Ionospheric parameter inversion method and device

Abstract

The application provides an ionosphere parameter inversion method and device, and belongs to the technical field of short wave communication. The method comprises the following steps: synchronously receiving signals of a very low frequency transmitting station at different transmitting and receiving distances, mapping the amplitude and phase difference obtained by actual measurement into low-order wave mode excitation amplitude and complex eigenvalues, quickly converging and solving by using the Newton-Raphson method, and cyclically correcting the ionosphere electron concentration parameter by using the gradient descent method, so that the residual error between the theoretical calculation result and the actual measurement value is stabilized within a preset threshold, the excessive dependence on the traditional ionosphere model is broken, the inversion accuracy of the low ionosphere parameter is significantly improved, and 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, 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, which 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, which provides technical support for establishing an accurate ionospheric model, improving the accuracy of quantitative analysis and efficiency evaluation of low-frequency signal transmission characteristics, etc.

[0006] In a first aspect, the present application provides an ionospheric parameter inversion method, which comprises:

[0007] S1, acquiring the measured amplitude and measured phase of the signals of each measuring point 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 quantities;

[0008] 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 superposition of each order wave mode of the measured point signal in the ground-ionosphere waveguide;

[0009] S3, establish a trans-cendental equation set between the measured propagation characteristic quantity and the unknowns;

[0010] 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;

[0011] 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;

[0012] 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, and output the current electron concentration parameter as the inversion result, to realize high-precision acquisition of ionospheric parameters.

[0013] 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:

[0014] Solving the spherical waveguide mode equation under the approximation of 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;

[0015] 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.

[0016] Further, the real part of the complex eigenvalue corresponds to the relative phase velocity, and the imaginary part corresponds to the spatial attenuation rate.

[0017] Further, the acquisition of the measured amplitude and measured phase of each measured point signal at different transmitting-receiving distances comprises:

[0018] Arranging not less than five synchronous receiving measured points at preset equal intervals within the target range of the same very low frequency transmitting station, and collecting time domain signals of a preset frequency transmitted by the same transmitting station based on Beidou time system;

[0019] Performing Fourier transform on the time domain signals to obtain the measured amplitude and measured phase of each measured point signal.

[0020] Further, the distance difference and the phase difference between the adjacent measuring points are determined based on the measured amplitude and the measured phase, comprising:

[0021] The distance difference between the adjacent measuring points is calculated according to the longitude and latitude of the adjacent measuring points;

[0022] The phase difference between the adjacent measuring points is calculated according to the phase value of the adjacent measuring points.

[0023] 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.

[0024] 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 measuring point signals at different transmitting-receiving distances, and to determine distance differences and phase differences between adjacent measuring points, so as to take the distance differences and the phase differences as measured propagation characteristic quantities;

[0025] 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 a ground-ionospheric waveguide propagation theory, wherein the series takes 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 the measuring point signal after superposition of each order wave mode in the ground-ionospheric waveguide;

[0026] An equation construction module is configured to establish a transendental equation set between the measured propagation characteristic quantities and the unknown quantities;

[0027] A second processing module is configured to iteratively solve the transendental equation set by using a Newton-Raphson method, and to construct an iteration 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;

[0028] 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 between the theoretical amplitude and the theoretical phase and the measured amplitude value and the measured phase value, so as to obtain a residual error;

[0029] An inversion module is configured to adjust an ionospheric electron concentration parameter by using a gradient descent method if a norm of the residual error is greater than a preset threshold, to repeat steps S4-S5 until the norm of the residual error is not greater than the threshold, and to output a current electron concentration parameter as an inversion result, so as to realize high-precision acquisition of the ionospheric parameter.

[0030] In the third aspect, the application provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes steps of the ionospheric parameter inversion method according to any one of the above aspects when executing the program.

[0031] In a fourth 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 steps of any of the ionospheric parameter inversion methods described above.

[0032] The ionospheric parameter inversion method and device provided by the present application have the following beneficial effects compared with the prior art:

[0033] The present application can realize the multi-point, multi-time and synchronous measurement of low-frequency signals by synchronously receiving signals of the same very low frequency transmitting station at different distances, and can accurately obtain the amplitude and phase of the signals as the calculation reference of the wave mode parameter value. The difference between the measured amplitude and phase is mapped to the low-order wave mode excitation amplitude and complex eigenvalue. Then, the Newton-Raphson method is used for fast convergence, and the gradient descent method is used for cyclic correction of the ionospheric electron concentration parameter, so that the residual error between the theoretical calculation result and the measured value is stabilized within the preset threshold, thereby breaking the excessive dependence on the traditional ionospheric model and significantly improving the inversion accuracy of the low ionospheric parameter. At the same time, the present application can be implemented based on the existing global distribution of high-power very low frequency stations, without the need to add expensive radars or special payloads, and can continuously obtain regional ionospheric spatio-temporal variation information in a long baseline range, thereby providing reliable data support for subsequent establishment of accurate ionospheric models, evaluation of low-frequency communication coverage performance, and improvement of navigation and positioning accuracy, and the entire 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

[0034] 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 for those skilled in the art, other drawings can also be obtained without creative labor.

[0035] Figure 1 is one of the flowcharts of the ionospheric parameter inversion method provided by the present application;

[0036] Figure 2 is another flowchart of the ionospheric parameter inversion method provided by the present application;

[0037] Figure 3 is a reference diagram showing the comparison between the wave mode eigenvalue parameters and the parameters corresponding to mode 1 in the LWPC model;

[0038] Figure 4 is a structural diagram of the electronic device provided by the present application. DETAILED DESCRIPTION

[0039] In order to make the objects, technical solutions and advantages of the present application clearer, the following will clearly and completely describe the technical solutions in the present application with reference to the drawings in the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0040] 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 the non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment. Without more limitation, the element defined by the statement "including a" does not exclude the presence of another identical element in the process, method, article or equipment including the element. Unless otherwise explicitly 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 inside 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.

[0041] 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 thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than that illustrated or described herein, and the objects distinguished by "first", "second" and the like are generally a category, and do not limit the number of objects, for example, the first object can be one or more.

[0042] The following will be described with reference to the drawings Figures 1-4 The ionospheric parameter inversion method and device provided by the embodiments of the present application are described.

[0043] 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:

[0044] S1, obtaining the measured amplitude and measured phase of the signal of each measuring point 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;

[0045] S2, based on the ground-ionosphere waveguide propagation theory, express the very low frequency total field as a complex exponential series of no 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 superposition of each order wave mode of the signal at the measuring point in the ground-ionosphere waveguide;

[0046] S3, establish a transendental equation set between the measured propagation characteristic quantity and the unknowns;

[0047] S4, iteratively solve the transendental equation set by the Newton-Raphson method, and construct an iterative formula by the Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue;

[0048] 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 error;

[0049] S6, if the norm of the residual error is greater than a preset threshold, adjust the ionospheric electron concentration parameter by the gradient descent method, repeat steps S4-S5 until the norm of the residual error is not greater than the threshold, and output the current electron concentration parameter as the inversion result, to realize high-precision acquisition of the ionospheric parameter.

[0050] Regarding step S1, the measured amplitude and measured phase of each measuring point signal of different transmitting-receiving distances are obtained, and the distance difference and phase difference of each adjacent measuring point are determined, and the distance difference and phase difference are taken as the measured propagation characteristic quantity.

[0051] In an optional embodiment, the embodiment provides an ionospheric parameter inversion method, wherein the measured amplitude and measured phase of each measuring point signal of different transmitting-receiving distances are obtained, including:

[0052] In the target range from the same very low frequency transmitting station, at least five synchronous receiving measuring points are arranged at preset equal intervals, and time domain signals of a preset frequency emitted 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.

[0053] The embodiment arranges a receiving measuring line on the east edge of the Eurasian continent, which is approximately directed to a very low frequency transmitting station in the middle of the Pacific Ocean along a great circle path, and synchronously collects electromagnetic signals with a frequency lower than 30 kHz at night when the ionospheric D region height is relatively stable.

[0054] Firstly, the Beidou time receiver is disciplined by a high-stability rubidium clock to provide a sub-microsecond common time reference for each measuring point; then the time-domain waveforms coupled to the antenna are recorded continuously, and after removing DC and windowing, the discrete Fourier transform is performed to extract the complex amplitude at the carrier frequency of the transmitting station, the real part and the imaginary part of which correspond to the measured amplitude and the measured phase of the measuring point position respectively.

[0055] In an optional embodiment, the ionospheric parameter inversion method provided by the embodiment determines the distance difference and the phase difference between adjacent measuring points based on the measured amplitude and the measured phase, comprising:

[0056] According to the latitude and longitude of the adjacent measuring points, the distance difference between the adjacent measuring points is calculated.

[0057] According to the phase values of the adjacent measuring points, the phase difference between the adjacent measuring points is calculated.

[0058] The embodiment takes the westernmost measuring point of the path as the reference to calculate the great-circle distance difference between it and the adjacent measuring points to the east, and simultaneously, the phase difference of the adjacent measuring points is obtained by multiplying the corresponding complex amplitudes by the conjugate and taking the amplitude angle. The distance difference and the phase difference are saved in pairs as the measured propagation characteristic quantities for subsequent operations. It is worth noting that the measured propagation characteristic quantities can only use the first measuring point as the 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.

[0059] Regarding step S2, based on the ground-ionospheric waveguide propagation theory, the very low frequency total field is represented as a complex exponential series of not more than two-order wave modes, and the series takes the excitation amplitude and the complex eigenvalue of each order wave mode as unknown quantities.

[0060] Among them, the very low frequency total field is the total electric field intensity of the signal of the measuring point superimposed by each order wave mode in the ground-ionospheric waveguide.

[0061] 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 represented as a complex exponential series superimposed by the first-order and 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. Among them, 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 a 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.

[0062] Regarding step S3, the transcendental equation set between the measured propagation characteristic quantities and the unknown quantities is established.

[0063] In the present 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 complex eigenvalue as unknown quantities can be listed. Among them, the number of equations is the same as the number of measuring points, and by increasing the distance difference and phase difference relationship between adjacent measuring points, it is further expanded to a redundant equation of twice the number of measuring points to provide constraints for subsequent iterations.

[0064] Regarding step S4, the transcendental equation set is solved by Newton-Raphson iteration, and the iteration formula is constructed by Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, and the converged wave mode excitation amplitude and wave mode complex eigenvalue are obtained.

[0065] In an optional embodiment, the present embodiment provides an ionospheric parameter inversion method, wherein the iteration formula is constructed by Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, and the converged wave mode excitation amplitude and wave mode complex eigenvalue are obtained, including:

[0066] The spherical waveguide mode equation is solved by using the ionospheric IRI index model and the Airy function approximation to obtain the excitation amplitude and complex eigenvalue of each order wave mode as the initial value of the transcendental equation set;

[0067] Based on the initial value and norm, the iteration formula is constructed by Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, and the converged wave mode excitation amplitude and wave mode complex eigenvalue are obtained.

[0068] In the present embodiment, to solve the transcendental equation set, the exponential distribution of electron concentration with height change can be given by the International Reference Ionosphere model, and the spherical waveguide characteristic equation is solved by combining the Airy function approximation to obtain the analytical initial value of the excitation amplitude and complex eigenvalue.

[0069] Then, Newton-Raphson iteration is performed: a residual vector with the excitation amplitude and complex eigenvalue as independent variables is constructed, its Jacobian matrix is solved, and the unknown quantities are updated according to the first-order Taylor expansion until the difference between the results of two consecutive iterations is less than a set threshold value, and it is considered that the excitation amplitude and complex eigenvalue have converged, and the final estimate of the wave mode excitation amplitude and wave mode complex eigenvalue is obtained.

[0070] Regarding step 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 residual error is obtained by difference operation between the measured amplitude value and the measured phase value.

[0071] In the present embodiment, the converged excitation amplitude and complex eigenvalue are substituted back into the exponential series, and the theoretical amplitude and theoretical phase are calculated point by point, and the complex residual error of each measuring point is obtained by subtracting the measured amplitude and measured phase corresponding to the foregoing; the two-norm of the vector composed of all measuring point residual errors is taken as the overall error measure.

[0072] If the norm of the residual is greater than a preset threshold, the ionospheric electron concentration parameter is adjusted by using a gradient descent method, steps S4-S5 are repeated until the norm of the residual is not greater than the threshold, and the current electron concentration parameter is output as an inversion result, so that high-precision ionospheric parameters are obtained.

[0073] In the embodiment, if the norm is greater than a preset threshold, it is determined that the current ionospheric parameter has not reached the precision requirement, and then the electron concentration profile is fine-tuned in a gradient descent manner along a negative gradient direction of the residual to the electron concentration parameter, the initial value of the characteristic equation is recalculated, and the Newton-Raphson iteration is repeated until the norm of the residual is reduced to below the threshold, and the output electron concentration parameter is the low ionospheric characteristic quantity obtained by inversion, and the high-precision ionospheric parameter is obtained.

[0074] Next, an ionospheric parameter inversion method provided by the present application is described in detail.

[0075] Five point synchronous receiving stations are arranged at intervals of 40km-60km within a range of 300km away from the foreign transmitting station at a distance of 1500km, and the Beidou is used as a time reference. Figure 2 is a second 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 are obtained by using the measured five-point time-domain data, and and the corresponding distance are obtained.

[0076] 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 direction of the incoming wave of the transmitting station or the included angle between the two is very small, the distance between the two adjacent points is preferably in the range of 40km-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 a sufficient distance difference between the transmitting station and each observation point;

[0077] The transmitting station signal frequency cannot be too high, and the distance from the observation point cannot be too close, so that the influence of the second order and above can be ignored.

[0078] After obtaining the synchronous time-domain signal data of the five points, the following processing is performed:

[0079] 1) Fourier transform is performed on the time-domain data to obtain the amplitude and phase values of each point;

[0080] 2) The distance difference between the two points is calculated according to the longitude and latitude of the two points.

[0081] 3) Calculate the phase difference between two points according to the phase values of the two adjacent points;

[0082] 4) Record the distance difference and phase difference of the four adjacent points.

[0083] At this point, the signals of the four points (except the reference point) can be represented in the form of amplitude and phase.

[0084] Further, according to the propagation characteristics of low-frequency electromagnetic waves in the ionosphere waveguide, the field strength series expression is established, that is, the total field is composed of the amplitude, phase velocity, attenuation rate and other propagation characteristic parameters of each order wave mode, thereby establishing the relationship between the measured signal and the characteristic parameters of each order wave mode. The following is the specific implementation process:

[0085] Since the propagation of low-frequency electromagnetic waves in the ionosphere waveguide 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 represented as:

[0086] (1)

[0087] In the above formula, B represents the very low frequency total field, which is the measured total field signal containing amplitude and phase information, the subscript n represents the receiving point number, and the method of obtaining amplitude and phase information has been described above. N represents the wave mode order, which is taken as 2 here, A represents the excitation amplitude, which is the amplitude of each order mode and is one of the unknown quantities, i is the imaginary unit, S represents the complex eigenvalue, which is the 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 receiving and transmitting points).

[0088] represents the wave number of electromagnetic waves in vacuum, when the working frequency is constant, is a constant, which can be calculated according to the following formula, where f is the working frequency, is a constant, which represents the dielectric constant and permeability of electromagnetic waves in vacuum, , .

[0089] (2)

[0090] Since is a constant, in order to simplify equation (1), define (m=1,2), whose real part reflects the phase velocity and imaginary part reflects the attenuation rate, equation (1) can be rewritten as

[0091] (1')

[0092] When only the first two modes are considered, the right side of equation (1') includes four unknowns, A1, A2, S1 and S2. To solve these four unknowns, at least four equations are required, that is, at least four sets of simultaneous 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 simultaneous measured data Bn and corresponding measured propagation distances dn are obtained, the unknowns A1, A2, S1 and S2 cannot be accurately solved by a finite number of algebraic operations because the equations are transcendental.

[0093] Further, the Newton-Raphson method is used to solve the unknowns in the above transcendental equations, and the core is to use the Jacobian matrix (the "derivative matrix" of a multivariate function) to construct an iterative formula. This method converges quickly, 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 is first obtained.

[0094] Because the amplitude, propagation phase velocity and attenuation rate of each order mode are closely related to the roots of the mode equation, the roots of the mode equation can be first solved according to the ionospheric IRI model (i.e., the classical exponential model) and the spherical waveguide propagation theory under the approximation of the Airy function to obtain the amplitude, propagation phase velocity and attenuation rate of each order mode, and then the initial solutions Am0, Am0, Sm0 and Sm0 of Am, Am, Sm and Sm (m represents the order of the mode) are calculated.

[0095] The specific method can be to express the electromagnetic field in the waveguide as a form of Helmholtz equation from the Maxwell equations, separate the Helmholtz equation into two ordinary differential equations, Legendre equation and Stokes equation, by using the separation of variables method, and further solve the mode equation of each order mode and the corresponding roots (i.e., the initial solutions Am0, Am0, Sm0 and Sm0) by using the ground and ionospheric boundary conditions and the ionospheric exponential model parameter values. Because a lot of theoretical research has been done by domestic and foreign scholars 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.

[0096] After obtaining the initial solutions, the norm is introduced, and the iterative formula is constructed by using the Jacobian matrix to make the four unknowns Am, Am, Sm and Sm quickly converge to the accurate values. The specific steps are as follows:

[0097] Assume that there are four sets of simultaneous data B1, B2, B3 and B4 at this time, and define

[0098] (3)

[0099] Define J as norm,

[0100] (4)

[0101] Differentiating with respect to k1, k2, A1, and A2 respectively, we get:

[0102] (5)

[0103] (6)

[0104] (7)

[0105] (8)

[0106] Thus, A1, A2, S1 and S2 can be obtained from the above iterative formulas (5) to (8), and then the amplitude and characteristic parameters (including phase velocity and decay rate) of the first and second order modes can be obtained.

[0107] (5) After obtaining the wave mode characteristics, substitute them into equation (3) to calculate p1, p2, p3, and p4 using the measured values ​​B1, B2, B3, and B4, and d1, d2, d3, and d4. Set the convergence threshold value of p1, p2, p3, and p4 to 10⁻⁵ (a value less than this threshold value meets the accuracy requirements). If the accuracy requirements are not met, use the gradient descent method to adjust the electron concentration parameters and iterate until the measured values ​​match the theoretical values. At this point, the corresponding ionospheric parameters that match the results can be output.

[0108] Figure 3 The figures show the relative phase velocities and decay rates of the first two transverse magnetic waves (TM1 and TM2) obtained by combining measured data and wave model characteristics in the ionospheric parameter inversion method of this invention. The comparison data are the relative phase velocities and decay rates of the first two transverse magnetic waves (TM1 and TM2) calculated according to the ionospheric electron concentration parameter in the US Navy's LWPC (Long-Wavelength Propagation Capability) model, using mode 1. It can be seen that the wave model characteristics obtained by combining the inverted ionospheric parameters of this invention agree well with the results obtained by the LWPC model.

[0109] The present invention also provides an ionospheric parameter inversion device, comprising:

[0110] The data acquisition module is used to acquire the measured data of the communication link passable frequency window output by the ionospheric detection device. The data acquisition module is used to acquire the measured amplitude and measured phase of the signal at each measurement point at different transmit and receive distances, and to determine the distance difference and phase difference between each adjacent measurement point, using the distance difference and phase difference as the measured propagation characteristic quantity.

[0111] The first processing module is configured to represent a very low frequency total field as a complex exponential series of no more than second order wave modes based on a ground-ionosphere waveguide propagation theory, the series taking an excitation amplitude and a complex eigenvalue of each order wave mode as unknowns; the very low frequency total field is a total electric field intensity of a measured point signal superimposed by each order wave mode in the ground-ionosphere waveguide;

[0112] The equation construction module is configured to establish a set of transcendental equations between the measured propagation characteristic quantity and the unknowns;

[0113] The second processing module is configured to iteratively solve the set of transcendental equations by using a 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 wave mode complex eigenvalue are obtained;

[0114] The 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 a theoretical amplitude and a theoretical phase, and to perform a difference operation on the measured amplitude value and the measured phase value, so that a residual is obtained;

[0115] The inversion module is configured to, if a norm of the residual 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 is not greater than the threshold, and output a current electron concentration parameter as an inversion result, so that high-precision ionospheric parameters are obtained.

[0116] 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 when actually running, and the embodiments of the present application will not be repeated here.

[0117] 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 (processor) 410, a communications interface (communications interface) 420, a memory (memory) 430 and a communications bus 440, wherein the processor 410, the communications interface 420 and the memory 430 complete mutual communication through the communications bus 440. The processor 410 can invoke a logical instruction in the memory 430 to execute an ionospheric parameter inversion method, the method including: S1, obtaining measured amplitudes and measured phases of each measured point signal at different transmission-reception distances, and determining distance differences and phase differences of each adjacent measured point, taking the distance differences and the phase differences as measured propagation characteristic quantities;

[0118] S2, based on the ground-ionosphere waveguide propagation theory, express the very low frequency total field as a complex exponential series of no 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 signal at the measuring point superimposed by each order wave mode in the ground-ionosphere waveguide;

[0119] S3, establish a trans-cendental equation set between the measured propagation characteristic quantity and the unknowns;

[0120] S4, iteratively solve the trans-cendental equation set by the Newton-Raphson method, and construct an iterative formula by the Jacobian matrix to make the excitation amplitude and complex eigenvalue converge, to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue;

[0121] 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;

[0122] S6, if the norm of the residual is greater than a preset threshold, adjust the ionospheric electron concentration parameter by the gradient descent method, repeat 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, to realize high-precision acquisition of the ionospheric parameter.

[0123] In addition, the logic instructions in the memory 430 described above can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part 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 method 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.

[0124] On the other hand, the present application also provides a computer program product, which comprises a computer program stored on a non-transitory computer readable storage medium, and the computer program comprises program instructions, when the program instructions are executed by a computer, the computer can execute the ionospheric parameter inversion method provided by the above-mentioned embodiments, and the method comprises:

[0125] S1, obtaining measured amplitudes and measured phases of signals of each measuring point at different distances of transmission and reception, and determining distance differences and phase differences of each adjacent measuring point, taking the distance differences and the phase differences as measured propagation characteristic quantities;

[0126] S2, based on a ground-ionosphere waveguide propagation theory, representing a very low frequency total field as a complex exponential series of not more than two order wave modes, the series taking 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 signals of each measuring point after superposition of each order wave mode in a ground-ionosphere waveguide;

[0127] S3, establishing a trans-cendental equation group between the measured propagation characteristic quantities and the unknown quantities;

[0128] S4, iteratively solving the trans-cendental equation group by using a Newton-Raphson method, and constructing an iterative formula by using a Jacobian matrix, so that the excitation amplitudes and the complex characteristic values converge, to obtain converged wave mode excitation amplitudes and wave mode complex characteristic values;

[0129] 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 to obtain residuals;

[0130] S6, if a norm of the residuals is greater than a preset threshold, adjusting an ionospheric electron concentration parameter by using a gradient descent method, repeating steps S4-S5 until the norm of the residuals is not greater than the threshold, and outputting a current electron concentration parameter as an inversion result, to realize high-precision acquisition of ionospheric parameters.

[0131] In another aspect, the application further provides a non-transitory computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement an ionospheric parameter inversion method provided by each of the above embodiments, and the method comprises:

[0132] S1, obtaining measured amplitudes and measured phases of signals of each measuring point at different distances of transmission and reception, and determining distance differences and phase differences of each adjacent measuring point, taking the distance differences and the phase differences as measured propagation characteristic quantities;

[0133] S2, based on a ground-ionosphere waveguide propagation theory, representing a very low frequency total field as a complex exponential series of not more than two order wave modes, the series taking 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 signals of each measuring point after superposition of each order wave mode in a ground-ionosphere waveguide;

[0134] S3, establishing a trans-cendental equation group between the measured propagation characteristic quantities and the unknown quantities;

[0135] 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;

[0136] S5, the wave mode excitation amplitude and wave mode complex eigenvalue are substituted into the complex exponential series, the theoretical amplitude and theoretical phase are calculated, and the residual error is obtained by difference operation between the measured amplitude value and the measured phase value;

[0137] 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, so as to realize high-precision acquisition of ionospheric parameters. The device embodiments described above are only schematic, wherein the units illustrated as separate components can be or can not be physically separated, and the components illustrated as units can be 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.

[0138] Through the description of the above embodiments, those skilled in the art can clearly understand that the embodiments can be realized by software and necessary general hardware platform, and of course, they can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of 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 method described in each embodiment or some parts of the embodiment.

[0139] Finally, it should be pointed out that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for some 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. An ionospheric parameter inversion method, characterized in that, The method comprises the following steps: S1, obtaining the measured amplitude and phase of the signals of each measuring point at different transmitting and receiving distances, and determining the distance difference and phase difference between adjacent measuring points, taking the distance difference and phase difference as the measured propagation characteristic quantity; 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 amplitude and 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 of the measuring point signal in the ground-ionospheric waveguide; S3, establishing a transendental equation set between the measured propagation characteristic quantity and the unknown quantity; S4, iteratively solving the transendental equation set by Newton-Raphson method, and constructing 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, substituting the wave mode excitation amplitude and wave mode complex eigenvalue into the complex exponential series to calculate the theoretical amplitude and theoretical phase, and performing difference operation on the measured amplitude value and measured phase value 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, and outputting the current electron concentration parameter as the inversion result, to realize high-precision acquisition of the ionospheric parameter.

2. The ionospheric parameter inversion method according to claim 1, wherein 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 excitation amplitude and complex eigenvalue of each order wave mode by using the ionospheric IRI index model and the spherical waveguide mode equation under Airy function approximation as initial values of the transendental equation set; constructing the iterative formula by Jacobian matrix based on the initial values and norm to make the excitation amplitude and complex eigenvalue converge to obtain the converged wave mode excitation amplitude and wave mode complex eigenvalue. The real part of the complex eigenvalue corresponds to the relative phase velocity, and the imaginary part corresponds to the spatial attenuation rate.

3. The ionospheric parameter inversion method of claim 1, wherein, 4. The ionospheric parameter inversion method according to claim 1, wherein the obtaining of the measured amplitude and phase of the signals of each measuring point at different transmitting and receiving distances comprises: arranging not less than five synchronous receiving measuring points at preset equal intervals within the target range of the same very low frequency transmitting station, and collecting the time domain signals of a preset frequency transmitted by the same transmitting station of each measuring point based on Beidou time system as a reference; performing Fourier transform on the time domain signals to obtain the measured amplitude and phase of the signals of each measuring point.

5. The ionospheric parameter inversion method according to claim 1, wherein the determination of the distance difference and phase difference between adjacent measuring points based on the measured amplitude and phase comprises: calculating the distance difference between adjacent measuring points according to the longitude and latitude of the adjacent measuring points; calculating the phase difference between adjacent measuring points according to the phase values of the adjacent measuring points.

6. The ionospheric parameter inversion method according to claim 1, wherein the measured propagation characteristic quantity only selects the first measuring point as the phase reference, and the phase difference of the remaining measuring points is calculated with respect to the reference. ​ ​ ​ ​ 7. The ionospheric parameter inversion method of claim 1, wherein, The output current electron concentration parameter as the inversion result further comprises: The electron concentration parameter obtained by inversion is substituted into the LWPC model to calculate the relative phase velocity and attenuation rate of TM1 and TM2 modes, and the converged wave mode complex eigenvalues are cross-verified, if the difference between them is less than a preset amount, the inversion result is confirmed to be valid, otherwise, return to step S1 to reacquire data.

8. An ionospheric parameter inversion apparatus, characterized by, Comprise: The measured data acquisition module is configured to acquire measured amplitudes and measured phases of signals of each measuring point at different transmitting-receiving distances, and determine distance differences and phase differences between adjacent measuring points, and take the distance differences and phase differences as measured propagation characteristics; The 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-ionosphere waveguide propagation theory, the series taking 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 superposition of each order wave mode in the ground-ionosphere waveguide; The equation construction module is configured to establish a transcendental equation set between the measured propagation characteristics and the unknown quantities; The second processing module is configured to solve the transcendental equation set by iteration using the Newton-Raphson method, and construct an iteration formula using a Jacobian matrix to make the excitation amplitudes and complex eigenvalues converge, to obtain converged wave mode excitation amplitudes and wave mode complex eigenvalues; The residual operation module is configured to substitute the wave mode excitation amplitudes and wave mode complex eigenvalues into the complex exponential series to calculate theoretical amplitudes and theoretical phases, and perform difference operation on the measured amplitude values and measured phase values to obtain residuals. The inversion module is configured to adjust the ionospheric electron concentration parameter using the gradient descent method if the norm of the residuals is greater than a preset threshold, repeat steps S4-S5 until the norm of the residuals is not greater than the threshold, output the current electron concentration parameter as the inversion result, and realize high-precision acquisition of ionospheric parameters.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the ionospheric parameter inversion method according to any one of claims 1 to 7. 10.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the ionospheric parameter inversion method according to any one of claims 1 to 7.

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