Ionosphere parameter inversion method and device

Abstract

The invention provides an ionosphere parameter inversion method and device, and belongs to the technical field of short-wave communication, and the method comprises the steps: enabling the actually-measured amplitude and phase difference to be mapped into a low-order wave mode excitation amplitude and a complex feature value through the synchronous receiving of the same very-low-frequency transmitting station signal at different transmitting and receiving distances on the ground; and then fast convergence solution is carried out by using a Newton-Raphson method, and ionosphere electron concentration parameters are circularly corrected by using a gradient descent method, so that the residual error of a theoretical calculation result and a measured value is stabilized within a preset threshold, thereby getting rid of excessive dependence on a traditional ionosphere mode, remarkably improving the inversion precision of low ionosphere parameters, and improving the reliability of the low ionosphere. The method has the advantages of simple operation, low cost and long-term operation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of low-frequency signal propagation, and in particular to an ionospheric parameter inversion method and device. BACKGROUND

[0002] Low-frequency electromagnetic waves (focusing on the very low frequency band below 30 kHz) have the characteristics of long wavelength, stable transmission channel, and small water attenuation, and can be applied to long-distance, large-depth cross-space water electromagnetic communication. The ground-ionospheric waveguide propagation characteristics are directly affected by the low ionospheric space-time variation parameters, and accurate acquisition of ionospheric parameters is the key to guaranteeing the coverage range, communication probability and navigation positioning evaluation accuracy of low-frequency communication, which is the common technical object of the present application and the prior art.

[0003] In the prior art, there are mainly two types of schemes for acquiring ionospheric parameters: one is the forward study of low-frequency signal propagation characteristics, that is, the signal transmission characteristics are calculated based on the waveguide mode algorithm and the classic ionospheric database model, and the ionospheric parameters are corrected by comparing a small amount of measured channel signal values to correct the propagation model; the other is to rely on alpha navigation signal detection inversion and medium frequency radar detection to build a low ionospheric database model, in which the medium frequency radar detects the 60-100km wind field through the Fresnel reflection of the ionospheric D layer and E layer.

[0004] However, the existing forward study lacks a large amount of effective measured sample data support, the complexity of ionospheric space-time variation leads to low inversion accuracy, and the parameters need to be re-corrected when the time or transmission path changes; the alpha navigation signal detection has the problems of few launch stations and monitoring sites, limited coverage, and the medium frequency radar is difficult to obtain long-term low ionospheric data in a large range due to its small number and high price, which cannot meet the demand for accurate acquisition of ionospheric parameters in actual application. SUMMARY

[0005] The present application provides an ionospheric parameter inversion method and device to overcome the defects of the prior art, by establishing a matrix relationship between the wave mode characteristic parameters and the measured signal amplitude / phase, and then solving the wave mode characteristic parameters to invert the ionospheric parameters, thereby providing technical support for establishing an accurate ionospheric model, improving the accuracy of low-frequency signal transmission characteristic quantitative analysis and performance evaluation, etc.

[0006] In a first aspect, the present application provides an ionospheric parameter inversion method, which comprises: S1, acquiring the measured amplitude and measured phase of each measurement point signal at different transmission and reception distances, and determining the distance difference and phase difference of each adjacent measurement point, taking the distance difference and phase difference as the measured propagation characteristic quantity; S2, based on the ground-ionosphere waveguide propagation theory, express the very low frequency total field as a complex exponential series of not more than two order wave modes, the series taking the excitation amplitude and complex eigenvalue of each order wave mode as unknowns; the very low frequency total field is the total electric field intensity of the measured point signal superimposed by each order wave mode in the ground-ionosphere waveguide; S3, establish a trans-cendental equation set between the measured propagation characteristic quantity and the unknowns; S4, iteratively solve the trans-cendental equation set by Newton-Raphson method, and construct an iterative formula by Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue; S5, substitute the wave mode excitation amplitude and wave mode complex eigenvalue into the complex exponential series to calculate the theoretical amplitude and theoretical phase, and perform difference operation on the measured amplitude value and measured phase value to obtain a residual; S6, if the norm of the residual is greater than a preset threshold, adjust the ionospheric electron concentration parameter by gradient descent method, repeat steps S4-S5 until the norm of the residual is not greater than the threshold, output the current electron concentration parameter as the inversion result, and realize high-precision acquisition of the ionospheric parameter.

[0007] Further, the construction of the iterative formula by Jacobian matrix to make the excitation amplitude and complex eigenvalue converge to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue comprises: Solving the spherical waveguide mode equation under the approximation of the ionospheric IRI index model and Airy function to obtain the excitation amplitude and complex eigenvalue of each order wave mode as the initial value of the trans-cendental equation set; Constructing an iterative formula by Jacobian matrix based on the initial value and norm to make the excitation amplitude and complex eigenvalue converge to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue.

[0008] Further, the real part of the complex eigenvalue corresponds to the relative phase velocity, and the imaginary part corresponds to the spatial attenuation rate.

[0009] Further, the acquisition of the measured amplitude and measured phase of each measured point signal at different transmitting-receiving distances comprises: Arranging not less than five synchronous receiving measured points at preset equal intervals within the target range from the same very low frequency transmitting station, and collecting time domain signals of a preset frequency transmitted by the same transmitting station of the Beidou time system at each measured point; Performing Fourier transform on the time domain signals to obtain the measured amplitude and measured phase of each measured point signal.

[0010] Further, the determination of the distance difference and phase difference between adjacent measured points based on the measured amplitude and measured phase comprises: Calculating the distance difference between adjacent measured points according to the longitude and latitude of the adjacent measured points. According to the phase value of the adjacent measuring point, the phase difference between the adjacent measuring points is calculated.

[0011] Further, the measured propagation characteristic quantity only selects the first measuring point as a phase reference, and the phase difference of the rest measuring points is calculated relative to the reference.

[0012] In the second aspect, the application further provides an ionospheric parameter inversion device, comprising: a measured data acquisition module, configured to acquire measured amplitudes and measured phases of signals of measuring points at different transmitting-receiving distances, and determine distance differences and phase differences of adjacent measuring points, so as to take the distance differences and the phase differences as measured propagation characteristic quantities; A first processing module is configured to represent a very low frequency total field as a complex exponential series of not more than two order wave modes based on a ground-ionospheric waveguide propagation theory, the series taking an excitation amplitude and a complex eigenvalue of each order wave mode as unknown quantities; the very low frequency total field is a total electric field intensity of signals of measuring points after superposition of each order wave mode in a ground-ionospheric waveguide; An equation construction module is configured to establish a transendental equation group between the measured propagation characteristic quantities and the unknown quantities; A second processing module is configured to iteratively solve the transendental equation group by using a Newton-Raphson method, and to construct an iterative formula by using a Jacobian matrix, so as to make the excitation amplitude and the complex eigenvalue converge, and to obtain the converged wave mode excitation amplitude and the wave mode complex eigenvalue; A residual error operation module is configured to substitute the wave mode excitation amplitude and the wave mode complex eigenvalue into the complex exponential series, to calculate a theoretical amplitude and a theoretical phase, and to perform a difference operation on the measured amplitude value and the measured phase value, so as to obtain a residual error; An inversion module is configured to, if a norm of the residual error is greater than a preset threshold, adjust an ionospheric electron concentration parameter by using a gradient descent method, repeatedly perform steps S4-S5 until the norm of the residual error is not greater than the threshold, and output a current electron concentration parameter as an inversion result, so as to realize high-precision acquisition of ionospheric parameters.

[0013] In the third aspect, the application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor realizes the steps of the ionospheric parameter inversion method according to any one of the above-mentioned aspects when executing the program.

[0014] In the fourth aspect, the application further provides a non-transitory computer readable storage medium, which stores a computer program, and the computer program realizes the steps of the ionospheric parameter inversion method according to any one of the above-mentioned aspects when executed by a processor.

[0015] The ionospheric parameter inversion method and device provided by the application have the following beneficial effects compared with the prior art: The present application can realize the measurement of low frequency signals by multiple points and multiple times through the synchronization of the same very low frequency signal received at different distances, and can accurately obtain the amplitude and phase of the signal as the calculation reference of the wave mode parameter value. The amplitude and phase difference obtained by the actual measurement is mapped to the low-order wave mode excitation amplitude and complex eigenvalue. Then, the Newton-Raphson method is used for fast convergence solution, and the ionospheric electron concentration parameter is corrected by the gradient descent method, so that the residual error between the theoretical calculation result and the measured value is stable within the preset threshold, thereby breaking the excessive dependence on the traditional ionospheric model, significantly improving the inversion accuracy of the low ionospheric parameter; at the same time, based on the existing global distribution of high-power very low frequency stations, it can be implemented without adding expensive radars or special loads, and can continuously obtain regional ionospheric spatio-temporal variation information in a long baseline range, providing reliable data support for subsequent establishment of accurate ionospheric model, evaluation of low frequency communication coverage performance and improvement of navigation and positioning accuracy, and the whole process is completed in a ground multi-point cooperative manner, which has the advantages of simple operation, low cost and long-term operation. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present application or prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0017] Figure 1 is one of the flowcharts of the ionospheric parameter inversion method provided by the present application; Figure 2 is the second flowchart of the ionospheric parameter inversion method provided by the present application; Figure 3 is a reference diagram for comparing the wave mode characteristic parameters and the parameters corresponding to mode 1 in the LWPC model provided by the present application; Figure 4 is a structural diagram of an electronic device provided by the present application. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of the present application more clear, the technical solutions in the present application will be described clearly and completely in the following with reference to the drawings in the present application. Obviously, the described embodiments are some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0019] It should be noted that in the description of the embodiments of the present application, the terms "comprising", "containing" 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 not only includes those elements, but also includes other elements not explicitly listed or inherent to such a process, method, article or device. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article or device comprising the element. Unless otherwise specified and limited, the terms "mounting", "connecting", "connecting" should be understood in a broad sense, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be the communication between two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0020] The terms "first", "second", and the like in the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are usually a class, and do not limit the number of objects, for example, the first object can be one or more.

[0021] The following will be described in detail Figures 1-4 The ionospheric parameter inversion method and device provided by the embodiments of the present application are described.

[0022] Figure 1 is one of the flowcharts of the ionospheric parameter inversion method provided by the present application, as Figure 1 shown, including but not limited to the following steps: S1, obtaining the measured amplitude and measured phase of each measuring point signal at different transmitting and receiving distances, and determining the distance difference and phase difference of each adjacent measuring point, taking the distance difference and phase difference as the measured propagation characteristic quantity; S2, based on the ground-ionospheric waveguide propagation theory, the very low frequency total field is expressed as a complex exponential series of not more than two order wave modes, and the series takes the excitation amplitude and complex eigenvalue of each order wave mode as unknown quantity; the very low frequency total field is the total electric field intensity of the superposition of each order wave mode of the measuring point signal in the ground-ionospheric waveguide; S3, establishing a transcendental equation set between the measured propagation characteristic quantity and the unknown quantity; S4, the transcendental equation is solved by Newton-Raphson method iteration, and the iteration formula is constructed by Jacobian matrix, so that the excitation amplitude and complex eigenvalue converge, and the converged wave mode excitation amplitude and wave mode complex eigenvalue are obtained; S5, the wave mode excitation amplitude and wave mode complex eigenvalue are substituted into the complex exponential series to calculate the theoretical amplitude and theoretical phase, and the difference between the measured amplitude value and the measured phase value is calculated to obtain the residual error; S6, if the norm of the residual error is greater than a preset threshold, the ionospheric electron concentration parameter is adjusted by gradient descent method, and steps S4-S5 are repeated until the norm of the residual error is not greater than the threshold, and the current electron concentration parameter is output as the inversion result, realizing high-precision acquisition of ionospheric parameters.

[0023] Regarding step S1, the measured amplitude and measured phase of each measuring point signal at different transmitting and receiving distances are obtained, and the distance difference and phase difference between adjacent measuring points are determined, and the distance difference and phase difference are taken as the measured propagation characteristic quantity.

[0024] In an optional embodiment, the present embodiment provides an ionospheric parameter inversion method, wherein the measured amplitude and measured phase of each measuring point signal at different transmitting and receiving distances are obtained, including: At least five synchronous receiving measuring points are arranged at preset equal intervals within the target range of the same very low frequency transmitting station, and time domain signals of a preset frequency transmitted by the same transmitting station are collected based on Beidou time system; the time domain signals are subjected to Fourier transform to obtain the measured amplitude and measured phase of each measuring point signal.

[0025] In the present embodiment, a receiving measuring line is arranged on the east edge of the Eurasian continent, which is approximately directed to the central very low frequency transmitting station of the Pacific Ocean along a great circle path, and electromagnetic signals with a frequency lower than 30 kHz are synchronously collected during the period when the ionospheric D region height is relatively stable at night.

[0026] First, a high-stability rubidium clock is used to tame the Beidou time receiver to provide a sub-microsecond common time reference for each measuring point; then the antenna is coupled to the electric field time domain waveform, which is continuously recorded, and after removing direct current and windowing, discrete Fourier transform is performed to extract the complex amplitude at the carrier frequency of the transmitting station, and the real part and imaginary part correspond to the measured amplitude and measured phase of the measuring point position respectively.

[0027] In an optional embodiment, the present embodiment provides an ionospheric parameter inversion method, wherein the distance difference and phase difference between adjacent measuring points are determined based on the measured amplitude and measured phase, including: The distance difference between adjacent measuring points is calculated according to the longitude and latitude of adjacent measuring points; The phase difference between adjacent measuring points is calculated according to the phase values of adjacent measuring points.

[0028] The embodiment takes the most western measuring point as a reference, sequentially calculates the great circle distance difference between the measuring point and the adjacent measuring point on the east side, and simultaneously multiplies the corresponding complex conjugate amplitude to obtain the phase difference of the adjacent measuring point by taking the amplitude. The distance difference and the phase difference are saved in pairs as the measured propagation characteristic quantity for subsequent operation. It is worth mentioning that the measured propagation characteristic quantity can only select the first measuring point as a phase reference, and the phase difference of the remaining measuring points is calculated with respect to the reference to reduce the error introduced by the system clock drift.

[0029] Regarding step S2, based on the ground-ionospheric waveguide propagation theory, the very low frequency total field is expressed as a complex exponential series of not more than two order wave modes, and the series takes the excitation amplitude and complex eigenvalue of each order wave mode as unknown quantities.

[0030] The very low frequency total field is the total electric field intensity of the superposition of each order wave mode of the measuring point signal in the ground-ionospheric waveguide.

[0031] In the embodiment, under the framework of the ground-ionospheric waveguide model, the ground and the low ionosphere are regarded as a spherical shell waveguide composed of two walls, and the very low frequency electric field is expressed as a complex exponential series of the superposition of the first order and the second order transverse magnetic wave modes propagating along the measuring line direction. The coefficient of each term of the series is the wave mode excitation amplitude to be solved, and the complex propagation constant in the index is the wave mode complex eigenvalue to be solved. The real part of the complex eigenvalue corresponds to the relative phase velocity, and the imaginary part corresponds to the spatial attenuation rate. Since the high order mode has been attenuated to be negligible at the distance of thousands of kilometers, the series only retains two terms, so that the total field can be simplified as a linear combination of two unknown excitation amplitudes and two unknown complex eigenvalues.

[0032] Regarding step S3, the transcendental equation set between the measured propagation characteristic quantity and the unknown quantity is established.

[0033] In the embodiment, the measured complex amplitude of each measuring point is equal to the theoretical value at the corresponding position of the series expression, and a nonlinear transcendental equation set with the excitation amplitude and the complex eigenvalue as unknown quantities can be listed. The number of equations is the same as the number of measuring points, and the distance difference and the phase difference relationship between the adjacent measuring points are further expanded to the redundant equations of twice the number of measuring points to provide constraints for subsequent iteration.

[0034] Regarding step S4, the Newton-Raphson method is used to iteratively solve the transcendental equation set, and the iteration formula is constructed by using the Jacobian matrix to make the excitation amplitude and the complex eigenvalue converge, so as to obtain the converged wave mode excitation amplitude and the wave mode complex eigenvalue.

[0035] In an alternative embodiment, the method for inverting ionospheric parameters provided by the embodiment includes the following steps: The ionospheric IRI index model and the spherical waveguide mode equation under Airy function approximation are used to solve the excitation amplitude and complex eigenvalue of each order wave mode, which are used as initial values of the transendental equation set; Based on the initial values and norm, the Jacobian matrix is used to construct an iterative formula to make the excitation amplitude and complex eigenvalue converge, and the converged wave mode excitation amplitude and wave mode complex eigenvalue are obtained.

[0036] In the embodiment, to solve the transendental equation set, the exponential distribution of electron density with height variation is given by the international reference ionospheric model, and the excitation amplitude and complex eigenvalue are obtained by solving the spherical waveguide characteristic equation with Airy function approximation.

[0037] Then, the Newton-Raphson method is used for iteration: a residual vector with the excitation amplitude and complex eigenvalue as independent variables is constructed, the Jacobian matrix thereof is solved, and the unknown quantity is updated inversely according to the first-order Taylor expansion until the difference between the results of two consecutive iterations is less than a set threshold, and it is considered that the excitation amplitude and complex eigenvalue have converged, and the final estimation of the wave mode excitation amplitude and wave mode complex eigenvalue is obtained.

[0038] Regarding step S5, the wave mode excitation amplitude and wave mode complex eigenvalue are substituted into the complex exponential series to obtain the theoretical amplitude and theoretical phase, and the difference between the theoretical amplitude and theoretical phase and the measured amplitude and measured phase is calculated to obtain the residual. In the embodiment, the converged excitation amplitude and complex eigenvalue are substituted back into the exponential series, the theoretical amplitude and theoretical phase are calculated point by point, and the complex residual of each measurement point is obtained by subtracting the measured amplitude and measured phase; and the two-norm of the vector composed of the residuals of all measurement points is taken as the overall error measure.

[0039] Regarding step S6, if the norm of the residual is greater than a preset threshold, the ionospheric electron density profile is fine-tuned in the negative gradient direction of the residual with respect to the electron density profile by using the gradient descent method, the initial values of the characteristic equation are recalculated, and the Newton-Raphson iteration is repeated until the norm of the residual is less than or equal to the threshold, and the current electron density profile is output as the inversion result, thereby achieving high-precision acquisition of the ionospheric parameters.

[0040] In the embodiment, if the norm is greater than the preset threshold, it is determined that the current ionospheric parameters have not reached the precision requirement, and then the electron density profile is fine-tuned in the negative gradient direction of the residual with respect to the electron density profile by using the gradient descent method, the initial values of the characteristic equation are recalculated, and the Newton-Raphson iteration is repeated until the norm of the residual is less than or equal to the threshold, and the output electron density profile is the inversion result of the low ionospheric characteristic quantity, thereby achieving high-precision acquisition of the ionospheric parameters.

[0041] Next, an ionospheric parameter inversion method according to an embodiment of the present application is described in detail.

[0042] Five point synchronous receiving stations are arranged at intervals of 40-60km within a range of 300km from the foreign transmitting station 1500km away, and the Beidou is used as the time reference. Figure 2 is a flowchart of the ionospheric parameter inversion method provided by the present application, as shown in Figure 2 , the amplitude and phase information of the signal is obtained by using the measured five point time domain data, and and the corresponding distance are obtained.

[0043] According to the time delay measurement principle, in order to ensure the accuracy of the method, the axial direction of the observation array is preferably parallel to the wave direction of the transmitting station or the included angle between the two is very small, the distance between the adjacent two points is preferably in the range of 40-60km, and the distance is much smaller than the distance between the observation point array and the transmitting station, so as to ensure that there is sufficient distance difference between the transmitting station and each observation point; wherein the frequency of the transmitting station signal cannot be too high, and the distance from the observation point cannot be too close, so as to ensure that the influence of the second order and above can be ignored. It should be noted that the distance between the adjacent two points is not the larger the better, because this method is applicable on the condition that the ionosphere changes very little within the range of the observation array, therefore, a compromise distance range of 40-60km is given in combination with the accuracy of the method.

[0044] After obtaining the synchronous time domain signal data of the five points, the following processing is performed: 1) Fourier transform is performed on the time domain data to obtain the amplitude value and phase value of each point; 2) the distance difference between the two points is calculated according to the longitude and latitude of the adjacent two points; 3) the phase difference between the two points is calculated according to the phase values of the adjacent two points; 4) the distance difference and the phase difference of the four adjacent points are recorded.

[0045] At this point, the signals of the four points (except the reference point) can be expressed in the form of amplitude and phase.

[0046] Further, according to the propagation characteristics of low-frequency electromagnetic waves in the ionosphere, a field strength series expression is established, that is, the total field is composed of the amplitude, phase velocity, and attenuation rate of each order wave mode, so as to establish the relationship between the measured signal and the characteristic parameters of each order wave mode. The following is the specific implementation process: Since the propagation mode of low-frequency electromagnetic waves in the ionosphere is in the form of wave mode superposition, when the propagation distance is far enough, the high-order mode has been rapidly attenuated, and only the low-order mode plays a major role. At the same time, in order to ensure the accuracy of the algorithm, the first two order modes are considered. The low-frequency electromagnetic wave signal can be expressed as: (1) In the above formula, B represents a very low frequency total field, which is a measured total field signal containing amplitude and phase information, subscript n represents the number of receiving points, and the method for obtaining the amplitude and phase information has been described above. N represents the wave mode order, which is 2 here, A represents the excitation amplitude, which is the amplitude of each order mode and is one of the unknown quantities, i is an imaginary unit, S represents a complex eigenvalue, which is a wave mode eigenvalue, and its real part reflects the relative phase velocity and its imaginary part reflects the spatial attenuation rate, which is also an unknown quantity, S is a complex number (the real part reflects the phase velocity and the imaginary part reflects the attenuation rate), and d represents the propagation distance (i.e. the straight-line distance between the transmitting and receiving points).

[0047] represents the wave number of an electromagnetic wave in a vacuum, when the operating frequency is constant, is a constant and can be calculated according to the following formula, where f is the operating frequency, is a constant, and represents the permittivity and permeability of an electromagnetic wave in a vacuum, respectively, , .

[0048] (2) Since is a constant, in order to simplify formula (1), define (m=1,2), whose real part reflects the phase velocity and whose imaginary part reflects the attenuation rate, formula (1) can be rewritten as (1') When only the first two order modes are considered, the right side of formula (1') includes four unknowns A1, A2, S1 and S2, and at least four equations are required to solve these four unknowns, that is, at least four sets of synchronous measured data Bn (n=1, 2, 3, 4) and corresponding measured propagation distances dn (n=1, 2, 3, 4) are required. However, even if four sets of synchronous measured data Bn and corresponding measured propagation distances dn are obtained, since the equation set is composed of transcendental equations, the unknowns A1, A2, S1 and S2 cannot be accurately solved by a finite number of algebraic operations.

[0049] Further, the present application uses the Newton-Raphson method to solve the unknowns in the above transcendental equation set, and the core is to use the Jacobian matrix (the "derivative matrix" of a multivariate function) to construct an iterative formula. This method has a large convergence speed, but depends on the selection of the initial value, that is, the initial value needs to be close to the true solution for convergence. Therefore, before using the iterative convergence method to solve the unknowns, the accurate initial value of the unknowns needs to be obtained first.

[0050] Since the amplitude, propagation phase velocity and attenuation rate of each wave mode are closely related to the roots of the mode equation, the roots of the mode equation can be solved first according to the ionospheric IRI model (i.e. the classical exponential model) and the spherical waveguide propagation theory under the Airy function approximation to obtain the amplitude, propagation phase velocity and attenuation rate of each wave mode, and then the initial solutions Am0, Am0, Sm0 and Sm0 of Am, Am, Sm and Sm (m represents the wave mode order) are calculated.

[0051] The specific method can be that electromagnetic field in the waveguide is expressed in the form of a Helmholtz equation from the Maxwell equations, the Helmholtz equation is separated into two ordinary differential equations of Legendre equation and Stokes equation by using the separation of variables method, and the mode equation and the corresponding roots (i.e. the initial solutions Am0, Am0, Sm0 and Sm0) of each wave mode are solved by using the ground and ionospheric boundary conditions and the ionospheric exponential model parameter values. Since a large amount of theoretical research has been done by scholars at home and abroad and there is a relatively mature calculation method, and this part does not belong to the protection point of the present application, it will not be described in detail.

[0052] After obtaining the initial solutions, the norm is introduced, and the iterative formula is constructed by using the Jacobian matrix to make Am, Am, Sm and Sm four unknowns quickly converge to the accurate values. The specific steps are as follows: Suppose that there are four points of synchronous data B1, B2, B3 and B4 at this time, and the definitions are (3) The norm of J is defined as (4)The derivatives of k1, k2, A1 and A2 are obtained respectively as (5) (6) (7) (8) At this time, A1, A2, S1 and S2 can be obtained according to the above (5) to (8) iterative formula, and then the amplitudes and characteristic parameters (including phase velocity and attenuation rate) of the first and second modes are obtained.

[0053] ​(5) after obtaining the wave mode characteristic parameters, the p1, p2, p3 and p4 can be calculated by substituting the formula (3) into the measured values B1, B2, B3 and B4 and d1, d2, d3 and d4, and the convergence threshold of p1, p2, p3 and p4 is set to 10-5 (less than the threshold, that is, the accuracy requirement is met). When the accuracy requirement is not met, the electron concentration parameter is adjusted by using the gradient descent method, and the iteration calculation is performed until the measured value and the theoretical value are consistent, and the ionospheric parameter corresponding to the consistent result can be output.

[0054] Figure 3 The relative phase velocity and attenuation rate corresponding to the first two order transverse magnetic waves (TM1 and TM2) of the ionospheric parameter method in the embodiment of the application combined with the measured data and the wave mode characteristics are obtained by inversion, and the comparison data is the relative phase velocity and attenuation rate corresponding to the first two order transverse magnetic waves (TM1 and TM2) calculated according to the ionospheric electron concentration parameter mode 1 in the LWPC model (Long-Wavelength Propagation Capability) of the US Navy. It can be seen that the wave mode characteristic parameters obtained by combining the ionospheric parameters after inversion and the results obtained by the LWPC model are in good agreement.

[0055] The application also provides an ionospheric parameter inversion device, comprising: A data acquisition module is configured to acquire the communication link passable frequency window measured data output by the ionospheric detection device. A measured amplitude and a measured phase of each measuring point signal at different transmitting and receiving distances are acquired, and a distance difference and a phase difference between adjacent measuring points are determined, and the distance difference and the phase difference are used as measured propagation characteristics. A first processing module is configured to represent a very low frequency total field as a complex exponential series of no more than two order wave modes based on the ground-ionospheric waveguide propagation theory, and the series takes the excitation amplitude and the complex eigenvalue of each order wave mode as unknown quantities. The very low frequency total field is the total electric field intensity of the superposition of each order wave mode in the ground-ionospheric waveguide. An equation construction module is configured to establish a transcendental equation group between the measured propagation characteristics and the unknown quantities. A second processing module is configured to solve the transcendental equation group by using the Newton-Raphson method, and to construct an iteration formula by using a Jacobian matrix, so that the excitation amplitude and the complex eigenvalue converge, and the converged wave mode excitation amplitude and the wave mode complex eigenvalue are obtained. A residual operation module is configured to substitute the wave mode excitation amplitude and the wave mode complex eigenvalue into the complex exponential series to calculate the theoretical amplitude and the theoretical phase, and to perform a difference operation on the measured amplitude value and the measured phase value to obtain a residual error. The inversion module is configured to adjust the ionospheric electron concentration parameter by using a gradient descent method if the norm of the residual is greater than a preset threshold, repeatedly perform steps S4-S5 until the norm of the residual is not greater than the threshold, and output the current electron concentration parameter as an inversion result, thereby achieving high-precision acquisition of the ionospheric parameter.

[0056] It should be noted that the ionospheric parameter inversion device provided in the embodiments of the present application can perform the ionospheric parameter inversion method described in any of the above embodiments during actual operation, and the embodiments will not be repeated here.

[0057] Figure 4 is a structural schematic diagram of an electronic device provided by the present application, as Figure 4 shown, the electronic device can include a processor 410, a communications interface 420, a memory 430, and a communications bus 440, wherein the processor 410, the communications interface 420, and the memory 430 can communicate with each other through the communications bus 440. The processor 410 can invoke a logical instruction in the memory 430 to execute an ionospheric parameter inversion method, which includes: S1, obtaining measured amplitudes and measured phases of signals of each measuring point at different transmitting-receiving distances, and determining distance differences and phase differences of adjacent measuring points, taking the distance differences and the phase differences as measured propagation characteristic quantities; S2, based on a ground-ionospheric waveguide propagation theory, representing a very low frequency total field as a complex exponential series of not more than two order wave modes, wherein the series takes excitation amplitudes and complex characteristic values of each order wave mode as unknown quantities; the very low frequency total field is a total electric field intensity of superposition of each order wave mode of the measuring point signal in the ground-ionospheric waveguide; S3, establishing a transcendental equation set between the measured propagation characteristic quantities and the unknown quantities; S4, iteratively solving the transcendental equation set by using a Newton-Raphson method, and constructing an iteration formula by using a Jacobian matrix to make the excitation amplitudes and the complex characteristic values converge, thereby obtaining the converged wave mode excitation amplitudes and the wave mode complex characteristic values; S5, substituting the wave mode excitation amplitudes and the wave mode complex characteristic values into the complex exponential series to calculate theoretical amplitudes and theoretical phases, and performing difference operation on the measured amplitude values and the measured phase values, thereby obtaining a residual; S6, if the norm of the residual is greater than a preset threshold, adjusting the ionospheric electron concentration parameter by using a gradient descent method, repeatedly performing steps S4-S5 until the norm of the residual is not greater than the threshold, and outputting the current electron concentration parameter as an inversion result, thereby achieving high-precision acquisition of the ionospheric parameter.

[0058] Further, the logic instructions in the memory 430 described above can be implemented in the form of software functional units and sold or used as independent products, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0059] In another aspect, the present application also provides a computer program product, which comprises a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the ionospheric parameter inversion method provided by the above-mentioned embodiments, the method comprising: S1, obtaining the measured amplitudes and measured phases of the signals of each measuring point at different transmitting-receiving distances, and determining the distance difference and phase difference of each adjacent measuring point, taking the distance difference and phase difference as the measured propagation characteristic quantities; S2, based on the ground-ionospheric waveguide propagation theory, representing the very low frequency total field as a complex exponential series of not more than two order wave modes, the series taking the excitation amplitudes and complex eigenvalues of each order wave mode as unknown quantities; the very low frequency total field is the total electric field intensity of the superposition of each order wave mode in the ground-ionospheric waveguide; S3, establishing a transendental equation set between the measured propagation characteristic quantities and the unknown quantities; S4, iteratively solving the transendental equation set by Newton-Raphson method, and constructing an iterative formula by Jacobian matrix to make the excitation amplitudes and complex eigenvalues converge, to obtain the converged wave mode excitation amplitudes and wave mode complex eigenvalues; S5, substituting the wave mode excitation amplitudes and wave mode complex eigenvalues into the complex exponential series to calculate the theoretical amplitudes and theoretical phases, and performing difference operation on the measured amplitude values and measured phase values to obtain the residual error; S6, if the norm of the residual error is greater than a preset threshold, adjusting the ionospheric electron concentration parameter by gradient descent method, repeating steps S4-S5 until the norm of the residual error is not greater than the threshold, outputting the current electron concentration parameter as the inversion result, and realizing high-precision acquisition of the ionospheric parameter.

[0060] In yet another aspect, the present application also provides a non-transitory computer readable storage medium having stored thereon a computer program, which, when executed by a processor, implements the ionospheric parameter inversion method provided by any of the above embodiments, and the method comprises: S1, obtaining measured amplitudes and measured phases of signals of each measuring point at different distances, and determining distance differences and phase differences of adjacent measuring points, taking the distance differences and phase differences as measured propagation characteristics; S2, based on the ground-ionospheric waveguide propagation theory, representing the very low frequency total field as a complex exponential series of no more than two order wave modes, the series taking the excitation amplitudes and complex eigenvalues of each order wave mode as unknown quantities; the very low frequency total field is the total electric field intensity of the superposition of each order wave mode in the ground-ionospheric waveguide; S3, establishing a trans-cendental equation set between the measured propagation characteristics and the unknown quantities; S4, iteratively solving the trans-cendental equation set by Newton-Raphson method, and constructing an iterative formula by Jacobian matrix to make the excitation amplitudes and complex eigenvalues converge, to obtain the converged wave mode excitation amplitudes and wave mode complex eigenvalues; S5, substituting the wave mode excitation amplitudes and wave mode complex eigenvalues into the complex exponential series to calculate the theoretical amplitudes and theoretical phases, and performing difference operation on the measured amplitude values and measured phase values to obtain residuals; S6, if the norm of the residuals is greater than a preset threshold, adjusting the ionospheric electron concentration parameter by gradient descent method, repeating steps S4-S5 until the norm of the residuals is not greater than the threshold, outputting the current electron concentration parameter as an inversion result, and realizing high-precision acquisition of ionospheric parameters. The device embodiments described above are only schematic, and the units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e. they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment scheme according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0061] Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software and necessary general hardware platforms, and of course can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, server, or network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0062] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the same; although the present application has been described in detail with reference to the foregoing examples, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for inverting ionospheric parameters, characterized in that, include: S1, acquire the measured amplitude and measured phase of the signal at each measuring point at different transmit and receive distances, and determine the distance difference and phase difference between each adjacent measuring point, using the distance difference and phase difference as the measured propagation characteristic quantity; S2, based on the propagation theory of earth-ionospheric waveguides, the very low frequency total field is expressed as a complex exponential series of no more than the second-order wave mode, wherein the excitation amplitude and complex eigenvalue of each order wave mode are unknowns; the very low frequency total field is the total electric field intensity of the signal at the measurement point after the superposition of each order wave mode in the earth-ionospheric waveguide. S3, establish a set of transcendental equations between the measured propagation characteristic quantities and the unknown quantities; S4. Solve the transcendental equations iteratively using the Newton-Raphson method, and construct an iterative formula using the Jacobian matrix to converge the excitation amplitude and complex eigenvalues, thereby obtaining the converged wave mode excitation amplitude and wave mode complex eigenvalues. S5, Substitute the wave mode excitation amplitude and wave mode complex characteristic value into the complex exponential series to calculate the theoretical amplitude and theoretical phase, and perform a difference operation with the measured amplitude value and measured phase value to obtain the residual; S6. If the norm of the residual is greater than a preset threshold, the ionospheric electron concentration parameter is adjusted by gradient descent. Steps S4-S5 are repeated until the norm of the residual is not greater than the threshold. The current electron concentration parameter is then output as the inversion result to achieve high-precision acquisition of ionospheric parameters.

2. The ionospheric parameter inversion method according to claim 1, characterized in that, The step of constructing an iterative formula using the Jacobian matrix to converge the excitation amplitude and complex eigenvalues, thereby obtaining the converged wave mode excitation amplitude and complex eigenvalues, includes: Using the ionospheric IRI exponential model and the spherical waveguide mode equations under the Airy function approximation, the excitation amplitudes and complex eigenvalues ​​of each wave mode are obtained and used as the initial values ​​of the transcendental equations. Based on the initial value and norm, an iterative formula is constructed using the Jacobian matrix to converge the excitation amplitude and complex eigenvalues, thereby obtaining the converged wave mode excitation amplitude and wave mode complex eigenvalues.

3. The ionospheric parameter inversion method according to claim 1, characterized in that, The real part of the complex eigenvalue corresponds to the relative phase velocity, and the imaginary part corresponds to the spatial decay rate.

4. The ionospheric parameter inversion method according to claim 1, characterized in that, The acquisition of the measured amplitude and measured phase of the signals at each measurement point at different transmission and reception distances includes: Within the target range of the same very low frequency transmitter, no fewer than five synchronous receiving measurement points are set up at preset equal intervals, and time domain signals of preset frequencies transmitted by the same transmitter at each measurement point are collected with the BeiDou time system as the reference. Perform a Fourier transform on the time-domain signal to obtain the measured amplitude and measured phase of the signal at each measurement point.

5. The ionospheric parameter inversion method according to claim 1, characterized in that, The determination of the distance difference and phase difference between adjacent measuring points based on the measured amplitude and measured phase includes: Calculate the distance difference between adjacent measuring points based on their latitude and longitude. The phase difference between adjacent measuring points is calculated based on the phase values ​​of adjacent measuring points.

6. The ionospheric parameter inversion method according to claim 1, characterized in that, The measured propagation characteristic quantity uses only the first measurement point as the phase reference, and the phase difference of the other measurement points is calculated relative to this reference.

7. The ionospheric parameter inversion method according to claim 1, characterized in that, After outputting the current electron concentration parameter as the inversion result, the following is also included: Substitute the electron concentration parameters obtained from the inversion into the LWPC model to calculate the relative phase velocity and decay rate of TM1 and TM2 modes, and cross-validate them with the complex eigenvalues ​​of the converged wave modes. If the difference between the two is less than the preset limit, the inversion result is confirmed to be valid; otherwise, return to step S1 to re-acquire data.

8. An ionospheric parameter inversion device, characterized in that, include: The measured data acquisition module is used to acquire the measured amplitude and measured phase of the signal at each measurement point at different transmission and reception distances, and to determine the distance difference and phase difference between each adjacent measurement point, using the distance difference and phase difference as measured propagation characteristic quantities. The first processing module is used to express the very low frequency total field as a complex exponential series of no more than two wave modes based on the earth-ionospheric waveguide propagation theory. The series has the excitation amplitude and complex eigenvalue of each wave mode as unknowns. The very low frequency total field is the total electric field intensity of the measurement point signal after the superposition of each wave mode in the earth-ionospheric waveguide. An equation construction module is used to establish a set of transcendental equations between the measured propagation characteristics and the unknowns; The second processing module is used to iteratively solve the transcendental equations using the Newton-Raphson method and construct an iterative formula using the Jacobian matrix to converge the excitation amplitude and complex eigenvalues, thereby obtaining the converged wave mode excitation amplitude and wave mode complex eigenvalues. The residual calculation module is used to substitute the wave mode excitation amplitude and wave mode complex characteristic value into the complex exponential series to calculate the theoretical amplitude and theoretical phase, and perform a difference calculation with the measured amplitude value and measured phase value to obtain the residual. The inversion module is used to adjust the ionospheric electron concentration parameter using the gradient descent method if the norm of the residual is greater than a preset threshold. Steps S4-S5 are repeated until the norm of the residual is no greater than the threshold, and the current electron concentration parameter is output as the inversion result, thereby achieving high-precision acquisition of ionospheric parameters.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the ionospheric parameter inversion method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the ionospheric parameter inversion method as described in any one of claims 1 to 7.

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