first electron information and the above first ion information to obtain the ionosphere simulation result, and then determines the electron number density and the electron content change rate corresponding to the ionosphere based on the above ionosphere simulation result, and finally determines the ionospheric delay based on the above electron number density and the above electron content change rate, and simulates the movement of ionospheric clouds from a physical perspective based on the ionospheric dynamics physical quantities, so that the simulation is closer to the actual situation, and can accurately calculate the delay caused by the ionosphere to the signal.

[0080] In order to obtain accurate ionospheric electron information and ion information, in some embodiments, the above S102 may include the following steps: S1021 to S1025.

[0081] S1021: According to the above-mentioned inversion model, based on the above-mentioned current electron information and the current ion information, the initial value of the ionospheric electron and ion distribution is determined, and the above-mentioned inversion model represents the changing relationship between the ionospheric electron information and the ion information.

[0082] In the specific implementation, the inversion model is constructed based on physical principles, statistical methods and previous observation data. Based on the output of the model, combined with the observed current electron information and ion information, an initial electron and ion distribution is determined. These initial values ​​are usually based on the mean of existing data or predicted values ​​calculated based on physical models.

[0083] S1022: Iteratively execute the following steps until the above initial value meets the preset convergence condition.

[0084] S1023: Calculate the error between the initial value and the actual observed data.

[0085] In a specific implementation, a preset error calculation method, such as mean square error, is used to calculate the error between the above initial value and the actual observed data.

[0086] S1024: Using a preset gradient descent algorithm, adjust the initial value according to the error.

[0087] In a specific implementation, during the inversion process, an iterative method may be used to optimize the initial electron and ion distribution, such as a gradient descent method, and the initial value may be adjusted according to the error by adjusting the gradient descent.

[0088] S1025: When the initial value satisfies a preset convergence condition, first electron information and first ion information are obtained according to the initial value.

[0089] In a specific implementation, at the end of the iteration, once the convergence condition is met, the electron number density distribution and ion density distribution of the current model will be used as the final first electron information and first ion information.

[0090] The above implementation of the embodiment of the present application minimizes the error between the model prediction value and the actual observation data by iteratively optimizing the initial model parameters. During the iteration process, the software continuously adjusts the distribution parameters through optimization methods such as the gradient descent algorithm, and finally obtains accurate ionospheric electron information and ion information.

[0091] In order to ensure the accuracy and stability of the simulation results, in some implementations, such as Figure 2 As shown, the above S103 may include the following steps: S1031 to S1035.

[0092] The following steps are iteratively performed until the physical parameters at multiple moments within a preset time period are obtained.

[0093] S1031: Calculate and obtain a first physical parameter of the ionosphere corresponding to the first moment based on the first electron information and the first ion information.

[0094] In a specific implementation, based on the first electron information and the first ion information, an appropriate physical model is used to calculate basic physical parameters of the ionosphere, for example, the motion equation of the ionosphere is used to describe the dynamic behavior of the ionosphere to obtain the physical parameters at the first moment.

[0095] S1032: Using the first physical quantity as a parameter, using a preset differential equation solving algorithm to solve the corresponding momentum equation and continuity equation, and obtaining a second physical parameter at a second moment, where the second moment is after the first moment.

[0096] In the specific implementation, in the simulation of the ionosphere, the momentum equation describes the movement of particles, including external influences such as electric and magnetic fields, and the continuity equation describes the conservation of particles, reflecting the flow and change of particles. Select a suitable numerical solution algorithm to solve these differential equations, and infer the physical parameters at the second moment through known initial conditions and boundary conditions.

[0097] S1033: Determine whether physical parameters at multiple moments within a preset time period are obtained.

[0098] S1034: If not, update the first moment to the second moment, and update the first physical parameter to the second physical parameter.

[0099] In a specific implementation, when the physical parameters at multiple moments in the preset time period are not obtained, the first moment is updated to the second moment, the first physical parameter is updated to the second physical parameter, and the process returns to step S1031.

[0100] S1035: When the physical parameters at multiple moments within a preset time period are obtained, ionosphere simulation is performed according to the physical parameters corresponding to the preset time period to obtain ionosphere simulation results.

[0101] In the specific implementation, after all time step calculations are completed, the physical parameters of each time point are sorted out, and the ionosphere simulation is performed to obtain the ionosphere simulation results.

[0102] The above-mentioned implementation method of the embodiment of the present application calculates the first physical parameter of the ionosphere corresponding to the first moment according to the above-mentioned first electronic information and the above-mentioned first ion information, takes the above-mentioned first physical quantity as a parameter, and uses a preset differential equation solving algorithm to solve the corresponding momentum equation and continuity equation to obtain the second physical parameter at the second moment. The above-mentioned second moment is after the first moment, and it is determined whether the physical parameters at multiple moments within the preset time period are obtained, the first moment is updated to the second moment, and the first physical parameter is updated to the second physical parameter. When the physical parameters at multiple moments within the preset time period are obtained, the ionosphere simulation is performed according to the physical parameters corresponding to the above-mentioned preset time period to obtain the ionosphere simulation result, thereby ensuring the accuracy and stability of the simulation result.

[0103] In order to accurately obtain the first physical parameter of the ionosphere, in some embodiments, the above S1031 may include the following steps: S10311 to S10313.

[0104] S10311: Calculate the corresponding electronic physical quantity based on the above-mentioned first electronic information.

[0105] In a specific implementation, based on the input first electronic information, a suitable physical model is selected to calculate the required electronic physical quantities, such as a thermodynamic equilibrium model or a particle momentum conservation equation, to obtain the corresponding electronic physical quantities.

[0106] S10312: Calculate the corresponding ion physical quantity based on the above-mentioned first ion information.

[0107] In a specific implementation, a suitable model is selected according to the input first ion information to calculate the ion physical quantity, and the corresponding ion physical quantity is calculated.

[0108] S10313: Based on the above-mentioned electronic physical quantity and the above-mentioned ion physical quantity, determine the first physical parameter of the ionosphere corresponding to the first moment.

[0109] In a specific implementation, the electron and ion information is integrated, the influence of the electric field and the magnetic field is considered, other important physical parameters of the ionosphere are calculated, and the first physical parameter of the ionosphere corresponding to the first moment is determined.

[0110] The above-mentioned implementation method of the embodiment of the present application uses a physical model to perform corresponding calculations based on the input electron and ion information, and finally integrates the electron and ion information through a suitable model to obtain the first-moment physical parameters of the ionosphere, thereby accurately obtaining the first physical parameters of the ionosphere.

[0111] In order to accurately obtain the second physical parameter of the ionosphere, in some embodiments, the above S1032 may include the following steps: S10321 to S10313.

[0112] S10321: Substitute the above first physical quantity as a parameter into the corresponding momentum equation and continuity equation.

[0113] In a specific implementation, previously calculated electron physical quantities and ion physical quantities are received as input, and these physical quantities are substituted into the momentum equation and the continuity equation. The corresponding momentum equation and the continuity equation are substituted into the corresponding momentum equation and the continuity equation, and the electric field, magnetic field and other related force terms are calculated according to the input physical quantities to obtain specific momentum and continuity equations.

[0114] S10322: Use a preset differential equation solving algorithm to solve the target derivative of the momentum equation to obtain the velocity change information of electrons and ions in the ionosphere.

[0115] In a specific implementation, a preset differential equation solving algorithm is used to solve the target derivative of the momentum equation. The algorithm is used to calculate the velocity changes of electrons and ions at the current moment, and the velocity change information of electrons and ions in the ionosphere is obtained.

[0116] S10323: Use a preset differential equation solving algorithm to solve the target derivative of the continuity equation to obtain density change information of electrons and ions in the ionosphere.

[0117] In the specific implementation, the numerical method of differential equations is used to solve the target derivative of the above continuity equation. During the iteration process of the algorithm, the density changes of electrons and ions are calculated to obtain the density change information of electrons and ions in the ionosphere.

[0118] S10324: Based on the speed change information and the density change information, a second physical parameter at a second moment is calculated.

[0119] In a specific implementation, the physical parameters at the second moment are calculated based on the speed change and density change of electrons and ions.

[0120] The above-mentioned implementation method of the embodiment of the present application takes the above-mentioned first physical quantity as a parameter, substitutes it into the corresponding momentum equation and continuity equation, and then uses a preset differential equation solving algorithm to solve the target derivative of the above-mentioned momentum equation to obtain the velocity change information of electrons and ions in the ionosphere. At the same time, a preset differential equation solving algorithm is used to solve the target derivative of the above-mentioned continuity equation to obtain the density change information of electrons and ions in the ionosphere, and then based on the above-mentioned velocity change information and the above-mentioned density change information, the second physical parameter at the second moment is calculated, and the second physical parameter at the second moment can be accurately obtained.

[0121] In order to accurately obtain the velocity change information of electrons and ions in the ionosphere, in some embodiments, the momentum equation includes:

[0122]

[0123] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, P represents pressure, μ represents the dynamic viscosity coefficient, λ represents the volume viscosity coefficient, f(t,x) represents the external force exerted on electrons and ions at time t and spatial position x, q represents the charge of electrons and ions, E represents the electric field strength, u represents the velocity vector of electrons and ions, and B represents the magnetic field strength.

[0124] In order to accurately obtain the density change information of electrons and ions in the ionosphere, in some embodiments, the continuity equation includes:

[0125]

[0126] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, and S represents the predefined source term.

[0127] In order to accurately reflect the dynamic changes of the ionosphere, in some embodiments, the above S104 may include the following steps: S1041 to S1042.

[0128] S1041: Integrate based on the above changes to obtain the electron number density within a preset time period.

[0129] In a specific implementation, relevant information about the change in electron density is received to obtain a corresponding ordinary differential equation, which is integrated. By integrating each time step, the change in electron number density is gradually accumulated to obtain the electron number density within a preset time period.

[0130] S1042: Calculate the electron content change rate within a preset time period based on the above electron number density.

[0131] The above implementation of the embodiment of the present application integrates the change of the electron number density to obtain the electron number density within a preset time period, and based on this, calculates the rate of change of the electron content, receives the input ionization rate and loss rate, and then calculates the change of the electron number density by a numerical integration method. Subsequently, the rate of change of the electron content can be calculated using the electron number density data, ensuring that each step of the calculation can accurately reflect the dynamic changes of the ionosphere.

[0132] As another implementation method of the present application, the electron density is inverted according to the data on the observation station to achieve the purpose of simulation. The steps of the simulator's space-time model involve using the ion motion equation to simulate the movement of the sample in space and time, and finally counting the number of ions in a small area to generate STEC from the satellite to the base station. The initial ion and electron information is determined by the inversion of the observed quantity on the observation station.

[0133] Specifically, solve the following problems:

[0134]

[0135] Among them, arg min means finding the variable that minimizes the objective function; ρ, u: represent the optimization variables, ρ is the density, u is the velocity vector; N represents the number of integration regions; T represents the time interval; Si represents the i-th integration region; ρ(t,s) represents the density at time t and spatial position s; ki(t) represents the observed or known density value at time t; R(…) represents the regularization term, which is used to control the smoothness of the solution or avoid overfitting.

[0136] Based on this, we solve the following momentum equation and continuity equation:

[0137] The momentum equation above includes:

[0138]

[0139] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, P represents pressure, μ represents the dynamic viscosity coefficient, λ represents the volume viscosity coefficient, f(t,x) represents the external force exerted on electrons and ions at time t and spatial position x, q represents the charge of electrons and ions, E represents the electric field strength, u represents the velocity vector of electrons and ions, and B represents the magnetic field strength.

[0140] The above continuity equation includes:

[0141]

[0142] Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, and S represents the predefined source term.

[0143] Afterwards, if Figure 3 As shown, a cyclic solution process is performed.

[0144] S301: Record speed and density. Record the current speed, density and other items to be used.

[0145] Then solve the necessary items, specifically, including:

[0146] S302: Calculate the pressure.

[0147] Specifically, solve the following equation:

[0148]

[0149] in, represents the pressure gradient vector; represents the partial derivative of pressure P in the x direction, that is, the rate of change of pressure in the x direction; represents the partial derivative of pressure P in the y direction, that is, the rate of change of pressure in the y direction; It represents the partial derivative of pressure P in the z direction, that is, the rate of change of pressure in the z direction.

[0150] S303: Solve the viscosity term.

[0151] Specifically, solve the following equation:

[0152]

[0153] Among them, μ represents the dynamic viscosity coefficient, u represents the velocity field, represents the second-order partial derivative of the velocity field u in the x direction, represents the second-order partial derivative of the velocity field u in the y direction, Represents the second-order partial derivative of the velocity field u in the z direction.

[0154] In addition, the specific calculation process is as follows:

[0155]

[0156] S304: Solve the expansion term.

[0157] Specifically, solve the following equation:

[0158]

[0159] Where u represents the velocity field, They represent the components of the velocity field u in the x, y, and z directions respectively.

[0160] S305: Solve the electric field force.

[0161] Specifically, solve the following equation:

[0162] F 电 =qE

[0163] Among them, F 电is the electric field force, which represents the force exerted on a charged particle in an electric field; q is the charge of the particle, which can be positive or negative; E is the electric field strength, which represents the strength and direction of the force of the electric field at a certain point in space.

[0164] S306: Solve for the Lorentz force.

[0165] Specifically, solve the following equation:

[0166]

[0167] Among them, μ0 is the magnetic permeability in a vacuum; μ is the magnetic moment of the Earth, representing the strength and direction of the Earth's magnetic field; r is the distance from the center of the Earth to the observation point; θ is the magnetic latitude measured from the magnetic north pole; r^ and θ^ are the radial and tangential unit vectors, respectively.

[0168] F 电 =q(u×B)

[0169] Among them, q is the charge of the charged particle; u is the velocity vector of the charged particle; B is the magnetic field vector.

[0170] S307: Solve the convective derivative of velocity.

[0171] Specifically, solve the following equation:

[0172]

[0173] Among them, u is the velocity vector, and its components are u, v, w, which represent the velocity components in the x, y, and z directions respectively; i, j, k are unit vectors along the x, y, and z directions.

[0174] S308: Solve the source term.

[0175] Specifically, operations are performed according to manually given source terms to solve the corresponding source terms.

[0176] S309: Using ordinary differential methods, the local derivative of velocity is obtained based on the momentum equation.

[0177] Specifically, using the ordinary differential equation method, according to the momentum equation, the local derivative of the velocity can be obtained. The Runge-Kutta algorithm can be used to solve the following equation:

[0178]

[0179] S310: Use velocity and density to find density based on the continuity equation.

[0180] Specifically, the new density is obtained based on the continuity equation using the ordinary differential equation method. The Runge-Kutta algorithm can be used.

[0181] Furthermore, in order to obtain the inversion algorithm for inversion, the formula is abstracted as:

[0182]

[0183] g(x, p) = 0

[0184] The dpf is obtained by the following method:

[0185]

[0186] Use the calculated dpf to update the parameter p of the objective function. Here, you can use the gradient descent method or Newton's method to solve. After obtaining the initial state p, use the forward method to update other solutions of the equation. Repeat this process until convergence.

[0187] After obtaining the electron density in the time period T, the electron amount in the specified area is obtained using the integral method, specifically:

[0188]

[0189] Use the definition to get the ROTI of the region:

[0190]

[0191] The embodiment of the present application starts from the principle of partial differential equations, simulates the movement of ionospheric clouds in the atmosphere, so as to know the density of the ionosphere at each point, and can accurately calculate the information (TEC and ROTI) of the required position. It does not rely on the inherent characteristics of the satellite system, does not require external data, and has universality. The obtained ionospheric simulation data can be combined with the observation data more conveniently, which is convenient for the simulation of the observation values. In order to facilitate the simulation and realization of various ionospheric movement effects, the model provides some parameters for adjustment. For example, by setting the area where the cloud is located, the direction of movement of the initial velocity of the cloud, etc., the ionosphere simulation of the area can be realized. Combined with satellite information, the vtec and roti values ​​of the station in the area can be obtained.

[0192] Based on the ionospheric delay determination method provided in the above embodiment, the present application also provides a specific implementation of the ionospheric delay determination device. Please refer to the following embodiment.

[0193] See first Figure 4 The ionospheric delay determination device 400 provided in the embodiment of the present application includes the following modules:

[0194] The determination module 401 is used to determine the current electron information and current ion information of the ionosphere based on the observation data of the ionosphere obtained by the observation station.

[0195] The inversion module 402 is used to perform inversion based on the current electron information and the current ion information to obtain the first electron information and the first ion information of the ionosphere at the first moment.

[0196] The simulation module 403 is used to perform ionosphere simulation according to the first electron information and the first ion information to obtain ionosphere simulation results.

[0197] The determination module 401 is further used to determine the electron number density and electron content change rate corresponding to the ionosphere based on the above ionosphere simulation results.

[0198] The determination module 401 is further used to determine the ionospheric delay according to the above electron number density and the above electron content change rate.

[0199] As an implementation of the present application, the inversion module 402 includes:

[0200] The determination unit is used to determine the initial value of the ionospheric electron and ion distribution according to the above-mentioned inversion model, based on the above-mentioned current electron information and the current ion information, and the above-mentioned inversion model represents the changing relationship between the ionospheric electron information and the ion information.

[0201] The iteration unit is used to iteratively execute the following steps until the above initial value meets the preset convergence condition.

[0202] The calculation unit is used to calculate the error between the initial value and the actual observation data.

[0203] The adjustment unit is used to adjust the initial value according to the error using a preset gradient descent algorithm.

[0204] The determination unit is further used to obtain the first electron information and the first ion information according to the initial value when the initial value meets a preset convergence condition.

[0205] As an implementation of the present application, the simulation module 403 includes:

[0206] The iteration unit is used to iteratively execute the following steps until the physical parameters at multiple moments within a preset time period are obtained.

[0207] A calculation unit is used to calculate the first physical parameter of the ionosphere corresponding to the first moment according to the first electron information and the first ion information.

[0208] The calculation unit is also used to use the above-mentioned first physical quantity as a parameter, use a preset differential equation solving algorithm to solve the corresponding momentum equation and continuity equation, and obtain a second physical parameter at a second moment, and the above-mentioned second moment is after the first moment.

[0209] The updating unit is used to update the first moment to the second moment and update the first physical parameter to the second physical parameter.

[0210] The simulation unit is used to perform ionospheric simulation according to the physical parameters corresponding to the preset time period to obtain ionospheric simulation results when the physical parameters at multiple moments in the preset time period are obtained.

[0211] As an implementation of the present application, a computing unit includes:

[0212] The calculation subunit is used to calculate the corresponding electronic physical quantity according to the above-mentioned first electronic information.

[0213] The calculation subunit is further used to calculate the corresponding ion physical quantity according to the above-mentioned first ion information.

[0214] The determination subunit is used to determine a first physical parameter of the ionosphere corresponding to a first moment based on the above-mentioned electronic physical quantity and the above-mentioned ion physical quantity.

[0215] As an implementation of the present application, a computing unit includes:

[0216] Substitute the subunit to describe the first physical quantity as a parameter and substitute it into the corresponding momentum equation and continuity equation.

[0217] The solving subunit is used to solve the target derivative of the momentum equation using a preset differential equation solving algorithm to obtain the velocity change information of electrons and ions in the ionosphere.

[0218] The solving subunit is also used to use a preset differential equation solving algorithm to solve the target derivative of the continuity equation and obtain the density change information of electrons and ions in the ionosphere.

[0219] The calculation subunit is used to calculate a second physical parameter at a second moment based on the speed change information and the density change information.

[0220] As an implementation of the present application, the determination module 401 includes:

[0221] The determination unit is used to integrate based on the above changes to obtain the electron number density within a preset time period.

[0222] The calculation unit is used to calculate the electron content change rate within a preset time period according to the above electron number density.

[0223] The various modules in the ionospheric delay determination device provided in the embodiment of the present application can implement the various steps in the above-mentioned ionospheric delay determination method and achieve the corresponding effects. For the sake of concise description, they will not be repeated here.

[0224] Figure 5 A schematic diagram of the structure of the ionospheric delay determination hardware provided in an embodiment of the present application is shown.

[0225] The ionospheric delay determination device may include a processor 501 and a memory 502 storing computer program instructions.

[0226] Specifically, the processor 501 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or may be configured to implement one or more integrated circuits of the embodiments of the present application.

[0227] The memory 502 may include a large capacity memory for data or instructions. By way of example and not limitation, the memory 502 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive or a combination of two or more of these. In appropriate cases, the memory 502 may include a removable or non-removable (or fixed) medium. In appropriate cases, the memory 502 may be inside or outside the integrated gateway disaster recovery device. In a specific embodiment, the memory 502 is a non-volatile solid-state memory.

[0228] The memory may include a read-only memory (ROM), a random access memory (RAM), a magnetic disk storage medium device, an optical storage medium device, a flash memory device, an electrical, optical or other physical / tangible memory storage device. Thus, generally, the memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., a memory device) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the ionospheric delay determination method according to any one of the embodiments of the present disclosure.

[0229] The processor 501 implements any one of the ionospheric delay determination methods in the above embodiments by reading and executing computer program instructions stored in the memory 502.

[0230] In one example, the ionospheric delay determination device may further include a communication interface 503 and a bus 510. Figure 5 As shown, the processor 501, the memory 502, and the communication interface 503 are connected via a bus 510 and communicate with each other.

[0231] The communication interface 503 is mainly used to implement communication between various modules, devices, units and / or equipment in the embodiments of the present application.

[0232] Bus 510 includes hardware, software or both, and the parts of online data flow billing equipment are coupled to each other. For example, but not limitation, bus may include accelerated graphics port (AGP) or other graphics bus, enhanced industrial standard architecture (EISA) bus, front-end bus (FSB), hypertransport (HT) interconnection, industrial standard architecture (ISA) bus, infinite bandwidth interconnection, low pin count (LPC) bus, memory bus, micro channel architecture (MCA) bus, peripheral component interconnection (PCI) bus, PCI-Express (PCI-X) bus, serial advanced technology attachment (SATA) bus, video electronics standard association local (VLB) bus or other suitable bus or two or more of these combinations. In appropriate cases, bus 510 may include one or more buses. Although the present application embodiment describes and shows a specific bus, the present application considers any suitable bus or interconnection.

[0233] In addition, in combination with the method for determining ionospheric delay in the above embodiment, the embodiment of the present application may provide a computer storage medium for implementation. The computer storage medium stores computer program instructions; when the computer program instructions are executed by the processor, any one of the methods for determining ionospheric delay in the above embodiment is implemented.

[0234] An embodiment of the present application also provides a computer program product, including a computer program, which, when executed, implements any one of the methods for determining ionospheric delay in the above embodiments.

[0235] It should be clear that the present application is not limited to the specific configuration and processing described above and shown in the figures. For the sake of simplicity, a detailed description of the known method is omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present application is not limited to the specific steps described and shown, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps after understanding the spirit of the present application.

[0236] The functional blocks shown in the above-described block diagram can be implemented as hardware, software, firmware or a combination thereof. When implemented in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present application are programs or code segments that are used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link by a data signal carried in a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, etc. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0237] It should also be noted that the exemplary embodiments mentioned in this application describe some methods or systems based on a series of steps or devices. However, this application is not limited to the order of the above steps, that is, the steps can be performed in the order mentioned in the embodiment, or in a different order from the embodiment, or several steps can be performed simultaneously.

[0238] Aspects of the present disclosure are described above with reference to the flowchart and / or block diagram of the method, device (system) and computer program product according to the embodiment of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine so that these instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the function / action specified in one or more boxes of the flowchart and / or block diagram. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit. It can also be understood that each box in the block diagram and / or flowchart and the combination of boxes in the block diagram and / or flowchart can also be implemented by dedicated hardware that performs a specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions.

[0239] The above is only a specific implementation of the present application. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the systems, modules and units described above can refer to the corresponding processes in the aforementioned method embodiments, and will not be repeated here. It should be understood that the protection scope of the present application is not limited to this. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in this application, and these modifications or replacements should be included in the protection scope of this application.

Claims

1. A method for determining ionospheric delay, characterized in that: include: Based on the observation data of the ionosphere obtained by the observation station, the current electron information and the current ion information of the ionosphere are determined; Perform inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at a first moment; Performing ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result; Determining the electron number density and electron content change rate corresponding to the ionosphere based on the ionosphere simulation result; The ionospheric delay is determined based on the electron number density and the electron content change rate.

2. The ionospheric delay determination method according to claim 1, characterized in that: The inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at the first moment includes: Determining initial values ​​of ionospheric electron and ion distributions according to an inversion model based on the current electron information and the current ion information, wherein the inversion model represents a changing relationship between the ionospheric electron information and the ion information; Iteratively perform the following steps until the initial value meets the preset convergence condition; Calculating the error between the initial value and the actual observed data; Using a preset gradient descent algorithm, adjusting the initial value according to the error; In a case where the initial value satisfies a preset convergence condition, first electron information and first ion information are obtained according to the initial value.

3. The ionospheric delay determination method according to claim 1, characterized in that: The performing ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result includes: Iteratively perform the following steps until physical parameters at multiple moments within a preset time period are obtained; Calculate and obtain a first physical parameter of the ionosphere corresponding to a first moment according to the first electron information and the first ion information; Using the first physical parameter as a parameter, solving the corresponding momentum equation and continuity equation using a preset differential equation solving algorithm to obtain a second physical parameter at a second moment, where the second moment is after the first moment; Updating the first moment to the second moment, and updating the first physical parameter to the second physical parameter; When the physical parameters at multiple moments within a preset time period are obtained, the ionosphere simulation is performed according to the physical parameters corresponding to the preset time period to obtain the ionosphere simulation result.

4. The ionospheric delay determination method according to claim 3, characterized in that: The step of calculating a first physical parameter of the ionosphere corresponding to a first moment according to the first electron information and the first ion information includes: Calculating a corresponding electronic physical quantity according to the first electronic information; Calculating corresponding ion physical quantities according to the first ion information; Based on the electron physical quantity and the ion physical quantity, a first physical parameter of the ionosphere corresponding to a first moment is determined.

5. The ionospheric delay determination method according to claim 3, characterized in that: The method uses the first physical parameter as a parameter and uses a preset differential equation solving algorithm to solve the corresponding momentum equation and continuity equation to obtain a second physical parameter at a second moment, wherein the second moment is after the first moment, and includes: Substituting the first physical parameter as a parameter into the corresponding momentum equation and continuity equation; Using a preset differential equation solving algorithm, solving the target derivative of the momentum equation, and obtaining velocity change information of electrons and ions in the ionosphere; Using a preset differential equation solving algorithm, the target derivative of the continuity equation is solved to obtain density change information of electrons and ions in the ionosphere; Based on the speed change information and the density change information, a second physical parameter at a second moment is calculated.

6. The ionospheric delay determination method according to claim 5, characterized in that: The momentum equation includes: Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, P represents pressure, μ represents the dynamic viscosity coefficient, λ represents the volume viscosity coefficient, f(t,x) represents the external force exerted on electrons and ions at time t and spatial position x, q represents the charge of electrons and ions, E represents the electric field strength, u represents the velocity vector of electrons and ions, and B represents the magnetic field strength.

7. The method for determining ionospheric delay according to claim 5, characterized in that: The continuity equation includes: Among them, ρ represents the density of electrons and ions, t represents time, V represents the velocity vector of electrons and ions, and S represents the predefined source term.

8. The method for determining ionospheric delay according to any one of claims 1 to 7, characterized in that: The determining, based on the ionosphere simulation result, the electron number density and the electron content change rate corresponding to the ionosphere comprises: Integrating the ionosphere simulation results to obtain the electron number density within a preset time period; The electron content change rate within a preset time period is calculated according to the electron number density.

9. An ionospheric delay determination device, characterized in that: The device comprises: A determination module is used to determine the current electron information and current ion information of the ionosphere based on the observation data obtained by the observation station for the ionosphere; determine the electron number density and the electron content change rate corresponding to the ionosphere based on the ionosphere simulation result; determine the ionosphere delay according to the electron number density and the electron content change rate; An inversion module, used for performing inversion based on the current electron information and the current ion information to obtain first electron information and first ion information of the ionosphere at a first moment; A simulation module is used to perform ionosphere simulation according to the first electron information and the first ion information to obtain an ionosphere simulation result.

10. An ionospheric delay determination device, characterized in that: The device comprises: a processor, and a memory storing computer program instructions; the processor reads and executes the computer program instructions to implement the ionospheric delay determination method according to any one of claims 1 to 8.

11. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer program instructions, and when the computer program instructions are executed by a processor, the ionospheric delay determination method according to any one of claims 1 to 8 is implemented.

12. A computer program product, characterized in that When the instructions in the computer program product are executed by a processor of an electronic device, the electronic device executes the ionospheric delay determination method as described in any one of claims 1-8.

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