Low-frequency radio wave propagation phase statistical property prediction method and related equipment

Abstract

The invention discloses a low-frequency radio wave propagation phase statistical characteristic prediction method and related equipment, and the method comprises the steps: obtaining the random characteristic of the field intensity of radio waves propagated in a random layered waveguide model through an S-FDTD method based on the Taylor series approximation idea, constructing a constraint equation related to the amplitude and phase variance of a radio wave signal, and carrying out the prediction of the phase statistical characteristic of the low-frequency radio wave propagation. Secondly, a Taylor series approximation thought is introduced again, a plurality of sampling points which are in the same period and approach to zero are searched in a time domain waveform of an electric wave mean field, and then a nonlinear equation set is established at the same time according to a statistical result of field intensity of the sampling points to explore statistical characteristics of an electric wave propagation phase; the low-frequency radio wave propagation phase statistical characteristics are represented by using the average value and the standard deviation of the low-frequency radio wave propagation phase, the prediction of the low-frequency radio wave propagation phase statistical characteristics is realized, and finally, the phase average value and the variance of the signal under the random medium background are successfully obtained only through one-time simulation. According to the phase uncertainty measurement method, thousands of times of brute force simulation limitation of the Monte Carlo method is avoided, and the solving efficiency is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio wave propagation signal processing and calculation, and in particular relates to a method for predicting low-frequency radio wave propagation phase statistical characteristics and related equipment. Background Art

[0002] Low-frequency (30kHz-300kHz) radio waves mainly propagate in the waveguide between the earth's surface and the lower edge of the lower ionosphere, usually in two ways: ground waves propagating along the earth's surface and sky waves reflected by the ionosphere. Ground waves have the advantages of low attenuation, stable transmission phase, wide coverage and strong anti-interference ability, and have been widely used in many fields such as navigation, timing and lightning location. In fact, during the long-distance propagation of low-frequency radio waves, the amplitude of the sky wave field is much larger than that of the ground wave field. In theory, the working range of sky waves is wider than that of ground waves. However, due to the randomness of the ionosphere, it is particularly difficult to accurately predict the propagation characteristics of low-frequency sky waves, which limits the accuracy improvement of related systems that work with this sky wave mode. In recent years, the Stochastic Finite-Difference Time-Domain (S-FDTD) method based on the Taylor series approximation idea has been proposed to study the problem of radio wave propagation in random media. Compared with the FDTD method based on Monte Carlo theory, the S-FDTD method can obtain the statistical characteristics of electric and magnetic fields through only a single simulation.

[0003] In fact, most of the existing research focuses on the time-varying mean and variance of the radio wave amplitude in random media, and rarely on the statistical characteristics of the radio wave phase. So far, no method has been proposed to directly obtain the statistical characteristics of the radio wave propagation phase based on the S-FDTD algorithm of a single simulation time. Summary of the invention

[0004] The purpose of the present invention is to provide a method and related equipment for predicting the statistical characteristics of low-frequency radio wave propagation phase, so as to solve the technical problem of low efficiency caused by multiple simulations required for obtaining the statistical characteristics of low-frequency radio wave propagation phase in the prior art.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme:

[0006] A method for predicting the statistical characteristics of the phase of low-frequency radio wave propagation is proposed. A random layered waveguide model is constructed and the S-FDTD method is used to obtain the random characteristics of the field intensity of the low-frequency radio wave propagating in the random layered waveguide model.

[0007] Based on the random characteristics of the low-frequency radio wave field strength, the time of the positive zero-crossing point of a carrier cycle in the time domain waveform of the low-frequency radio wave mean field is determined as the arrival time, and the average value of the low-frequency radio wave propagation phase is obtained;

[0008] Establish the constraint equations of the amplitude and phase of the low-frequency radio wave signal, and then derive the constraint equations of the random characteristics of the low-frequency radio wave field intensity and the phase variance;

[0009] Select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase;

[0010] The average value and standard deviation of the low-frequency wave propagation phase are used to characterize the statistical characteristics of the low-frequency wave propagation phase, so as to realize the prediction of the statistical characteristics of the low-frequency wave propagation phase.

[0011] Furthermore, in the random layered waveguide model, the signal source is an electric dipole source, and a Loran-C long-wave navigation timing signal with a carrier frequency of 100 kHz is used.

[0012] Furthermore, the random characteristics of the low-frequency radio wave strength include the mean and standard deviation of the electromagnetic field strength.

[0013] Furthermore, the steps for solving the average value of the low-frequency radio wave propagation phase are:

[0014] Based on the random characteristics of low-frequency radio wave field strength, the time domain waveform of the low-frequency radio wave mean field is constructed;

[0015] The positive zero-crossing point of a carrier cycle of the low-frequency radio wave mean field time domain waveform is taken as the sampling point, and the time of the sampling point is determined as the arrival time, and the total phase of the low-frequency radio wave propagation is obtained;

[0016] Based on the relationship between the total phase of low-frequency radio wave propagation and the fluctuation of the phase of low-frequency radio wave propagation, the average value of the phase of low-frequency radio wave propagation is obtained.

[0017] Furthermore, the relationship between the total phase of the low-frequency radio wave propagation and the fluctuation of the low-frequency radio wave propagation phase is:

[0018] φ=φ 0 +Δφ

[0019] Among them, φ is the total phase of low-frequency radio wave propagation, φ 0 is the phase of the wave propagating in the air, and Δφ is the phase fluctuation caused by the change of the propagation environment;

[0020] The average value of the total phase of low-frequency radio wave propagation is obtained by the total phase of low-frequency radio wave propagation, where the average value of the low-frequency radio wave propagation phase is the average value of the total phase of low-frequency radio wave propagation and φ 0 The difference.

[0021] Furthermore, the constraint equations of the random characteristics of the low-frequency radio wave field intensity and the phase variance are:

[0022]

[0023] In the formula, represents the time domain mean value of the electric field intensity E, represents the time domain mean of the signal amplitude, σ{A} represents the time domain standard deviation of the signal amplitude, represents the mean of the phase, σ{θ} represents the standard deviation of the phase, where σ{θ}=σ{△φ}, ρ A,θ Indicates the degree of correlation between signal amplitude and phase.

[0024] Furthermore, the constraint equations for the amplitude and phase of the low-frequency radio wave signal are established based on the standard form of the dipole radiation field expression.

[0025] In a second aspect, a low-frequency radio wave propagation phase statistical characteristic prediction system is provided, comprising an acquisition module, a first calculation module, an establishment module, a second calculation module and a prediction module, wherein:

[0026] Acquisition module: used to construct a random layered waveguide model and use the S-FDTD method to obtain the random characteristics of the low-frequency radio wave field intensity propagating in the random layered waveguide model;

[0027] The first calculation module is used to determine the time of the positive zero crossing point of a carrier cycle in the low-frequency radio wave mean field time domain waveform as the arrival time based on the random characteristics of the low-frequency radio wave field strength, and obtain the average value of the low-frequency radio wave propagation phase;

[0028] Establishing module: Establishing constraint equations for amplitude and phase of low-frequency radio wave signals, and then deriving constraint equations for random characteristics of low-frequency radio wave field intensity and phase variance;

[0029] The second calculation module: select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase;

[0030] The prediction module uses the average value and standard deviation of the low-frequency radio wave propagation phase to characterize the statistical characteristics of the low-frequency radio wave propagation phase, so as to realize the prediction of the statistical characteristics of the low-frequency radio wave propagation phase.

[0031] In a third aspect, a terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0032] In a fourth aspect, a computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0033] Compared with the prior art, the present invention has the following beneficial technical effects:

[0034] The present invention provides a method for predicting the statistical characteristics of the phase of low-frequency radio wave propagation. First, the S-FDTD method based on the Taylor series approximation idea obtains the random characteristics of the radio wave field intensity propagating in the random layered waveguide model. Then, the constraint equation related to the amplitude and phase variance of the radio wave signal is constructed, and the Taylor series approximation idea is introduced again to find multiple sampling points of the same period and approaching zero in the time domain waveform of the radio wave mean field. Secondly, according to the statistical results of the field intensity of these sampling points, a nonlinear equation group is established at the same time to explore the statistical characteristics of the radio wave propagation phase. The average value and standard deviation of the low-frequency radio wave propagation phase are used to characterize the statistical characteristics of the low-frequency radio wave propagation phase, and the prediction of the statistical characteristics of the low-frequency radio wave propagation phase is realized. Finally, the phase mean and variance of the signal under the random medium background are successfully obtained through only one simulation. The phase uncertainty measurement method avoids the limitation of the Monte Carlo method of thousands of brute force simulations, and greatly improves the solution efficiency.

[0035] The method for predicting the statistical characteristics of low-frequency radio wave propagation phase of the present invention not only has beneficial technical effects in improving the performance of communication systems, enhancing radar and detection capabilities, and promoting the development of remote sensing monitoring technology, but also provides a certain theoretical basis and technical support for achieving more efficient and reliable signal transmission and processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of a method for predicting statistical characteristics of low-frequency radio wave propagation phase according to an embodiment of the present invention.

[0037] Figure 2 Schematic diagram of phase sampling points of a Loran-C one-hop skywave propagation in a random geo-ionospheric waveguide according to an embodiment of the present invention.

[0038] Figure 3 Schematic diagram of time domain waveform comparison of sky wave mean signal and standard deviation signal in an embodiment of the present invention.

[0039] Figure 4 Schematic diagram of comparison of mean results of Loran-C one-hop skywave phase obtained by different algorithms in an embodiment of the present invention.

[0040] Figure 5 1 is a comparison diagram of standard deviation results of the Loran-C one-hop skywave phase obtained by different algorithms when only the relative dielectric constant in the ionosphere is a random variable in an embodiment of the present invention.

[0041] Figure 6 3 is a comparison diagram of standard deviation results of the Loran-C one-hop skywave phase obtained by different algorithms when the relative dielectric constant and conductivity in the ionosphere are both random variables in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0043] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0044] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0046] like Figure 1 As shown, a method for predicting the statistical characteristics of low-frequency radio wave propagation phase includes the following steps:

[0047] Step 1: construct a random layered waveguide model, and use the S-FDTD method to obtain the random characteristics of the low-frequency radio wave field intensity propagating in the random layered waveguide model;

[0048] Specifically, the random characteristics of the low-frequency radio wave strength include the mean and standard deviation of the electromagnetic field strength, among which the two-dimensional cylindrical coordinates are constructed. Maxwell's equations mainly include the electromagnetic field components: E r 、E z and Three components. Random media only consider two random parameters: conductivity σr and relative dielectric constant ε r . The relative magnetic permeability μ is not considered r The S-FDTD method can be used to obtain the mean and standard deviation of the electromagnetic field strength. and The iterative formulas are shown in formula (1), formula (2) and formula (3) respectively:

[0049]

[0050] in

[0051]

[0052] in

[0053]

[0054] in

[0055] Based on the S-FDTD method, the standard deviation of the electric and magnetic fields σ{E r}, σ{E z}and The derivation results are shown in formula (4), formula (5) and formula (6) respectively:

[0056]

[0057] in

[0058]

[0059] in

[0060]

[0061] in

[0062] Where n represents the time step, △t represents the time step. △z, △r represent the space step. μ 0 is the magnetic permeability of free space. r is the relative magnetic permeability. and Represent the standard deviation of relative permittivity and conductivity, respectively. r} and σ{σ r} represent the standard deviation of relative permittivity and conductivity respectively. ρ represents the correlation between the electric field and random parameters.

[0063] Step 2: Based on the random characteristics of the low-frequency radio wave field strength, the time of the positive zero-crossing point of a carrier cycle in the low-frequency radio wave mean field time domain waveform is determined as the arrival time, and the average value of the low-frequency radio wave propagation phase is obtained;

[0064] Specifically, in order to observe the average value of the low-frequency radio wave propagation phase, the time when the positive zero crossing point of a certain carrier cycle of the low-frequency radio wave average field signal is determined as the arrival time. The total phase φ of the low-frequency radio wave propagation can be expressed as:

[0065] φ=φ 0 +Δφ (7)

[0066] where φ 0 is the phase of the wave propagating in the air. Assuming that the entire propagation path is air, L is the total propagation length of the radio wave, n s is the atmospheric refractive index near the ground surface on the propagation path. c is the speed of light in a vacuum. △φ represents the phase fluctuation caused by the change in the propagation environment. For a given observation point, φ can be calculated from the time when the wave reaches the sampling point T 0 Calculated, this moment depends on the location of the sampling point. Extract T from the time domain waveform of the mean field 0 The mean of φ 0 The average value of the phase of low-frequency radio wave propagation It can be obtained by solving equation (7);

[0067] Specifically, the average value of the total phase of low-frequency radio wave propagation is obtained by the total phase of low-frequency radio wave propagation, wherein the average value of the low-frequency radio wave propagation phase is the average value of the total phase of low-frequency radio wave propagation and φ 0 The difference.

[0068] Step 3: Establish the constraint equations of the amplitude and phase of the low-frequency radio wave signal, and then derive the constraint equations of the random characteristics of the low-frequency radio wave field strength and the phase variance;

[0069] According to the standard form of the dipole radiation field expression, the constraint equations of the amplitude and phase of the low-frequency radio wave signal are established, and the expression of the low-frequency radio wave field strength relationship is shown in (8):

[0070] E∝Asin(ωt-θ) (8)

[0071] In the formula, E represents the electric field strength of the low-frequency radio wave, A is the signal amplitude, and θ is the phase. According to the first-order Taylor series expansion method, ignoring the high-order terms and introducing the covariance equation, the variance approximate expression of the propagation electric field strength of the low-frequency radio wave is obtained as shown in (9).

[0072]

[0073] In the formula, xi and x j represents the random variable in the function, and represents the respective mean of the random variables. Cov{x i ,x j} represents x i and x j There are two random variables A and θ in formula (8), and formula (10) can be simplified as shown below.

[0074]

[0075] In the formula, represents the time domain mean value of the electric field intensity E, represents the time domain mean of the signal amplitude, σ{A} represents the time domain standard deviation of the signal amplitude, represents the mean of the phase, and σ{θ} represents the standard deviation of the phase. Here, σ{θ}=σ{△φ}, ρ A,θ Indicates the degree of correlation between signal amplitude and phase.

[0076] Step 4: Select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase;

[0077] For any given moment (given ), the electric field component and σ 2 {E} can be calculated by the S-FDTD method in step 1. The quantities that need to be solved are: σ{A}, σ{θ} and ρ A,θ Here, the Taylor series expansion method is introduced to find multiple sampling points with the same period and close to zero in the time domain waveform of the average field of the radio wave. The above unknown quantities can be obtained by establishing The relevant statistical results of these sampling points are substituted into (10) to establish the nonlinear equation group (11). By solving the nonlinear equations, the standard deviation σ{θ} of the low-frequency radio wave propagation phase can be obtained.

[0078]

[0079] In one embodiment provided by the present invention, the specific implementation process of the present invention is described by taking the propagation of a Loran-C one-hop skywave in a random earth-ionosphere waveguide model as an example. The present invention is further described in detail below with reference to the accompanying drawings:

[0080] The following steps are involved:

[0081] Step 1:

[0082] See also Figure 2 , based on the S-FDTD method, an isotropic random ionosphere-air layer-stratum stratification model, i.e., a schematic diagram of a random stratified waveguide model, is constructed. This model is a uniform stratification model, in which the medium parameters of the air layer and the stratum are fixed and uniform electrical parameters. The medium parameters of the ionosphere have random properties. The upper and right boundaries of the model are perfect matching layer boundaries. The lower interface of the ionosphere is 60km above the ground, and the maximum propagation distance is 400km. The schematic diagram of the model is shown in Figure 4 The signal source is an electric dipole source, using the Loran-C long-wave navigation timing signal with a carrier frequency of 100kHz. The transmitter is located on the ground, which is regular and flat. The parameter of the air layer is set to ε r =1,σ r =0S / m. The formation parameter is set to ε r =13,σ r =3×10 -3 S / m. The average values ​​of the relative permittivity and conductivity of the ionosphere are set to Its relative dielectric constant ε r and conductivity σ r Standard Deviation and Among them, Δ 1 and Δ 2 are the relative changes of relative permittivity and conductivity, respectively.

[0083] According to the Taylor series approximation method, it is assumed that the solution of the random variable function has the characteristics of Taylor series expansion. Define the function g[X i ], g is a function of multiple random variables, X i is a random variable.

[0084] g[X i ]=g(x 1 ,x 2 ,x 2 ,...,x n ) (12)

[0085] For the mean approximation, the function g[X i ] Expand to get the mean value of the random variable Then get the overall average The approximate expression of the mean of the Taylor series approximation method is:

[0086]

[0087] According to the first-order Taylor series expansion method, ignoring the higher-order terms, the variance approximate expression of the Taylor series approximation method is obtained as shown in (14).

[0088]

[0089] Among them, x i and x j represents the random variable in the function, and represents the respective mean of the random variables. Cov{x i ,x j} represents x i and x j The covariance of .

[0090] In 2D cylindrical coordinates Taking TM wave propagation as an example, Maxwell's equations mainly include electromagnetic field components: E r 、E z and Three components. Random media only consider two random parameters: conductivity σ r and relative dielectric constant ε r . The relative magnetic permeability μ is not considered r In the S-FDTD method, the average value of the electromagnetic field is calculated by taking the average values ​​of the parameters in the medium. The iterative formula for the average value of the electromagnetic field in the S-FDTD method is the same as that in the traditional FDTD method. The average value of the electric and magnetic fields and The iterative formulas are shown in formula (1), formula (2) and formula (3) respectively:

[0091]

[0092] in

[0093]

[0094] in

[0095]

[0096] in

[0097] The S-FDTD method based on Taylor series expansion is used to derive the r 、E z and The standard deviation of the three components of the electric and magnetic fields σ{E r}, σ{E z}and The iterative formulas are shown in equations (4), (5) and (6) respectively.

[0098]

[0099] in

[0100]

[0101] in

[0102]

[0103] in

[0104] Where n represents the time step, △t represents the time step. △z, △r represent the space step. μ 0 is the magnetic permeability of free space. r is the relative magnetic permeability. and Represent the standard deviation of relative permittivity and conductivity, respectively. r} and σ{σ r} represent the standard deviation of relative permittivity and conductivity respectively. ρ represents the correlation between the electric field and random parameters.

[0105] Step 2:

[0106] Referring to the acquisition process of the ground wave propagation phase in the Loran-C system, the propagation phase of the low-frequency one-hop sky wave average field is obtained. In the traditional Loran-C signal, the time of the positive zero crossing point of the third carrier cycle of the Loran-C average field signal is determined as the arrival time, see Figure 2 This sampling point is selected to observe the average and standard deviation of the single-hop skywave propagation phase. The total phase φ of one-hop skywave propagation at the transmitting and receiving points can be expressed as:

[0107] φ=φ 0 +Δφ (7)

[0108] where φ 0 is the phase of the wave propagating in the air. Assuming that the entire propagation path is air, L is the total propagation length of a skywave ray jump, n s is the atmospheric refractive index near the ground surface on the propagation path, n s = 1. c is the speed of light in vacuum. When the conductivity and relative permittivity in the random medium are taken at their respective mean values, the mean sky wave phase can be obtained. For a given observation point, φ can be calculated from the time when the wave reaches the sampling point T 0 Calculated, this moment depends on the location of the sampling point, such as Figure 2Therefore, T can be extracted from the time domain waveform of the mean field. 0 The mean of φ 0 The mean value of the sky wave propagation phase △φ of the Loran-C signal It can be obtained by solving equation (7). △φ represents the phase deviation caused by the change of the propagation environment, and △φ can be further expressed as shown in equation (15).

[0109] Δφ=ωt w (15)

[0110] ω is the angular frequency, ω = 2 × 10 5 π.t w Indicates delay fluctuation.

[0111] Step 3:

[0112] According to the standard form of the dipole radiation field expression, the electric field strength can be expressed in a form that includes amplitude and phase. Although the Loran-C signal is a modulated Gaussian pulse, the single-hop skywave field strength relationship at the receiving point within a given period is expressed as shown in (8).

[0113] E∝Asin(ωt-θ) (8)

[0114] In the formula, E represents the skywave electric field strength, A is the signal amplitude, and θ is the phase. There are two random variables A and θ in the formula. According to the approximate formula (3) of the Taylor series expansion variance in step 1, the approximate expression of the variance of the Roland-C one-hop skywave field strength is shown in formula (16):

[0115]

[0116] represents the time domain mean value of the electric field intensity E; represents the time domain mean of the signal amplitude; σ{A} represents the time domain standard deviation of the signal amplitude; represents the mean of the phase, and σ{θ} represents the standard deviation of the phase. Here, σ{θ}=σ{Δφ}, ρ A,θ Indicates the correlation between signal amplitude and phase. Substituting equation (8) into equation (16), we can obtain the variance σ of the sky wave intensity. 2 The approximate expression of {E} is:

[0117]

[0118] Step 4:

[0119] For any given moment (given ), and σ 2{E} can be calculated by the S-FDTD method in step 1. The quantities that need to be solved are: σ{A}, σ{θ}, ρ A，θ The Taylor series expansion method is introduced to find multiple sampling points with the same period and close to zero in the time domain waveform of the sky wave average field. The above unknown quantities can be obtained by establishing and σ{E} electric field equations to solve. For ease of explanation, Figure 3 The time domain normalized waveform comparison of the mean and standard deviation of the sky wave signal is shown in Figure 1. The time domain waveform comparison of the mean and standard deviation of the sky wave signal under random media background is shown in Figure 1. Figure 3 As shown in Figure 1, the blue solid line represents the time domain waveform of the sky wave signal average value. The orange dotted line represents the time domain waveform of the sky wave signal standard deviation. In the time domain waveform of the sky wave signal average value, four sampling points are selected in the same carrier cycle. 1 , O 2 , O 3 and O 4 . Let the corresponding time t 1 , t 2 , t 3 With t 4 In order to meet the approximate requirement of (14), the sampling point selection principle is as follows: Substituting the relevant statistical parameters of these sampling points into equation (10), the nonlinear equation group (11) is established. By solving the nonlinear equation, the standard deviation σ{θ} of the sky wave phase can be obtained.

[0120]

[0121] See also Figure 4 , and the results of the variation of the low-frequency sky wave phase mean with the distance from the receiving point are given. With the wave jump theory as a reference, the number of simulations using the MC idea is 5000. For the ionosphere-ground waveguide model, when the distance between the transmitting source and the receiving point is greater than 10km, the mean results of one-hop sky waves obtained by the two algorithms are well consistent.

[0122] See also Figure 5 , when the relative dielectric constant of the ionospheric electrical parameters in the layered waveguide model is a random variable (△ 1 =0.2,△ 2=0), and the results of the phase standard deviation changing with the distance from the receiving point are given. With the wave-jump theory as a reference, the number of simulations using the MC idea is 5000. The correlation coefficients of the S-FDTD algorithm are 1, 0.85 and 0.75 respectively. The standard deviation of the one-hop skywave phase when the correlation coefficient of the S-FDTD algorithm is 0.85 is compared with the wave-jump theory to obtain good consistency. With the increase of the receiving distance, the standard deviation of the one-hop skywave phase shows a trend of first increasing and then decreasing. When the receiving distance is about 120km, the standard deviation increases to a maximum point, and then gradually decreases, thus reaching a convergence state.

[0123] See also Figure 6 , when the relative permittivity and conductivity of the ionospheric electrical parameters in the layered waveguide model are both random variables (△ 1 =0.2,△ 2 =0.2), the results of the phase standard deviation changing with the distance from the receiving point are given. With the wave jump theory as a reference, the number of simulations using the MC idea is 5000. The correlation coefficients of the S-FDTD algorithm are 1, 0.85 and 0.75 respectively. When the correlation coefficient of the S-FDTD algorithm is 0.75, the standard deviation result of the one-hop skywave phase is compared with the wave jump theory to obtain good consistency. With the increase of the receiving distance, the standard deviation result of the one-hop skywave phase shows a trend of first increasing and then decreasing. When the receiving distance is about 125km, the standard deviation increases to a maximum point, and then gradually decreases, thus reaching a convergence state.

[0124] Depend on Figures 5 and 6 By comparison, it can be seen that the more random variables there are in the ionosphere, the larger the standard deviation of the phase will be, that is, the greater the uncertainty of the propagation phase will be.

[0125] The present invention also provides a low-frequency radio wave propagation phase statistical characteristic prediction system, comprising an acquisition module, a first calculation module, a building module, a second calculation module and a prediction module, wherein:

[0126] Acquisition module: used to construct a random layered waveguide model and use the S-FDTD method to obtain the random characteristics of the low-frequency radio wave field intensity propagating in the random layered waveguide model;

[0127] The first calculation module is used to determine the time of the positive zero crossing point of a carrier cycle in the low-frequency radio wave mean field time domain waveform as the arrival time based on the random characteristics of the low-frequency radio wave field strength, and obtain the average value of the low-frequency radio wave propagation phase;

[0128] Establishing module: Establishing constraint equations for amplitude and phase of low-frequency radio wave signals, and then deriving constraint equations for random characteristics of low-frequency radio wave field intensity and phase variance;

[0129] The second calculation module: select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase;

[0130] The prediction module uses the average value and standard deviation of the low-frequency radio wave propagation phase to characterize the statistical characteristics of the low-frequency radio wave propagation phase, so as to realize the prediction of the statistical characteristics of the low-frequency radio wave propagation phase.

[0131] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0132] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0133] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0134] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1The steps for the functions specified in one or more boxes.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit its protection scope. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that after reading the present invention, those skilled in the art can still make various changes, modifications or equivalent substitutions to the specific implementation methods of the invention, but these changes, modifications or equivalent substitutions are all within the protection scope of the pending claims of the invention.

Claims

1. A method for predicting the statistical characteristics of low-frequency radio wave propagation phase, characterized in that: The following steps are involved: A random layered waveguide model is constructed, and the S-FDTD method is used to obtain the random characteristics of the low-frequency electric wave field intensity propagating in the random layered waveguide model; Based on the random characteristics of the low-frequency radio wave field strength, the time of the positive zero-crossing point of a carrier cycle in the time domain waveform of the low-frequency radio wave mean field is determined as the arrival time, and the average value of the low-frequency radio wave propagation phase is obtained; Establish the constraint equations of the amplitude and phase of the low-frequency radio wave signal, and then derive the constraint equations of the random characteristics of the low-frequency radio wave field intensity and the phase variance; Select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase; The average value and standard deviation of the low-frequency wave propagation phase are used to characterize the statistical characteristics of the low-frequency wave propagation phase, so as to realize the prediction of the statistical characteristics of the low-frequency wave propagation phase.

2. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 1, characterized in that: In the random layered waveguide model, the signal source is an electric dipole source, and a Loran-C long-wave navigation timing signal with a carrier frequency of 100 kHz is used.

3. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 1, characterized in that: The random characteristics of the low-frequency radio wave field strength include the mean and standard deviation of the electromagnetic field strength.

4. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 1, characterized in that: The steps for solving the average value of the low-frequency radio wave propagation phase are: Based on the random characteristics of low-frequency radio wave field strength, the time domain waveform of the low-frequency radio wave mean field is constructed; The positive zero-crossing point of a carrier cycle of the low-frequency radio wave mean field time domain waveform is taken as the sampling point, and the time of the sampling point is determined as the arrival time, and the total phase of the low-frequency radio wave propagation is obtained; Based on the relationship between the total phase of the low-frequency radio wave propagation and the fluctuation of the phase of the low-frequency radio wave propagation, the average value of the phase of the low-frequency radio wave propagation is obtained.

5. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 4, characterized in that: The relationship between the total phase of low-frequency radio wave propagation and the fluctuation of low-frequency radio wave propagation phase is: φ=φ0+Δφ Among them, φ is the total phase of low-frequency radio wave propagation, φ0 is the phase of the wave propagating in the air, and Δφ is the phase fluctuation caused by the change of the propagation environment; The average value of the total phase of low-frequency radio wave propagation is obtained through the total phase of low-frequency radio wave propagation, wherein the average value of the low-frequency radio wave propagation phase is the difference between the average value of the total phase of low-frequency radio wave propagation and φ0.

6. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 1, characterized in that: The constraint equations of the random characteristics of the low-frequency radio wave field intensity and the phase variance are: In the formula, represents the time domain mean value of the electric field intensity E, represents the time domain mean of the signal amplitude, σ{A} represents the time domain standard deviation of the signal amplitude, represents the mean of the phase, σ{θ} represents the standard deviation of the phase, where σ{θ}=σ{△φ}, ρ A,θ Indicates the degree of correlation between signal amplitude and phase.

7. A method for predicting low-frequency radio wave propagation phase statistical characteristics according to claim 1, characterized in that: The constraint equations for the amplitude and phase of the low-frequency radio wave signal are established based on the standard form of the dipole radiation field expression.

8. A system for predicting the statistical characteristics of low-frequency radio wave propagation phase, characterized in that: It includes an acquisition module, a first calculation module, a building module, a second calculation module and a prediction module, wherein: Acquisition module: used to construct a random layered waveguide model and use the S-FDTD method to obtain the random characteristics of the low-frequency radio wave field intensity propagating in the random layered waveguide model; The first calculation module is used to determine the time of the positive zero crossing point of a carrier cycle in the low-frequency radio wave mean field time domain waveform as the arrival time based on the random characteristics of the low-frequency radio wave field strength, and obtain the average value of the low-frequency radio wave propagation phase; Establishing module: Establishing constraint equations for amplitude and phase of low-frequency radio wave signals, and then deriving constraint equations for random characteristics of low-frequency radio wave field intensity and phase variance; The second calculation module: select multiple sampling points of the same period and close to zero in the time domain waveform of the low-frequency radio wave mean field, establish a nonlinear equation group based on the random characteristics of the low-frequency radio wave field strength and the constraint equation of the random characteristics of the low-frequency radio wave field strength and the phase variance, and obtain the standard deviation of the low-frequency radio wave propagation phase; The prediction module uses the average value and standard deviation of the low-frequency radio wave propagation phase to characterize the statistical characteristics of the low-frequency radio wave propagation phase, so as to realize the prediction of the statistical characteristics of the low-frequency radio wave propagation phase.

9. A terminal 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, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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