Distributed unmanned aerial vehicle towed very low frequency transmitting system and radiation performance evaluation method thereof

Abstract

The application discloses a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmitting system, which is composed of multiple UAV platforms towing antenna units to form a distributed array, and high-precision synchronization and phase control of each node are realized by using enhanced Loran and global positioning system (GPS) double time signals, so that the problems of low survivability of traditional fixed stations and insufficient radiation power of single mobile platform are solved. The application also proposes a radiation performance evaluation method for the distributed VLF transmitting system, random phase disturbance of cable deformation caused by wind load is modeled as a phase disturbance conforming to a specific statistical distribution, a quantitative mapping relationship between the standard deviation of phase error and the probability of meeting the array radiation performance is established by calculating the cumulative distribution function of the array relative gain. The application can provide a design basis for the UAV flight control precision and time synchronization index of the distributed transmitting system, and realize high survivability and megawatt equivalent radiation power in a high dynamic environment.

Description

Technical Field

[0001] This application relates to the field of radio communication technology, and more specifically, to a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system and a method for evaluating its radiation performance. Background Technology

[0002] Very low frequency (VLF, 3-30 kHz) radio waves occupy an irreplaceable position in communications due to their unique propagation characteristics. VLF signals have extremely low path attenuation (approximately 2-3 dB / 1000 km) and can penetrate seawater to depths of tens of meters using the skin effect. This makes VLF the only reliable means of communicating with underwater vehicles.

[0003] However, existing very low frequency (VLF) transmission technology has significant limitations: 1. The vulnerability and immobility of shore-based stations: Currently, the highest-level VLF transmission stations typically have transmitters with an output power of 1-2 megawatts (MW), with antenna arrays supported by giant iron towers reaching 300 to 400 meters in height, and top-loaded networks covering several square kilometers. This massive physical size makes them virtually impossible to miss under modern satellite reconnaissance. These fixed stations are key targets in the first wave of attacks. Once the antenna tower collapses or the tuning room is destroyed, the repair work is extremely lengthy, leading to a break in the command link. 2. Power and efficiency bottlenecks of mobile platforms: To improve survivability, systems such as TACAMO (E-6B Mercury aircraft) and tethered balloons have been developed historically. Limited by the payload, power supply capacity, and corona voltage threshold and current carrying capacity of the antenna cables, the radiated power of these systems is usually difficult to exceed 100 kW, making them unable to replace the coverage capabilities of shore-based stations. 3. Technical Challenges of Distributed Arraying: The theoretical approach to solving the aforementioned problems is to achieve an equivalent high-power transmitter by spatially combining multiple low-power sources and utilizing the high-gain directional beam of the array antenna. However, in the very low frequency band, wavelengths can exceed 10 kilometers, meaning the spacing between array elements is enormous (several kilometers). The natural environment in which each element is located varies significantly. When a drone tows an antenna cable up to 1500 meters long, the cable will exhibit a complex catenary shape under wind conditions and sway with the wind. This dynamic deformation leads to random phase jitter in the radiation. If the phase error is too large, the electromagnetic waves emitted by each element will not coherently superimpose in the far field, or even destructive interference will occur, resulting in the failure of "spatial power combining".

[0004] In summary, existing technologies lack a very low frequency (VLF) transmission scheme that can provide megawatt-level radiated power while also possessing high survivability and mobility. Furthermore, there is a lack of effective assessment methods for the impact of phase disturbances on flexible antenna arrays. Summary of the Invention

[0005] In response to at least one defect or improvement requirement in the prior art, this application provides a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system and its radiation performance evaluation method, which can solve at least one of the problems existing in the background art.

[0006] To achieve the above objectives, according to the first aspect of this application, a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system is provided, comprising: Multiple independent airborne transmission nodes, each of which includes an unmanned aerial vehicle platform, a very low frequency transmitting antenna unit towed by the platform, a tuning module, and a transmission module; A synchronization and control unit is used to provide each of the airborne transmission nodes with high-precision time synchronization signals and phase control commands; The multiple independent airborne transmitting nodes are arranged in the air according to a preset spatial geometry to form a distributed array. Each airborne transmitting node independently transmits very low frequency signals. The transmission phase of each node is adjusted by the synchronization and control unit to achieve spatial power synthesis, so as to form a coherently superimposed electromagnetic field radiation beam in the target direction. The system is configured to maintain the equivalent radiated power above a preset threshold under conditions of phase disturbance caused by mechanical deformation of the very low frequency transmitting antenna element due to environmental wind load.

[0007] Furthermore, in the aforementioned distributed UAV towed very low frequency transmission system, the synchronization and control unit adopts an enhanced Loran system as the master clock source and a global satellite navigation system as the backup clock source.

[0008] Furthermore, in the aforementioned distributed UAV-towed very low frequency (VLF) transmission system, the VLF transmission antenna unit serves as both a radiator and a tether cable for the UAV platform. The lower end of the cable is connected to a tuning unit and a grounding device. The grounding device comprises multiple grounding wires arranged radially.

[0009] Furthermore, in the aforementioned distributed UAV-towed very low frequency transmission system, the attitude control accuracy of the UAV platform is configured such that, at a predetermined wind speed, the standard deviation of the phase disturbance caused by cable deformation remains within the threshold range required to maintain the effective radiated power of the system.

[0010] According to a second aspect of this application, a method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system is also provided, based on a distributed UAV-towed VLF transmission system as described in any of the preceding claims, comprising the following steps: Step S1: Establish a theoretical model of the distributed transmission array, which includes multiple antenna elements towed by the UAV flight platform; Step S2: Construct a phase disturbance statistical model for the antenna element. The phase disturbance statistical model is used to characterize the signal phase deviation caused by the deformation of the dragging cable due to environmental load. Step S3: Based on the set phase error standard deviation, generate multiple sets of random phase samples that conform to the phase perturbation statistical model using the Monte Carlo method; Step S4: For each set of random phase samples, calculate the array relative gain of the distributed transmission array; Step S5: Perform statistical analysis on the calculated relative gains of multiple arrays, generate the cumulative distribution function, and establish a quantitative mapping relationship between the standard deviation of phase error and the array radiation performance index.

[0011] Furthermore, in the above-mentioned method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, the construction of the phase perturbation statistical model for the antenna element specifically includes: The phase perturbation of the antenna element is assumed to follow a zero-mean Gaussian normal distribution; The phase perturbation The probability density function is determined by the set standard deviation. Decide.

[0012] Furthermore, in the above-mentioned method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, the specific steps for calculating the array relative gain of the distributed transmission array are as follows: Define array gain The directional coefficients are contributed solely by the array factor; Calculation in the presence of phase perturbation The gain of the disturbed array at that time; Calculate the ideal array gain without phase perturbation; The ratio of the disturbed array gain to the ideal array gain is taken as the array relative gain.

[0013] Furthermore, in the above-mentioned method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, the array factor... The calculation formula is:

[0014] Where N is the number of antenna elements, I n h is the current amplitude. n For effective height, For spatial phase difference, The excitation phase used for beam pointing control, For random phase perturbation, j It is the imaginary unit.

[0015] Furthermore, in the above-mentioned method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, the establishment of the quantization mapping relationship includes: Iterate through different phase error standard deviation values; Extract the median of the array relative gain for each standard deviation; Determine the maximum standard deviation threshold of phase error allowed for the distributed emission array to maintain a predetermined equivalent radiated power at a specific confidence level.

[0016] Furthermore, the aforementioned method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system also includes calibrating the radiation efficiency of a single antenna element based on the ground wave propagation formula: The peak radiation field intensity E of a single antenna element is obtained at a preset distance range d. m ; Based on formula Obtain the radiated power P of a single antenna r ; The radiation efficiency of a single antenna is calculated based on the input power, and the total equivalent radiated power of the system is calculated by combining the array gain.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived in this application can achieve the following beneficial effects: The distributed UAV-towed VLF transmission system provided in this application adopts an architecture consisting of multiple UAVs towed cable antennas equipped with low-power transmitters, arranged in an orderly manner in the air to form a distributed array. It uses high-precision synchronization timing technology to coordinate the transmission phase of each node to achieve spatial power synthesis. At the same time, it combines a phase disturbance evaluation method based on Monte Carlo simulation to provide quantitative basis for the system's wind resistance design and performance assurance. It can integrate the traditional large-scale fixed megawatt-level VLF transmission capability into a highly mobile distributed platform. While ensuring that the system obtains the equivalent radiation power of a large fixed station, it significantly improves its survivability and reconfiguration capability when facing threats. It also solves the engineering problem of the difficulty in assessing and controlling random phase errors caused by wind-induced antenna swaying. This allows the system to reliably maintain the equivalent radiation power above a preset threshold level even in complex weather conditions.

[0018] The distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application establishes an array theoretical framework including a phase perturbation statistical model and uses the Monte Carlo method to perform large-scale simulation sampling and statistical analysis of random phase deviations caused by environmental wind loads. This method can transform the mechanical deformation factors that affect the performance of distributed UAV towed arrays and are difficult to predict accurately into a clear quantitative mapping relationship between the standard deviation of phase error and the system radiation performance. This provides key wind resistance performance indicators and tolerance boundaries for the system in the engineering design stage, enabling engineers to determine the specific requirements for the flight control stability and cable attitude control of the UAV platform based on clear probabilistic performance. This fundamentally solves the problem of performance evaluation and quantitative design of flexible distributed arrays in dynamic environments. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This application provides an embodiment of a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system. Figure 2 This is a block diagram of a single-transmitter node structure provided in an embodiment of this application; Figure 3 A flowchart for radiation performance evaluation based on the Monte Carlo method is provided for embodiments of this application; Figure 4 This is a schematic diagram of the spatial arrangement of a 16-element 2×8 rectangular array provided in an embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. Furthermore, the technical features involved in the various embodiments described below can be combined with each other as long as they do not conflict with each other.

[0022] The terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0023] Figure 1 This application provides an embodiment of a distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system, such as... Figure 1 As shown in the figure, a distributed UAV towed very low frequency transmission system provided in this application includes: Multiple independent airborne transmission nodes, each of which includes an unmanned aerial vehicle platform, a very low frequency transmitting antenna unit towed by the platform, a tuning module, and a transmission module; A synchronization and control unit is used to provide each of the airborne transmission nodes with high-precision time synchronization signals and phase control commands; The feature is that the multiple independent airborne transmitting nodes are arranged in the air according to a preset spatial geometric configuration to form a distributed array. Each airborne transmitting node independently transmits very low frequency signals. The transmission phase of each node is adjusted by the synchronization and control unit to achieve spatial power synthesis, so as to form a coherently superimposed electromagnetic field radiation beam in the target direction. The system is configured to maintain the equivalent radiated power above a preset threshold under conditions of phase disturbance caused by mechanical deformation of the very low frequency transmitting antenna element due to environmental wind load.

[0024] Specifically, this application provides a distributed UAV-towed very low frequency (VLF) transmission system, which includes multiple independent airborne transmission nodes, such as a transmission unit consisting of 16 heavy-duty UAVs in one specific embodiment. Each of the airborne transmission nodes is as follows: Figure 2 As shown, the system specifically includes a drone platform, a very low frequency (VLF) transmitting antenna unit towed by the platform, a tuning module, and a transmitting module. The drone platform must have sufficient payload capacity; the VLF transmitting antenna unit is an approximately 1500-meter-long aluminum alloy stranded cable towed beneath the drone, which serves as both the radiator and the physical tether; the tuning module includes a tuning inductor and a coupling transformer to achieve impedance matching between the transmitter and the long cable antenna; and the transmitting module generates a VLF signal at a specific frequency.

[0025] The synchronization and control unit provides high-precision time synchronization signals and phase control commands to each of the airborne transmitting nodes. It employs a dual-backup timing scheme: the primary method uses the enhanced Loran (e-Loran) system, which utilizes low-frequency ground waves for timing with an accuracy better than 100 nanoseconds; the backup method uses Global Positioning System (GPS) satellite timing. The central controller calculates the initial feed phase required by each node to compensate for spatial path difference based on the target direction using a formula. β n The system generates phase control commands and sends them to each node via a wireless link. Each node's local oscillator locks its phase based on the received synchronization time base, ensuring that all nodes can operate on a unified time base.

[0026] The multiple independent airborne transmitting nodes are arranged in the air, taking 16 nodes as an example, in a rectangular distributed array of 2 rows and 8 columns. Along the X-axis (corresponding to the longer side), the spacing between the 8 elements is 6000 meters; along the Y-axis (corresponding to the shorter side), the spacing between the 2 elements is 3000 meters. The entire array covers an airspace of approximately 42 kilometers by 3 kilometers. Each airborne transmitting node independently transmits a very low frequency signal (e.g., 10kW per node), and the synchronization and control unit precisely adjusts the transmission phase of each node so that all nodes are aligned in the far-field target direction (…). θ 0, φ The electromagnetic waves emitted from 0) are superimposed in phase, a process known as "spatial power combining". A coherently superimposed high-gain electromagnetic field radiation beam is formed in the target direction, so that the equivalent radiated power (ERP) of the entire system reaches the coherent combined value of the power of each unit. Ideally, 16 10kW units can generate an equivalent radiated power of about 2026kW.

[0027] The system is configured to maintain the equivalent radiated power above a preset threshold under conditions of phase disturbance caused by mechanical deformation of the very low frequency transmitting antenna element due to environmental wind loads. The core of this configuration is based on the Monte Carlo radiation performance evaluation method. Specifically, wind forces cause complex deformation and swaying of the cable, thereby introducing random phase errors Δ. ψ nBy modeling the phase perturbation as a Gaussian distribution with zero mean and standard deviation σ, and conducting extensive simulations using the Monte Carlo method, the impact of phase perturbation on the synthesized gain can be quantitatively evaluated. For example, the evaluation results show that when the standard deviation σ of the phase perturbation is controlled within 50 degrees, the system has a 50% probability (i.e., median performance) of maintaining the equivalent radiated power above approximately 10¹⁵ kW. Therefore, in system design and control algorithm development, a clear phase tolerance index (e.g., σ < 50°) can be set based on this evaluation result, and by optimizing the stability of the UAV flight control system and the cable attitude control, it can be ensured that the system performance meets the preset power threshold requirement of "megawatt level" (e.g., > 1000 kW) in actual wind farm environments.

[0028] The distributed UAV-towed VLF transmission system provided in this application adopts an architecture consisting of multiple UAVs towed cable antennas equipped with low-power transmitters, arranged in an orderly manner in the air to form a distributed array. It uses high-precision synchronization timing technology to coordinate the transmission phase of each node to achieve spatial power synthesis. At the same time, it combines a phase disturbance evaluation method based on Monte Carlo simulation to provide quantitative basis for the system's wind resistance design and performance assurance. It can integrate the traditional large-scale fixed megawatt-level VLF transmission capability into a highly mobile distributed platform. While ensuring that the system obtains the equivalent radiation power of a large fixed station, it significantly improves its survivability and reconfiguration capability when facing threats. It also solves the engineering problem of the difficulty in assessing and controlling random phase errors caused by wind-induced antenna swaying. This allows the system to reliably maintain the equivalent radiation power above a preset threshold level even in complex weather conditions.

[0029] Optionally, in the distributed UAV towed very low frequency transmission system provided in this application embodiment, the synchronization and control unit adopts an enhanced Loran system as the master clock source and a global satellite navigation system as the backup clock source.

[0030] Optionally, in the distributed UAV towed very low frequency (VLF) transmission system provided in this application embodiment, the VLF transmission antenna unit is used as a radiator and also as a tether cable for the UAV platform. The lower end of the cable is connected to a tuning unit and a grounding device. The grounding device includes multiple grounding wires arranged radially.

[0031] Optionally, in the distributed UAV-towed very low frequency transmission system provided in this application embodiment, the attitude control accuracy of the UAV platform is configured such that, at a predetermined wind speed, the standard deviation of the phase disturbance caused by cable deformation remains within the threshold range required to maintain the effective radiated power of the system.

[0032] Specifically, the following is a detailed description of the distributed UAV towed very low frequency transmission system and reverse navigation provided in this application, using a specific 24 kHz basic distributed array embodiment: This embodiment constructs a distributed launch system consisting of 16 UAV nodes.

[0033] System Configuration: Platform: 16 heavy-duty drones, each with a payload capacity of ≥200kg.

[0034] Antenna: Each unit tows a 1500-meter-long aluminum alloy stranded cable (100g / m linear density). Aluminum alloy has a better strength-to-weight ratio than copper wire, making it suitable for aerial towing. The lower end of the cable connects to the tuning unit via a feeder, and is matched to the transmitter through a tuning inductor and a coupling transformer. The cable serves as both the radiator and the tether cable.

[0035] Grounding: Four 80m long radial ground wires are laid on the ground at each node to form a good very low frequency grounding network.

[0036] Layout: 2×8 rectangular array, such as Figure 4 As shown. X-axis direction: 8 units, spacing 6000 meters; Y-axis direction: 2 units, spacing 3000 meters; Total coverage area: approximately 42km × 3km of airspace.

[0037] Frequency: 24kHz (corresponding wavelength) This frequency was chosen to be comparable to the existing NAA Cutler station.

[0038] Workflow: 1. Deployment: The drone flies to the designated airspace and releases 1,500 meters of cable.

[0039] 2. Synchronization: To ensure that the 16 nodes, which are several kilometers apart, can work as a whole, this system adopts a "dual backup" timing scheme: Primary: Enhanced Loran (e-Loran) system, using low-frequency ground wave timing, with a timing accuracy better than 100ns. Backup: Global Positioning System (GPS) satellite timing.

[0040] 3. Beamforming: The central controller determines the orientation of the target underwater vehicle. The theoretical phase of each node is calculated using the formula. The signal is then transmitted to each node via a wireless link. Each node's local oscillator locks its phase according to the timing signal, thus achieving spatial beamforming.

[0041] 4. Launch: Each unit launches at a power of 10 kW.

[0042] Performance metrics: Based on FEKO simulation: Single antenna radiation efficiency: 68.1% at 24kHz.

[0043] Array gain: Ideally, the gain of a 16-element array is approximately 12.7 dB.

[0044] Equivalent radiated power:

[0045] This power level exceeds the nominal radiated power of the Cutler station (approximately 1600kW) and has the capability for mobile deployment.

[0046] This application also provides a method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, based on the distributed UAV-towed VLF transmission system described in any of the above embodiments, including the following steps: Step S1: Establish a theoretical model of the distributed transmission array, which includes multiple antenna elements towed by the UAV flight platform; Step S2: Construct a phase disturbance statistical model for the antenna element. The phase disturbance statistical model is used to characterize the signal phase deviation caused by the deformation of the dragging cable due to environmental load. Step S3: Based on the set phase error standard deviation, generate multiple sets of random phase samples that conform to the phase perturbation statistical model using the Monte Carlo method; Step S4: For each set of random phase samples, calculate the array relative gain of the distributed transmission array; Step S5: Perform statistical analysis on the calculated relative gains of multiple arrays, generate the cumulative distribution function, and establish a quantitative mapping relationship between the standard deviation of phase error and the array radiation performance index.

[0047] Specifically, the distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application embodiment is based on the aforementioned UAV-towed distributed VLF transmission system and aims to quantitatively evaluate the impact of wind-induced phase disturbances on system performance.

[0048] Step S1: Establish a theoretical model of the distributed transmission array. This model models the system as an array of N antenna elements, each antenna element being defined by its spatial coordinates ( x n , y n As defined by [reference needed], its radiation field includes the artificially controlled initial phase of the feed. β n (For beam pointing) and random phase perturbations Δ caused by the environment ψ n The array is in any direction in the far field ( θ , φ The radiation characteristics of ) are determined by the array factor f ( θ , φ The model is described as the vector sum of the radiation fields of each element, which already includes the aforementioned phase term. This model forms the basis for all subsequent quantitative analyses.

[0049] Step S2: Construct a statistical model of the phase disturbance of the antenna element. Considering the uncertainty of the swaying of the drag cable caused by wind, the signal phase deviation Δ caused by this mechanical deformation is considered. ψ n The model is a zero-mean random variable. More specifically, the phase perturbation is set to follow a Gaussian (normal) distribution N(0, σ). 2 ), where σ (standard deviation of phase error) is a key parameter for measuring the strength of environmental disturbances (such as wind speed). This statistical model transforms fuzzy physical deformations into probability distributions that can be used for mathematical analysis and simulation.

[0050] Step S3: Based on the set standard deviation of the phase error, generate random phase samples using the Monte Carlo method, such as... Figure 3 As shown, for a given phase error standard deviation σ (e.g., σ = 45°), a large number (e.g., M = 100 sets) of N(0, σ) random number generators are generated. 2 The system generates random phase samples distributed as follows: Each sample set contains N random phase values, simulating a random phase disturbance applied to N antenna elements. By iteratively generating multiple sample sets, various possible statistical scenarios of phase disturbances can be covered.

[0051] Step S4: For each set of random phase samples, calculate the array relative gain. For each set of random phase samples generated in step S3, {Δ ψ 1, …, Δ ψ N Substitute this value into the array factor theoretical model established in step S1. First, calculate the array gain with the presence of this set of perturbations, and then calculate its ratio to the array gain under ideal, perturbation-free conditions, thus obtaining the relative gain for this sampling. This step transforms the abstract phase perturbation value into an intuitive indicator characterizing the degree of performance degradation.

[0052] Step S5: Perform statistical analysis on the relative gains of multiple arrays to establish a quantitative mapping relationship. Statistical analysis is performed on the large number (M) relative gain samples obtained through step S4. Specifically, these gain values ​​are sorted by magnitude, and their cumulative distribution function (CDF) curves are plotted. Key statistics, such as the median (the gain value corresponding to a cumulative probability of 0.5), can be extracted from the CDF curves. By changing different phase error standard deviations σ (e.g., from 0° to 180°) and repeating steps S3 to S5, a mapping curve of phase error standard deviation versus relative gain median can be obtained. This mapping relationship can be directly used to guide engineering design. For example, if the system is required to maintain power above a certain threshold with a 50% probability, the maximum allowable phase error standard deviation σ can be derived from this curve, thus providing clear electromagnetic performance constraints for the design of the UAV wind-resistant stability control system.

[0053] The distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application establishes an array theoretical framework including a phase perturbation statistical model and uses the Monte Carlo method to perform large-scale simulation sampling and statistical analysis of random phase deviations caused by environmental wind loads. This method can transform the mechanical deformation factors that affect the performance of distributed UAV towed arrays and are difficult to predict accurately into a clear quantitative mapping relationship between the standard deviation of phase error and the system radiation performance. This provides key wind resistance performance indicators and tolerance boundaries for the system in the engineering design stage, enabling engineers to determine the specific requirements for the flight control stability and cable attitude control of the UAV platform based on clear probabilistic performance. This fundamentally solves the problem of performance evaluation and quantitative design of flexible distributed arrays in dynamic environments.

[0054] Optionally, the distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application embodiment, wherein constructing the phase perturbation statistical model of the antenna element specifically includes: The phase perturbation of the antenna element is assumed to follow a zero-mean Gaussian normal distribution; The phase perturbation The probability density function is determined by the set standard deviation. Decide.

[0055] Optionally, the method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system provided in this application includes the following steps for calculating the array relative gain of the distributed transmission array: Define array gain The directional coefficients are contributed solely by the array factor; Calculation in the presence of phase perturbation The gain of the disturbed array at that time; Calculate the ideal array gain without phase perturbation; The ratio of the disturbed array gain to the ideal array gain is taken as the array relative gain.

[0056] Optionally, in the distributed very low frequency (VLF) emission system radiation performance evaluation method provided in this application embodiment, the array factor... The calculation formula is:

[0057] Where N is the number of antenna elements, I n h is the current amplitude. n For effective height, For spatial phase difference, The excitation phase used for beam pointing control, For random phase perturbation, j It is the imaginary unit.

[0058] Optionally, the method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system provided in this application embodiment includes establishing the quantization mapping relationship as follows: Iterate through different phase error standard deviation values; Extract the median of the array relative gain for each standard deviation; Determine the maximum standard deviation threshold of phase error allowed for the distributed emission array to maintain a predetermined equivalent radiated power at a specific confidence level.

[0059] Optionally, the distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application embodiment further includes calibrating the radiation efficiency of a single antenna element based on the ground wave propagation formula: The peak radiation field intensity E of a single antenna element is obtained at a preset distance range d. m ; Based on formula Obtain the radiated power P of a single antenna r ; The radiation efficiency of a single antenna is calculated based on the input power, and the total equivalent radiated power of the system is calculated by combining the array gain.

[0060] Specifically, this application abandons the traditional approach of high-power transmission via a single antenna and adopts a "divide and conquer" strategy. The system consists of N (e.g., 16) independent UAV launching units. Each unit transmits only a low power (e.g., 10kW), but in the target direction, through precise phase control, the electromagnetic waves are superimposed in phase. According to antenna array theory, the ideal combined power density is proportional to the square of the number of units (N... 2 Therefore, 16 units with a power of 10kW can theoretically produce a single antenna radiation effect equivalent to 2560kW, successfully reaching the standard of a megawatt-level station.

[0061] To address the synchronization challenges of distributed nodes, this application employs the enhanced Loran (e-Loran) signal as the primary time synchronization source. E-Loran is a low-frequency ground wave navigation system with excellent anti-interference capabilities and penetration, achieving a timing accuracy of 100 ns. At 24 kHz, a 100 ns time synchronization corresponds to a phase error of only 0.86 ms. o This is far below the tolerance threshold required for coherent synthesis. The system also incorporates both the Global Positioning System (GPS) and a local atomic clock, constructing a triple-redundant synchronization system.

[0062] Given the randomness of wind-induced deformation, this application establishes a statistical evaluation framework.

[0063] (1) Modeling: The phase disturbance caused by wind The model is a zero-mean Gaussian random variable.

[0064] (2) Simulation: A large number of random samples were generated using the Monte Carlo method, and the standard deviation of the array at different phase errors was calculated. The relative gain distribution under the given conditions.

[0065] (3) Decision Support: The availability probability of the system under adverse weather conditions (high wind speed, large disturbances) is quantified using the cumulative distribution function (CDF). For example, the evaluation results show that in Under extreme disturbances, the system still has a 50% probability of maintaining an equivalent power of over 1000 kW, which provides a quantitative safety boundary for the system's engineering design.

[0066] Assume there are N drone-towed antenna elements distributed on the xoy plane. Model the antennas as vertically polarized (Z-axis) monopoles. Treat the ground as an ideal conductor (PEC).

[0067] In the far field, the array factor determines the shape of the radiation pattern. Influenced by wind loads, the coordinates of the nth element are (x... n y n The actual radiation field contains random phase perturbations. .direction Array factor Expressed as:

[0068] The variables are defined as follows: N: The total number of antenna elements in the array.

[0069] I n : The current amplitude of the nth unit. In this application, it is assumed to be uniformly distributed.

[0070] h n: The effective height of the nth unit. Due to cable bending, the effective height is less than the physical length.

[0071] : Random phase disturbance term caused by wind.

[0072] : The initial phase of the feed artificially applied for beam scanning.

[0073] j: Imaginary unit.

[0074] For those located The geometric phase difference determined by the spatial position of the element at that location. for:

[0075] Here For wave number, where λ is the wavelength and c is the speed of light. f For operating frequency, The pitch angle, It is the azimuth angle.

[0076] The excitation phase actively applied by the transmitter is used for beam scanning. This is to ensure that the maximum array radiation is directed in the desired direction. The spatial path difference from different array elements to this direction should be compensated, and the feed phase of each element should be adjusted accordingly. Spatial path difference in this direction must be compensated:

[0077] Compensation in the expected direction Spatial phase difference,

[0078] thereby

[0079] Ideally when At that time, all units are in the direction The same phase is superimposed to achieve maximum gain. And when... When there are random fluctuations, the superposition degenerates from "completely coherent" to "partially coherent", which is the root cause of the decrease in spatial power synthesis gain.

[0080] Starting from the basic definition of electromagnetic radiation, directionality is defined as:

[0081] in, Radiation intensity (radiation power per unit solid angle).

[0082] In the far region of the array, if the differences in the radiation patterns of individual elements are ignored or considered as common factors, the radiation intensity can be approximated as:

[0083] To isolate the influence of the unit radiation pattern and focus on array synthesis efficiency and array gain Defined as the orientation coefficient generated by the array factor:

[0084] The physical meaning of the above formula is the ratio of the radiation intensity of the array in the direction of maximum radiation to the average radiation intensity. The array gain only characterizes the spatial synthesis gain / directivity contribution brought about by the array factor.

[0085] This application introduces relative gain. As an evaluation metric, relative gain is defined as the array gain with phase perturbation present. Compared to the ideal array gain under undisturbed conditions The ratio (usually expressed in dB):

[0086] This metric reflects the degree of performance degradation caused by phase error.

[0087] When array element phase control is achieved through timing synchronization, timing error This will introduce a phase error:

[0088] For example: if f =24kHz, =100ns, then

[0089] It can meet the phase accuracy requirements of array spatial synthesis.

[0090] Because the wavelength in the Very Low Frequency (VLF) band is extremely long, antenna efficiency cannot be directly measured. This application uses the ground wave propagation formula to inversely deduce the efficiency. For the radiated power of a single VLF cell, the radiated power P... r It can be approximated as:

[0091] E m Peak electric field strength (unit: V / m).

[0092] d: Measurement distance (unit: m, usually taken as 30km to meet far-field conditions and ignore the influence of Earth's curvature, and the ground attenuation is relatively small).

[0093] Extract the electric field strength E at a distance d mThe radiated power P can be calculated by using the formula. r Then the radiation efficiency is:

[0094] The core metric for distributed systems is equivalent radiated power. For N units, the total equivalent radiated power is calculated as follows:

[0095] P0: Transmit power of a single unit.

[0096] Radiation efficiency of a single unit.

[0097] The array synthesis gain after considering phase perturbation is taken into account.

[0098] Given the randomness of wind fields, this application assumes phase perturbation. Modeled as having a mean of 0 and a standard deviation of normal distribution random variables, i.e. .in The standard deviation of the phase error is a key parameter for measuring the severity of environmental conditions.

[0099] For a given standard deviation Generate M sets of random phase perturbation vectors And calculate the relative gain samples for each group:

[0100] Sort the calculated M relative gain values ​​in ascending order:

[0101] The cumulative probability (CDF) of the k-th sorted value is:

[0102] Based on this, a cumulative distribution function (CDF) curve is plotted. The relative gain corresponding to a cumulative probability of 0.5 is called the median, and the median value (0.5) is extracted. Change (e.g., 0) o Up to 180 o And calculate each The median of the phase perturbation standard deviation can be used to obtain the mapping curve of "phase perturbation standard deviation - relative gain median".

[0103] The distributed very low frequency (VLF) transmission system radiation performance evaluation method provided in this application has extremely high survivability and resilience. It adopts a distributed architecture, so single-point damage does not lead to system paralysis or is no longer fatal, but only causes a slight decrease in power, completely solving the problem of "easy system-wide paralysis" of fixed stations. It can break through the power limit of mobile platforms and achieve an equivalent radiation power of 2000kW, which is difficult for mobile platforms to reach, through coherent synthesis of 16 or more elements, with performance comparable to large fixed stations. It can provide quantitative design guidance and proposes for the first time a Monte Carlo-based phase perturbation evaluation system, providing clear electromagnetic index constraints for UAV flight control stability and wind resistance design.

[0104] The following is a specific embodiment of the radiation performance evaluation method for the distributed very low frequency transmission system provided in this application. This embodiment describes how to evaluate the performance of the above system in an actual wind field and determine the wind resistance index of the UAV.

[0105] Step 1: Aerodynamic-Electromagnetic Coupling Modeling The ambient wind speed was set to 10 m / s. Computational fluid dynamics software was used to simulate the steady-state shape of a 1500 m long antenna cable under wind load. The cable exhibited a catenary or more complex curved shape. This physical displacement is the root cause of phase errors.

[0106] Step 2: Setting phase perturbation parameters Although the wind speed appears constant, gusts and the slight movements of drones cause the cables to vibrate in real time. The phase change caused by this vibration is modeled as a zero-mean Gaussian distribution.

[0107] Set the standard deviation of the phase error to be evaluated. The range is 0 o Up to 180 o .

[0108] Step 3: Monte Carlo simulation loop Set the Monte Carlo sample size M = 100. For each Values ​​(e.g.) =45 o ): 1. Using a computer random number generator, generate 16 numbers that follow the order of... random phase value .

[0109] 2. Substitute these values ​​into the formula to calculate the array factor.

[0110] 3. Calculate the array gain for this sampling by integrating the formula. .

[0111] 4. Repeat the above process 100 times to obtain 100 gain samples.

[0112] Step 4: Result Analysis and Design Threshold Determination Perform statistical analysis on the simulation data: when =50 o At that time, the median of the relative gain was -3dB.

[0113] This means that if the drone flight control system can control the cable phase jitter within a standard deviation of 50... o Within this range, there is a 50% probability that the system's output power is greater than [a certain value]. .

[0114] To ensure the system has a megawatt-level radiation capability (>1000kW), the design requirements necessitate limiting phase error. This quantitative indicator directly guides the selection of unmanned aerial vehicle (UAV) platforms and the development of tethered control algorithms.

[0115] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0116] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0117] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some service interface; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0118] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0119] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0120] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of embodiments of this disclosure upon considering the specification and practicing the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described herein. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

[0121] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0122] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A distributed unmanned aerial vehicle (UAV) towed very low frequency (VLF) transmission system, characterized in that, include: Multiple independent airborne transmission nodes, each of which includes an unmanned aerial vehicle platform, a very low frequency transmitting antenna unit towed by the platform, a tuning module, and a transmission module; A synchronization and control unit is used to provide each of the airborne transmission nodes with high-precision time synchronization signals and phase control commands; The multiple independent airborne transmitting nodes are arranged in the air according to a preset spatial geometry to form a distributed array. Each airborne transmitting node independently transmits very low frequency signals. The transmission phase of each node is adjusted by the synchronization and control unit to achieve spatial power synthesis, so as to form a coherently superimposed electromagnetic field radiation beam in the target direction. The system is configured to maintain the equivalent radiated power above a preset threshold under conditions of phase disturbance caused by mechanical deformation of the very low frequency transmitting antenna element due to environmental wind load.

2. The distributed UAV-towed very low frequency transmission system as described in claim 1, characterized in that, The synchronization and control unit uses the enhanced Loland system as the master clock source and the global satellite navigation system as the backup clock source.

3. The distributed UAV-towed very low frequency transmission system as described in claim 1, characterized in that, The very low frequency transmitting antenna unit is used as a radiator and also as a tether cable for the UAV platform. The lower end of the cable is connected to a tuning unit and a grounding device. The grounding device includes multiple grounding wires arranged radially.

4. The distributed UAV towed very low frequency transmission system as described in claim 1, characterized in that, The attitude control accuracy of the unmanned aerial vehicle platform is configured such that, at a predetermined wind speed, the standard deviation of the phase disturbance caused by cable deformation remains within the threshold range required to maintain the effective radiated power of the system.

5. A method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system, based on the distributed unmanned aerial vehicle (UAV) towed VLF transmission system as described in any one of claims 1-4, characterized in that, Includes the following steps: Step S1: Establish a theoretical model of the distributed transmission array, which includes multiple antenna elements towed by the UAV flight platform; Step S2: Construct a phase disturbance statistical model for the antenna element. The phase disturbance statistical model is used to characterize the signal phase deviation caused by the deformation of the dragging cable due to environmental load. Step S3: Based on the set phase error standard deviation, generate multiple sets of random phase samples that conform to the phase perturbation statistical model using the Monte Carlo method; Step S4: For each set of random phase samples, calculate the array relative gain of the distributed transmission array; Step S5: Perform statistical analysis on the calculated relative gains of multiple arrays, generate the cumulative distribution function, and establish a quantitative mapping relationship between the standard deviation of phase error and the array radiation performance index.

6. The method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system as described in claim 5, characterized in that, The specific steps of constructing the phase perturbation statistical model for the antenna element include: The phase perturbation of the antenna element is assumed to follow a zero-mean Gaussian normal distribution; The phase perturbation The probability density function is determined by the set standard deviation. Decide.

7. The method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system as described in claim 5, characterized in that, The specific steps for calculating the relative gain of the distributed transmission array are as follows: Define array gain The directional coefficients are contributed solely by the array factor; Calculation in the presence of phase perturbation The gain of the disturbed array at that time; Calculate the ideal array gain without phase perturbation; The ratio of the disturbed array gain to the ideal array gain is taken as the array relative gain.

8. The method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system as described in claim 7, characterized in that, The array factor The calculation formula is: Where N is the number of antenna elements, I n h is the current amplitude. n For effective height, For spatial phase difference, The excitation phase used for beam pointing control, For random phase perturbation, j It is the imaginary unit.

9. The method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system as described in claim 5, characterized in that, The establishment of the quantization mapping relationship includes: Iterate through different phase error standard deviation values; Extract the median of the array relative gain for each standard deviation; Determine the maximum standard deviation threshold of phase error allowed for the distributed emission array to maintain a predetermined equivalent radiated power at a specific confidence level.

10. The method for evaluating the radiation performance of a distributed very low frequency (VLF) transmission system as described in claim 5, characterized in that, It also includes calibrating the radiation efficiency of a single antenna element based on the ground wave propagation formula: The peak radiation field intensity E of a single antenna element is obtained at a preset distance range d. m ; Based on formula Obtain the radiated power P of a single antenna r ; The radiation efficiency of a single antenna is calculated based on the input power, and the total equivalent radiated power of the system is calculated by combining the array gain.

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