Roran-C system ground wave propagation ASF statistical property prediction method and related equipment

Abstract

The invention discloses a Loran-C system ground wave propagation ASF statistical property prediction method and related equipment, and the method comprises the steps: firstly obtaining the mean value and standard deviation of the electric field intensity in a random stratum-atmosphere waveguide environment based on a PCE-FDTD method, and on this basis, further positioning the position of a forward zero crossing point in a specific carrier period of a mean value time domain signal; therefore, the mean value of the ground wave propagation ASF of the Loran-C system is accurately calculated. Then, a linear approximation method is introduced, two sampling moments are selected at adjacent positions of mean value signals in the same period, and the propagation standard deviation of the ground wave propagation ASF signals of the Loran-C system on the flat terrain is rapidly obtained; finally, according to the method, the ASF mean value and the standard deviation of the Loran-C signal under the random medium background can be successfully obtained only through single simulation, and the solving efficiency is remarkably improved. The research provides a valuable insight for improving the accuracy of a PNT system and enhancing the stability and reliability of a communication system.

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 the statistical characteristics of ground wave propagation ASF of a Loran-C system and related equipment. Background Art

[0002] The Loran-C system uses 100 kHz signals for information transmission, and its main propagation path is along the boundary between the earth's surface (covering land and ocean) and the atmosphere. Compared with other frequency bands, the Loran-C system signal has a longer wavelength, excellent diffraction ability, and relatively stable propagation loss and transmission characteristics. These characteristics make it widely used in long-range precision navigation, precision timing, and frequency calibration. In the actual operation of the Loran-C system, the signal needs to traverse complex and changing terrain and weather conditions. In this context, the Additional Secondary Phase Factor (ASF) becomes a key factor affecting the accuracy of path delay. If the influence of ASF is ignored, serious errors of up to several kilometers may be introduced. It is worth noting that the atmospheric and geological conditions are highly complex and dynamic, including but not limited to periodic day and night alternations, seasonal climate changes, rapidly changing weather conditions, uneven vegetation coverage, and diverse soil types and geological structures. These complex and changeable environmental factors may cause significant fluctuations in the atmospheric refractive index and soil electrical properties in time and space, which in turn may induce complex refraction and scattering effects during ground wave propagation, ultimately leading to random fluctuations in time delay.

[0003] In response to the challenges brought by ASF, the traditional Loran-C system has made significant progress in ASF error correction and prediction technology. Specifically, starting from the ground and atmosphere dimensions, researchers have extensively and deeply studied the specific impact mechanisms of propagation range, surface topography changes, geoelectric parameters, and spatial non-uniform distribution of atmospheric refractive index on ASF changes with the help of numerical simulation and experimental observation methods. Although many achievements have been made in this field, research on rapid prediction methods for the statistical characteristics of ASF of Loran-C signals is still relatively scarce and needs further exploration. . 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 ground wave propagation ASF in a Loran-C system, so as to solve the technical problem of low efficiency caused by multiple simulations required for obtaining the statistical characteristics of radio wave propagation delay in the prior art.

[0005] In order to achieve the above object, the present invention adopts the following technical scheme: A method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system, comprising the following steps: A random stratum-atmosphere layered waveguide model is constructed, and the PCE-FDTD method is used to obtain the mean and standard deviation of the electric wave field strength at each moment of ground wave propagation in the random stratum-atmosphere layered waveguide model. The ground wave mean field time domain waveform is obtained according to the average value of the electric field strength, and the position of the positive zero crossing point is located in a specific carrier cycle of the ground wave mean field time domain waveform, and the average value of the ground wave propagation ASF of the Loran-C system is obtained; Based on the mean and standard deviation of the electric field intensity, two adjacent sampling moments are selected in the same carrier cycle of the ground wave mean field time domain waveform, and the standard deviation of the ground wave propagation ASF of the Loran-C system is obtained according to the linear approximation method. The average value and standard deviation of ground wave propagation ASF are used to characterize the statistical characteristics of ground wave propagation ASF of Loran-C system, so as to predict the statistical characteristics of ground wave propagation ASF of Loran-C system.

[0006] Furthermore, the random stratum-atmosphere layered waveguide model is a uniformly layered smooth flat ground waveguide model, which is divided into an air layer and a stratum from top to bottom. 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.

[0007] Furthermore, the steps for solving the mean value of the ground wave propagation ASF of the Loran-C system are: The dielectric constant and conductivity of regular and flat strata are regarded as random variables. Based on the PCE-FDTD method, the mean equations of the three field components of TM waves in the two-dimensional cylindrical coordinate system can be obtained, and the time domain waveform of the mean field of ground waves can be constructed. The positive zero-crossing point of a carrier cycle of the ground 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 of the ground wave at the receiving position, and the average total delay of ground wave propagation is obtained; Based on the relationship between the total ground wave propagation delay of Loran-C and the additional secondary delay ASF of ground wave propagation, the average value of the ground wave propagation ASF of the Loran-C system is obtained.

[0008] Furthermore, the relationship between the total ground wave propagation delay and the additional secondary delay is:

[0009] In the formula, It is the total delay of the ground wave from the transmitting source to the receiving position, PF is the "basic delay", SF is the delay caused by assuming that the actual path is seawater, and ASF is the additional secondary delay. is the reference moment in the current source applied to the antenna corresponding to the extracted carrier cycle moment, is the initial phase difference between the excitation current and the radiation field signal; The mean of the additional quadratic delay is:

[0010] In the formula, represents the mean value of the additional quadratic delay, Represents the average value of the total ground wave propagation delay.

[0011] Furthermore, the sampling moments of the two adjacent positions are determined by a PCE-FDTD method.

[0012] Furthermore, the conditions for determining the sampling times of the two adjacent positions are: One of the sampling moments is the positive zero-crossing moment, and the mean value of the radio wave field strength is 0: The mean value of the electric wave field strength at another sampling moment is the same as the standard deviation of the electric wave field strength at the positive zero crossing moment.

[0013] Furthermore, the standard deviation of the additional quadratic delay of ground wave propagation is the difference between two sampling moments.

[0014] In a second aspect, a Loran-C system ground wave propagation ASF statistical characteristics prediction system is provided, including an acquisition module, an ASF mean calculation module, an ASF standard deviation calculation module and a characterization prediction module, wherein: Acquisition module: used to construct a random stratum-atmosphere layered waveguide model, and use the PCE-FDTD method to obtain the mean and standard deviation of the electric wave field strength at each moment during the propagation of ground waves in the random stratum-atmosphere layered waveguide model; ASF mean value calculation module: used to obtain the ground wave mean field time domain waveform according to the mean value of the electric field strength, locate the position of the positive zero crossing point in a specific carrier cycle of the ground wave mean field time domain waveform, and obtain the mean value of the ground wave propagation ASF of the Loran-C system; ASF standard deviation calculation module: It is used to select two adjacent sampling moments in the same carrier cycle of the ground wave mean field time domain waveform based on the mean value and standard deviation of the electric field strength, and obtain the standard deviation of the ground wave propagation ASF of the Loran-C system according to the linear approximation method; The prediction module is used to characterize the statistical characteristics of the ground wave propagation ASF of the Loran-C system by using the average value and standard deviation of the ground wave propagation ASF, so as to realize the prediction of the statistical characteristics of the ground wave propagation ASF of the Loran-C system.

[0015] 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.

[0016] 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.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention discloses a method for predicting the statistical characteristics of ground wave propagation ASF of a Roland-C system. First, based on the PCE-FDTD method, the mean and standard deviation of the electric field strength in a random stratum-atmosphere waveguide environment are simulated and quantified with high precision. On this basis, by accurately locating the positive zero-crossing position in a specific carrier period of the mean time domain signal, the present invention can accurately calculate the ASF mean of ground wave propagation of the Roland-C system. This process not only reflects a deep understanding of the ground wave propagation characteristics of the Roland-C system, but also provides key parameters for subsequent standard deviation analysis. Next, a linear algebra method is introduced to quickly analyze the standard deviation of the ground wave propagation ASF signal of the Roland-C system on flat terrain by selecting two sampling times at adjacent positions of the mean signal of the same period. This step not only significantly improves the analysis efficiency, but also ensures the accuracy and practicality of the results. The technical effect of the present invention is very significant. Compared with the traditional statistical simulation method, the present invention can successfully obtain the ASF mean and standard deviation of the Roland-C signal under the background of random media through only one simulation process. This breakthrough not only greatly improves the solution efficiency and reduces the computational cost, but also provides a new perspective and method for studying the statistical characteristics of the ASF of the Roland-C system.

[0018] From the application level, the present invention is of great significance in improving navigation and positioning accuracy, optimizing system performance, promoting the research and development of related technologies, and promoting the application and development of integrated navigation systems. By deeply studying the statistical characteristics of ground wave propagation ASF in the Loran-C system, the delay error can be predicted and corrected more accurately, thereby improving the navigation and positioning accuracy of the Loran-C system, and providing strong support for the optimization design and performance improvement of the integrated navigation system. This will help promote the widespread application and development of integrated navigation systems in the fields of navigation, aviation, aerospace, etc.

[0019] Preferably, the step of solving the mean value of the ground wave propagation ASF of the Loran-C system involves advanced technologies such as polynomial chaos expansion and time domain finite difference, which promotes the development of electromagnetic wave propagation and navigation positioning technology. By constructing the time domain waveform of the ground wave mean field and selecting the positive zero-crossing point of the carrier cycle as the sampling point, the process of determining the arrival time of the ground wave can be simplified. This method avoids complex waveform analysis and processing and improves calculation efficiency.

[0020] Preferably, in the process of solving the ASF standard deviation, one sampling moment is the positive zero-crossing moment, the mean of the radio wave field strength is 0, and the mean of the radio wave field strength at another sampling moment and the standard deviation of the radio wave field strength at the positive zero-crossing moment are used as the determination conditions of the two sampling moments, thereby enhancing the data correlation. At the same time, during the sampling process, only these two specific moments need to be paid attention to, without the need for complex analysis or processing of the entire waveform, thereby optimizing the data processing flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flow chart of a method for predicting the statistical characteristics of ground wave propagation ASF in a Loran-C system according to an embodiment of the present invention; Figure 2 Schematic diagram of a PCE-FDTD prediction model for Loran-C ground wave propagation in a random stratum-atmosphere waveguide according to an embodiment of the present invention; Figure 3 Schematic diagram of time domain waveform comparison of Loran-C ground wave mean signal and standard deviation signal in an embodiment of the present invention; Figure 4 It is a schematic diagram of comparison results of mean values ​​of statistical results of Loran-C ground wave propagation ASF under different random electrical parameter conditions in an embodiment of the present invention; Figure 5 Schematic diagram of comparison of standard deviations of statistical results of Loran-C ground wave propagation ASF under different random electrical parameter conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] 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.

[0023] 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.

[0024] 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.

[0025] Glossary: PCE-FDTD method: stochastic finite-difference time-domain method based on polynomial chaotic expansion.

[0026] TM wave: transverse magnetic wave.

[0027] ASF: Additional Secondary Delay.

[0028] The present invention is further described in detail below in conjunction with the accompanying drawings: like Figure 1 As shown, a method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system comprises the following steps: Step 1: construct a random stratum-atmosphere layered waveguide model, and use the PCE-FDTD method to obtain the mean and standard deviation of the electric wave field strength at each moment when the ground wave propagates in the random stratum-atmosphere layered waveguide model; Specifically, the random stratum-atmosphere layered waveguide model is a uniformly layered smooth flat ground waveguide model, which is divided into an air layer (free space) and a stratum from top to bottom. The signal source is an electric dipole source, and a Loran-C long-wave navigation timing signal with a carrier frequency of 100kHz is used: The dielectric constant and conductivity of the medium are considered as random variables in the model. Assume that the dielectric constant of the formation is and conductivity are independent random parameters that follow a Gaussian distribution, and their means are , , and the standard deviations are , Strata and The standard deviation of is shown in equations (1) and (2).

[0029] (1) (2) in and are the relative changes of the random variables relative permittivity and conductivity. and The uncertainty can be expressed as the uncertainty about the random variable and The mean and standard deviation of the TM wave electromagnetic field are derived in two-dimensional cylindrical coordinates. Taking the field as an example, the mean and standard deviation are shown in equations (3) and (4).

[0030] (3) (4) in is a random variable , The ath expansion term of the orthogonal polynomial basis function of the chaotic expansion determined by the distribution function. yes Corresponds to The coefficient equation of the expansion order is, P is the number of expanded items.

[0031] Step 2: According to the average value of the electric field intensity, the ground wave mean field time domain waveform is obtained, and the position of the positive zero crossing point is located in a specific carrier cycle of the ground wave mean field time domain waveform to obtain the average value of the ground wave propagation ASF of the Loran-C system; Specifically, based on the statistical characteristics of the ground wave electric field strength, the time of the positive zero crossing point of a carrier cycle in the time domain waveform of the electric wave mean field is determined as the arrival time, and the average value of the total ground wave propagation delay is obtained: The steps to solve the mean value of the ASF of the Loran-C system ground wave propagation are: The dielectric constant and conductivity of regular and flat strata are regarded as random variables. Based on the PCE-FDTD method, the mean equations of the three field components of TM waves in the two-dimensional cylindrical coordinate system can be obtained, and the time domain waveform of the mean field of ground waves can be constructed. The positive zero-crossing point of a carrier cycle of the ground 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 of the ground wave at the receiving position, and the average total delay of ground wave propagation is obtained; Based on the relationship between the total delay of Loran-C ground wave propagation and the additional secondary delay ASF of ground wave propagation, the average value of the ground wave propagation ASF of the Loran-C system is obtained, where the average value of the low-frequency radio wave propagation phase is the average value of the total phase of the low-frequency radio wave propagation and The difference.

[0032] In the study of ground wave propagation delay, for a certain receiving position, the positive zero-crossing moment of the vertical electric field waveform in a certain time domain steady-state period in the mean signal is extracted and accurately measured as the average arrival time of the signal, recorded as .

[0033] According to the relationship between the total ground wave propagation delay and the additional secondary delay ASF in Loran-C, the mean value of the Loran-C ground wave propagation ASF is obtained; Specifically, the relationship between the total delay of Loran-C ground wave propagation and the additional secondary delay ASF of ground wave propagation is shown in formula (5).

[0034] (5) In the formula, It is the total delay of the ground wave from the transmitting source to the receiving position. PF is the basic delay. When it is assumed that the entire propagation path is completely in the air medium, the time taken for the electromagnetic wave signal to propagate from the transmitting antenna to the receiving antenna. SF represents the delay generated when the actual path is assumed to be seawater. ASF reflects the additional delay change caused by the long-wave ground wave signal under the actual land propagation path compared to when the entire path is seawater. is the reference moment in the current source applied to the antenna corresponding to the extracted carrier cycle moment, It is the initial phase difference between the excitation current and the radiation field signal.

[0035] Specifically, the average total delay of radio wave propagation is obtained by the time when the radio wave in the radio wave time domain waveform arrives at the receiving location. As shown in formula (6).

[0036] (6) In the formula, represents the mean value of the additional quadratic delay, Represents the average value of the total ground wave propagation delay.

[0037] Step 3: Based on the mean and standard deviation of the electric field strength, two adjacent sampling moments are selected in the same carrier cycle of the ground wave mean field time domain waveform, and the standard deviation of the ground wave propagation ASF of the Loran-C system is obtained according to the linear approximation method; Specifically, the sampling point selection principle in the radio wave time domain waveform mean field signal is: Two sampling moments are selected at adjacent positions of a carrier cycle in the mean field of the radio wave time domain waveform obtained by the PCE-FDTD method and are recorded as and .in, It is the moment when the carrier cycle crosses zero in the positive direction. The mean value of the electric field intensity corresponding to the time The standard deviation of the electric field strength corresponding to the sampling time is the same. and The principles of satisfaction are shown in equations (7) and (8) respectively.

[0038] (7) (8) In the formula, yes The mean value of the electric field strength at time , yes The mean value of the electric field strength at time , yes The standard deviation of the electric field strength at that moment. In the formula, yes The mean value of the electric field strength at time , yes The mean value of the electric field strength at time , yes The standard deviation of the electric field strength at that moment.

[0039] Specifically, due to the sampling time and At adjacent positions in the same carrier cycle, the linear approximation method is used here to obtain the standard deviation of the ground wave propagation ASF of the Loran-C system As shown in formula (9).

[0040] (9) 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: The following steps are involved: Step 1: See also Figure 2 , in two-dimensional cylindrical coordinates Taking the propagation of TM waves as an example, a uniformly layered smooth flat ground waveguide model is established, which is divided into air layer (free space) and ground layer from top to bottom. The upper and right boundaries of the model are perfectly matched layer (PML) boundaries. The left side of the model (z axis) is set as an axisymmetric boundary. The calculation area is in the propagation direction ( direction) takes 100km, height direction ( The distance (direction) is 5.625km, and the layer thickness is set to 0.75km. Ground waves propagate along the surface of the earth between the transmitting point and the receiving point on the ground. is the transmitting antenna position, is the receiving position. The signal power of the transmitting source is 1 kW. The PCE-FDTD grid is fixed at 9.375 m. The ground electrical parameters are set to three values, and the average values ​​of the dielectric constant and conductivity are: S / m; S / m; S / m. The electrical parameters of the formation are modeled using Gaussian distribution and are used as independent random variables , .

[0041] The dielectric constant and conductivity of the medium are considered as random variables in the model. Assume that the dielectric constant of the formation is and conductivity are independent random parameters that follow a Gaussian distribution, and their means are , , and the standard deviations are , Strata and The standard deviation of is shown in equations (1) and (2).

[0042] (1) (2) in and are the relative changes of the random variables relative permittivity and conductivity. and The uncertainty can be expressed as the uncertainty about the random variable and The mean and variance expressions of the TM wave electromagnetic field are derived in two-dimensional cylindrical coordinates.

[0043] The mean and variance of the field are shown in equations (3) and (10).

[0044] (3) (10) in is a random variable , The ath expansion term of the orthogonal polynomial basis function of the chaotic expansion determined by the distribution function. The orthogonal basis function is selected from the WeinerAskey scheme, and its distribution depends on the distribution of the random variable under consideration. Because the random variable here obeys a Gaussian distribution, the corresponding orthogonal polynomial type is the Hermite polynomial. yes Corresponds to The coefficient equation of the expansion order is, P is the number of expanded items. As shown in formula (11): (11) Where n represents the time step, represents the time step, i , k represents the space step, represents the spatial step length, , The random variables are , The a-th and b-th expansion terms of the orthogonal polynomial basis function of the chaotic expansion determined by the distribution function, For magnetic field The coefficients of the polynomial expansion of , the time domain waveforms of the mean field and variance field of the ground wave at R are obtained. Figure 2 .

[0045] Step 2: Based on the statistical characteristics of the ground wave electric field strength, the time of the positive zero crossing point of a carrier cycle in the time domain waveform of the electric wave mean field is determined as the arrival time, and the average value of the total ground wave propagation delay is obtained.

[0046] See also Figure 2 In the study of ground wave propagation delay, for a certain receiving position, the positive zero-crossing moment of the vertical electric field waveform in a certain time domain steady-state period in the mean signal is extracted and accurately measured as the average arrival time of the signal, recorded as .

[0047] According to the relationship between the total ground wave propagation delay and the additional secondary delay ASF in Loran-C, the mean value of the Loran-C ground wave propagation ASF is obtained; Specifically, the relationship between the total delay of Loran-C ground wave propagation and the additional secondary delay ASF of ground wave propagation is shown in formula (5): (5) In the formula, It is the total delay of the ground wave from the transmitting source to the receiving position. PF is the basic delay. When it is assumed that the entire propagation path is completely in the air medium, the time taken for the electromagnetic wave signal to propagate from the transmitting antenna to the receiving antenna. SF represents the delay generated when the actual path is assumed to be seawater. ASF reflects the additional delay change caused by the long-wave ground wave signal under the actual land propagation path compared to when the entire path is seawater. is the reference moment in the current source applied to the antenna corresponding to the extracted carrier cycle moment, It is the initial phase difference between the excitation current and the radiation field signal.

[0048] Specifically, the average total delay of radio wave propagation and the mean value of ASF are obtained through the time when the radio wave arrives at the receiving position in the radio wave time domain waveform. As shown in formula (6): (6) Step 3, selecting two adjacent sampling moments in the same carrier cycle of the time domain waveform of the radio wave mean field, and obtaining the standard deviation of the ground wave propagation delay based on the linear approximation method; Specifically, the sampling point selection principle in the radio wave time domain waveform mean field signal is: See also Figure 3 , two sampling moments are selected from adjacent positions of a carrier cycle in the mean field of the radio wave time domain waveform obtained by the PCE-FDTD method, and are recorded as and .in, It is the moment when the carrier cycle crosses zero in the positive direction. The mean value of the electric field intensity corresponding to the time The standard deviation of the electric field strength corresponding to the sampling time is the same. and The principles satisfied are shown in equations (7) and (8) respectively: (7) (8) In the formula, yes The mean value of the electric field strength at time , yes The mean value of the electric field strength at time , yes The standard deviation of the electric field strength at that moment.

[0049] Specifically, due to the sampling time and At adjacent positions in the same carrier cycle, the linear approximation method is used here to obtain the standard deviation of the ground wave propagation ASF of the Loran-C system As shown in formula (9): （9） See also Figure 4 , taking the results of 5000 Monte Carlo simulations performed by the analytical method as a reference, the mean results of the Loran-C ground wave propagation ASF obtained by the second-order PCE-FDTD method are observed. Under different formation parameter conditions, as the receiving distance increases, the statistical results of the ground wave ASF show an increasing trend. S / m, , Under the condition of , when the distance between the receiving point and the transmitting source reaches 100 kilometers, the mean value of the Loran-C ground wave ASF calculated by the PCE-FDTD method reaches the maximum value, specifically 3.8µs. At this time, the error between the mean values ​​of the Loran-C ground wave ASF obtained by the PCE-FDTD method and the MC method is only 4ns.

[0050] See also Figure 5 , taking the results of 5000 Monte Carlo simulations performed by the analytical method as a reference, the mean results of the Loran-C ground wave propagation ASF obtained by the second-order PCE-FDTD method are observed. Under different formation parameter conditions, as the receiving distance increases, the standard deviation results of the ground wave ASF show different trends. S / m, , Under the condition of , as the receiving distance changes from near to far, the standard deviation of the ground wave first shows an upward trend, and then gradually decreases. When the distance between the receiving point and the transmitting source reaches 100 kilometers, the standard deviation of the Loran-C ground wave propagation ASF calculated by the PCE-FDTD method is 85 ns. At this time, the error of the Loran-C ground wave ASF standard deviation obtained by the PCE-FDTD method and the MC method is the largest, which is 2.5ns. This error can be regarded as negligible in practical applications.

[0051] The present invention also provides a Loran-C system ground wave propagation ASF statistical characteristics prediction system, comprising an acquisition module, an ASF mean value calculation module, an ASF standard deviation calculation module and a characterization prediction module, wherein: Acquisition module: used to construct a random stratum-atmosphere layered waveguide model, and use the PCE-FDTD method to obtain the mean and standard deviation of the electric wave field strength at each moment during the propagation of ground waves in the random stratum-atmosphere layered waveguide model; ASF mean value calculation module: used to obtain the ground wave mean field time domain waveform according to the mean value of the electric field strength, locate the position of the positive zero crossing point in a specific carrier cycle of the ground wave mean field time domain waveform, and obtain the mean value of the ground wave propagation ASF of the Loran-C system; ASF standard deviation calculation module: It is used to select two adjacent sampling moments in the same carrier cycle of the ground wave mean field time domain waveform based on the mean value and standard deviation of the electric field strength, and obtain the standard deviation of the ground wave propagation ASF of the Loran-C system according to the linear approximation method; The prediction module is used to characterize the statistical characteristics of the ground wave propagation ASF of the Loran-C system by using the average value and standard deviation of the ground wave propagation ASF, so as to realize the prediction of the statistical characteristics of the ground wave propagation ASF of the Loran-C system.

[0052] 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.

[0053] 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.

[0054] 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.

[0055] 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 1 The steps for the functions specified in one or more boxes.

[0056] 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 ground wave propagation ASF in a Loran-C system, characterized in that: The following steps are involved: A random stratum-atmosphere layered waveguide model is constructed, and the PCE-FDTD method is used to obtain the mean and standard deviation of the electric wave field strength at each moment of ground wave propagation in the random stratum-atmosphere layered waveguide model. The ground wave mean field time domain waveform is obtained according to the average value of the electric field strength, and the position of the positive zero crossing point is located in a specific carrier cycle of the ground wave mean field time domain waveform, and the average value of the ground wave propagation ASF of the Loran-C system is obtained; Based on the mean and standard deviation of the electric field intensity, two adjacent sampling moments are selected in the same carrier cycle of the ground wave mean field time domain waveform, and the standard deviation of the ground wave propagation ASF of the Loran-C system is obtained according to the linear approximation method. The average value and standard deviation of ground wave propagation ASF are used to characterize the statistical characteristics of ground wave propagation ASF of Loran-C system, so as to predict the statistical characteristics of ground wave propagation ASF of Loran-C system.

2. The method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system according to claim 1, characterized in that: The random stratum-atmosphere layered waveguide model is a uniformly layered smooth flat ground waveguide model, which is divided into an air layer and a stratum from top to bottom. 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. The method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system according to claim 1, characterized in that: The steps for solving the mean value of the ground wave propagation ASF of the Loran-C system are: The dielectric constant and conductivity of regular and flat strata are regarded as random variables. Based on the PCE-FDTD method, the mean equations of the three field components of TM waves in the two-dimensional cylindrical coordinate system can be obtained, and the time domain waveform of the mean field of ground waves can be constructed. The positive zero-crossing point of a carrier cycle of the ground 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 of the ground wave at the receiving position, and the average total delay of ground wave propagation is obtained; Based on the relationship between the total ground wave propagation delay of Loran-C and the additional secondary delay ASF of ground wave propagation, the average value of the ground wave propagation ASF of the Loran-C system is obtained.

4. The method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system according to claim 1, characterized in that: The relationship between the total ground wave propagation delay and the additional secondary delay is: In the formula, It is the total delay of ground wave propagating from the transmitting source to the receiving position, PF is the "basic delay", SF is the delay caused by assuming that the actual path is seawater, and ASF is the additional secondary delay. is the reference moment in the current source applied to the antenna corresponding to the extracted carrier cycle moment, is the initial phase difference between the excitation current and the radiation field signal; The mean of the additional quadratic delay is: In the formula, represents the mean value of the additional quadratic delay, Represents the average value of the total ground wave propagation delay.

5. The method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system according to claim 1, characterized in that: The sampling moments of the two adjacent positions are determined by the PCE-FDTD method.

6. A method for predicting the statistical characteristics of ground wave propagation ASF in a Loran-C system according to claim 1 or 5, characterized in that: The conditions for determining the sampling moments of the two adjacent positions are: One of the sampling moments is the positive zero-crossing moment, and the mean value of the radio wave field strength is 0: The mean value of the electric wave field strength at another sampling moment is the same as the standard deviation of the electric wave field strength at the positive zero crossing moment.

7. The method for predicting the statistical characteristics of ground wave propagation ASF of a Loran-C system according to claim 1, characterized in that: The standard deviation of the additional quadratic delay of ground wave propagation is the difference between two sampling moments.

8. A Loran-C system ground wave propagation ASF statistical characteristics prediction system, characterized by: It includes an acquisition module, an ASF mean calculation module, an ASF standard deviation calculation module and a characterization prediction module, wherein: Acquisition module: used to construct a random stratum-atmosphere layered waveguide model, and use the PCE-FDTD method to obtain the mean and standard deviation of the electric wave field strength at each moment during the propagation of ground waves in the random stratum-atmosphere layered waveguide model; ASF mean value calculation module: used to obtain the ground wave mean field time domain waveform according to the mean value of the electric field strength, locate the position of the positive zero crossing point in a specific carrier cycle of the ground wave mean field time domain waveform, and obtain the mean value of the ground wave propagation ASF of the Loran-C system; ASF standard deviation calculation module: It is used to select two adjacent sampling moments in the same carrier cycle of the ground wave mean field time domain waveform based on the mean value and standard deviation of the electric field strength, and obtain the standard deviation of the ground wave propagation ASF of the Loran-C system according to the linear approximation method; The prediction module is used to characterize the statistical characteristics of the ground wave propagation ASF of the Loran-C system by using the average value and standard deviation of the ground wave propagation ASF, so as to realize the prediction of the statistical characteristics of the ground wave propagation ASF of the Loran-C system.

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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