An air-ground channel dynamic modeling method and system for high-maneuverable unmanned aerial vehicles

Abstract

The application is suitable for the field of wireless communication technology, and provides a kind of air-ground channel dynamic modeling method and system for high maneuverable unmanned aerial vehicle, the method includes the following steps: constructing unmanned aerial vehicle dynamics model, and quantifying the antenna position offset caused by unmanned aerial vehicle attitude change;Based on terrain data and obstacle data, a three-dimensional digital scene model that restores the real scene is constructed, ray tracing method is used to simulate multipath propagation, and channel statistical characteristic parameters are extracted;A statistical model of unmanned aerial vehicle jitter characteristics is constructed, and the position offset of unmanned aerial vehicle under the action of jitter is quantified;According to unmanned aerial vehicle dynamics model, channel statistical characteristic parameters and the statistical model of unmanned aerial vehicle jitter characteristics, the channel model that fuses attitude dynamics and jitter effect is constructed by using analytical method.The method solves the problem of how to fully consider attitude dynamics and jitter effect to accurately model channel characteristics and quantify key parameters in unmanned aerial vehicle communication, and has high applicability to complex and variable unmanned aerial vehicle communication scenarios.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and in particular relates to a method and system for dynamic modeling of air-to-ground channels for highly maneuverable unmanned aerial vehicles (UAVs). Background Technology

[0002] Currently, the widely deployed 5G technologies are insufficient to meet the demands of emerging services for existing communication performance. Next-generation mobile communication systems will extend to natural spaces such as space, sky, and land, achieving ubiquitous connectivity with full-domain intelligence. Unmanned aerial vehicles (UAVs), as small aircraft, play a crucial role in achieving global, three-dimensional, and deep 6G air-space coverage. The UAV communication network is a vital component of the UAV system; it is the neural network enabling UAVs to communicate externally, facilitating information exchange between UAVs or between UAVs and other receiving stations, thus meeting the information transmission needs of the UAV platform. The UAV air-to-ground channel model reflects the propagation patterns of wireless signals in specific communication scenarios and serves as an important reference for UAV communication network planning and system design. As UAV communication scenarios become increasingly widespread, higher demands are placed on the universality, accuracy, and complexity of UAV channel models.

[0003] To efficiently and reliably design and evaluate the performance of UAV wireless communication systems, it is crucial to accurately characterize the wireless propagation channel using appropriate methods, thereby establishing a reliable, accurate, and easy-to-use UAV communication channel model. When designing, simulating, and optimizing wireless communication systems, a mathematical description of the wireless propagation channel is used, and the complex and ever-changing channel is abstracted to obtain a channel model. However, compared to traditional terrestrial communication channels such as cellular and vehicle-mounted communications, UAV air-to-ground wireless communication channels have their unique characteristics, mainly reflected in:

[0004] 1. Significantly high dynamics: The high-speed movement, attitude angle changes, and random jitter of UAVs cause the distance, relative speed, and propagation path between the transmitter and receiver to change rapidly over time, resulting in strong time-varying characteristics of channel parameters, which poses a significant challenge to channel stability.

[0005] 2. Complex propagation environment: UAVs fly at extremely wide altitudes, covering both low and high altitudes. This means their propagation paths may simultaneously include line-of-sight (LoS), non-line-of-sight (NLoS), and reflection and scattering paths from ground structures, vegetation, water surfaces, etc. Furthermore, the proportion and attenuation characteristics of these paths vary significantly in different flight environments, increasing the complexity of channel modeling.

[0006] 3. Prominent Three-Dimensional Spatial Characteristics: Unlike terrestrial communication, which primarily relies on two-dimensional planar propagation, UAV air-to-ground channels involve three-dimensional spatial issues. Furthermore, changes in UAV attitude can alter the directivity of antenna gain. Therefore, the channel fading characteristics in the three-dimensional angular domain must be fully considered during modeling to accurately characterize the channel.

[0007] Currently, existing models simplify UAVs into point masses for analysis, focusing only on the position and trajectory of their center of mass, ignoring the direct impact of UAV attitude changes and random jitter on the channel. This results in insufficient model accuracy, making it difficult to meet the design and optimization requirements of highly maneuverable UAV communication systems. Summary of the Invention

[0008] The purpose of this invention is to provide a dynamic modeling method for air-to-ground communication channels for highly maneuverable unmanned aerial vehicles (UAVs), aiming to solve the aforementioned technical problems.

[0009] This invention is implemented as follows: a dynamic modeling method for air-to-ground communication channels for highly maneuverable unmanned aerial vehicles (UAVs), comprising the following steps:

[0010] Construct a dynamic model of the UAV and quantify the antenna position offset caused by changes in UAV attitude;

[0011] Based on the collected terrain and obstacle data, a three-dimensional digital scene model that recreates the real scene is constructed.

[0012] Based on a three-dimensional digital scene model, ray tracing is used to simulate multipath propagation and extract channel statistical characteristic parameters.

[0013] Construct a statistical model of the drone's jitter characteristics and quantify the drone's positional shift under jitter.

[0014] Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, an analytical method is used to construct a channel model that integrates attitude dynamics and jitter effects.

[0015] Furthermore, the steps for constructing a UAV dynamics model and quantifying the antenna position offset caused by changes in UAV attitude include:

[0016] The basic physical parameters of the UAV are set as physical constraints. The physical constraints are input and combined with real-time IMU data. The discretized Euler integral method is used to establish the dynamic equations. The rotation matrix is ​​used to realize the force and torque conversion between the machine system and the inertial frame. The dynamic equations are iteratively updated to complete the complete mapping from control input to global motion trajectory. This realizes the UAV dynamic modeling that combines hard constraints of physical parameters with soft feedback of real-time state, and obtains the UAV dynamic model.

[0017] Based on the attitude data output by the UAV dynamics model, a position offset model caused by the UAV attitude is established. The position offset caused by the attitude angle is converted into pitch and azimuth angles in the ground coordinate system through the attitude matrix, and the antenna position offset is quantified.

[0018] Furthermore, the dynamic equation is:

[0019] ;

[0020] In the formula, This represents the angular velocity of the UAV at time t in the body coordinate system. Let J represent the roll, pitch, and yaw angles of the body coordinate system relative to the inertial coordinate system at time t, where J is the moment of inertia matrix and W is the angular velocity transformation matrix. This represents the velocity of the UAV at time t in the ground coordinate system. This represents the position of the UAV at time t in the ground coordinate system; and These represent the control torque and total tension in the body coordinate system, respectively. The matrix represents the rotation of the body coordinate system, and m and g represent the mass and gravitational acceleration of the UAV.

[0021] The position offset model caused by the drone's attitude is as follows:

[0022] ;

[0023] In the formula, This represents the position offset caused by the drone's attitude. and These are the azimuth and elevation angles, respectively. and This represents the displacement caused by the swaying at that angle; the models for the azimuth and pitch angles are as follows:

[0024] ;

[0025] In the formula, , and These are the pitch angle, roll angle, and yaw angle output by the UAV dynamics model, respectively.

[0026] Furthermore, the steps of constructing a 3D digital scene model that recreates the real scene based on the collected terrain and obstacle data specifically include:

[0027] Digital analysis of real-world scenes is performed; specifically, for elevation maps, key information is extracted through algorithms: elevation values ​​are converted into vertex heights in three-dimensional space, geographic coordinates are mapped into position parameters in a digital coordinate system, and the physical characteristics of real terrain are transformed into computable geometric data to form an initial terrain framework and obtain a terrain grid.

[0028] The parsed real-world scene data is classified, modeled, and fused to obtain obstacle models. For static obstacles, geometric models are constructed using their size and coordinate data. For dynamic obstacles, positional change parameters over time are associated to form digital volumes with temporal information. These obstacle models are aligned with the terrain grid according to their real-world spatial locations, and collision detection algorithms are used to ensure that their spatial relationships conform to physical logic, thus avoiding spatial conflicts in the digital scene.

[0029] Achieving model standardization and scene integration: Converting terrain meshes and obstacle models into the universal OBJ format, unifying their coordinate system and data structure, using vertex coordinates to record spatial positions, using texture mapping to restore surface materials, and using normal vectors to define surface orientation, ultimately achieving digital mapping of the real scene and obtaining a 3D digital scene model.

[0030] Furthermore, based on the three-dimensional digital scene model, the steps of simulating multipath propagation using ray tracing and extracting channel statistical characteristic parameters specifically include:

[0031] Configure ray emission and scene association: Set the three-dimensional coordinates of the signal source and receiver in the three-dimensional digital scene model, set the basic parameters, and define the ray propagation angle range and maximum tracking distance based on the distribution characteristics of scatterers in the scene to ensure that the ray can cover the area where all potential scatterers are located; the basic parameters include the frequency of the transmitted signal, the initial power, and the antenna type.

[0032] The ray tracing algorithm is initiated: Based on the geometric properties of the terrain mesh, obstacles, and scatterers in the 3D digital scene model, and the corresponding physical properties of their materials, the interaction point between the ray and the scatterer is located using a collision detection algorithm. Combining the scattering angle, incident power, and scatterer material characteristics, the power attenuation of each scattering path is derived using scattering theory formulas. The propagation time of the ray from the emission source to the scatterer and then to the receiving point is recorded simultaneously to determine the time delay parameters of the scattering path. The azimuth and elevation angles of the ray incident on the scatterer, as well as the scattering exit angle, are extracted through vector calculations to form a complete set of angle parameters. The geometric properties include dimensions, spatial coordinates, and surface normal vectors; the corresponding physical properties of the material include the scattering coefficient and dielectric constant.

[0033] Channel statistical characteristic parameters are aggregated as follows: First, the loss power, delay, and angle data collected from all scattering paths are systematically classified and organized. After obtaining the statistical sample set, the pitch angle, yaw angle, scatterer loss, and delay parameters in the sample set are first organized, and outliers with too low energy or invalidity are removed to ensure data validity. The mean and variance of each of the above parameters are calculated using statistical tools. For delay, the root mean square delay spread parameter is also calculated. At the same time, frequency histograms of each parameter are plotted. Based on the histograms, the probability density function is fitted using the maximum likelihood estimation method, and the cumulative distribution function is obtained by integrating the probability density function. Finally, the fitted probability density function and cumulative distribution function are compared and verified with typical channel models to determine the optimal fitting parameters, thereby obtaining the final channel statistical characteristics.

[0034] Furthermore, a statistical model of the drone's jitter characteristics is constructed, and the steps for quantifying the drone's positional shift under jitter are detailed, including:

[0035] Statistical models are used to quantify the azimuth and pitch angle shifts caused by UAV jitter, and then the position change caused by the UAV is calculated based on geometric relationships. UAV jitter includes internal jitter caused by rotor vibration and external jitter caused by external factors. The position shift of the UAV under jitter is modeled as follows:

[0036] ;

[0037] In the formula, The positional offset of the drone under jitter. This refers to the positional offset of the drone due to internal jitter. This represents the positional offset of the drone under external jitter.

[0038] Furthermore, regarding internal vibration, based on the structural parameters and dynamic characteristics of the UAV, and combined with historical vibration data, the periodic variation law of the azimuth and pitch angles caused by the rotor mechanical motion is described by the amplitude, frequency, and phase of a sine function. The specific model is as follows:

[0039] ;

[0040] In the formula, and These are the azimuth and pitch angles generated by the drone's shaking due to internal jitter. and This is the displacement caused by the swaying at that angle;

[0041] ;

[0042] In the formula, It is the internal jitter frequency.

[0043] Furthermore, regarding external jitter, influencing factors include wind speed fluctuations and airflow disturbances. These factors exhibit a random distribution, while the real-time compensation mechanism of the UAV flight control system ensures that the changes in azimuth and pitch angles statistically follow a normal distribution with zero mean and stable variance. The specific model is as follows:

[0044] ;

[0045] In the formula, and These are the azimuth and pitch angles generated by the drone's shaking under external vibrations. and This represents the displacement caused by the shaking at that angle.

[0046] Furthermore, based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the steps for constructing a channel model that integrates attitude dynamics and jitter effects using analytical methods specifically include:

[0047] The analytical expression for the time-varying characteristics of the channel is derived using analytical methods. The channel impulse response formula is as follows:

[0048] ;

[0049] In the formula, H LoS and H NLoS These are the impulse response matrices for the direct and indirect beam paths, respectively. The transmitter uses a P-row, Q-column two-dimensional antenna array containing P*Q transmitting antennas; the receiver uses an A-row, B-column two-dimensional antenna array containing A*B receiving antennas. Therefore, each matrix contains P*Q*A*B elements, as detailed below:

[0050] ;

[0051] ;

[0052] In the formula, and Let be the channel impulse responses of the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively, expressed by the following formulas:

[0053] ;

[0054] ;

[0055] In the formula, and , respectively, are the antenna gains along the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna; and Let be the direct and indirect large-scale fading from the qp-th transmitting antenna to the ab-th receiving antenna, respectively. and These are the signal phase change factors for the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively.

[0056] Next, the parameters constituting the channel impulse response are described separately. In the UAV air-to-ground communication system, the modeling of antenna gain needs to comprehensively consider the influence of platform dynamic characteristics and hardware losses. The effective aperture of the antenna is the equivalent area that the antenna can actually receive or transmit electromagnetic waves. Its actual effectiveness will be directionally attenuated due to UAV attitude deviation and high-frequency random jitter. When the antenna main lobe deviates from the target direction, the equivalent effective aperture can be regarded as the projection of the antenna physical aperture on the signal pointing direction, forming a gain attenuation factor related to the attitude error angle. At the same time, hardware losses correct the antenna gain through a loss factor independent of spatial pointing. The attitude deviations include roll, pitch, and yaw angle changes.

[0057] ;

[0058] ;

[0059] The total antenna gain can be expressed as the product of the ideal gain, the effective aperture efficiency correction factor caused by attitude and jitter, and the hardware loss factor. The specific model is as follows:

[0060] ;

[0061] in, Indicates the wavelength of electromagnetic waves. and These are the time delays for direct and indirect beams, respectively. and It is the hardware loss of the transmitting antenna qp and the receiving antenna ab, which follows a chi-square distribution; and The effective apertures of the transmitting and receiving antennas under direct illumination conditions are given by the following formula:

[0062] ;

[0063] ;

[0064] In the formula, It is the position of the transmitter at time t. It is the position of the receiver at time t. Indicates the spacing between the antenna elements at the transmitting end. Indicates the spacing between antenna elements at the receiving end;

[0065] Immediately afterwards, and The effective apertures of the transmitting and receiving antennas under non-direct illumination conditions are given by the following formula:

[0066] ;

[0067] in, The physical area of ​​the transmitting QP antenna. This represents the mutual coupling matrix of the transmitting antenna. The physical area of ​​the receiver's ab antenna. This represents the mutual coupling matrix of the receiving antenna. and They are time t and t+ respectively. Consider the non-direct path distance of antenna qp-ab after jitter offset;

[0068] ;

[0069] ;

[0070] in and Representing t and scattering body at time Location;

[0071] Large-scale fading is used to characterize the slowly varying characteristics of signal strength in wireless communication over a large spatial and environmental range, including path loss and shadow fading (SH). The formulas for direct-path large-scale fading and indirect-path large-scale fading are as follows:

[0072] ;

[0073] ;

[0074] Path loss originates from the signal propagation distance and the propagation environment, causing energy to attenuate with distance or complex scenarios. It determines the basic signal coverage and received strength. Quantized attitude and jitter offsets are incorporated into the path loss calculation, specifically the path loss of the direct path. Path loss of non-direct path The formula is expressed as follows:

[0075] ;

[0076] ;

[0077] Where c=2 is the free space loss model; c=3~5 is the urban environment; and These are the direct and indirect trajectory lengths after incorporating quantized attitude and jitter parameters, respectively, expressed by the following formulas:

[0078] ;

[0079] ;

[0080] In the formula, This represents the position offset caused by the drone's attitude.

[0081] When radio waves encounter obstacles in their propagation path, a shadow is formed, causing a slow change in the median signal strength. This phenomenon is known as the shadowing effect. Statistically, it follows a log-normal distribution, and its probability density function can be expressed as:

[0082] ;

[0083] in, and These are the mean and variance of shadow fading, respectively.

[0084] Next, we model the small-scale parameters of the channel. The small-scale parameters caused by jitter and attitude are represented by the position offsets modeled in the above statistical model. Here, we only describe the influence caused by velocity. Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the small-scale parameter model of the UAV is obtained as follows:

[0085] ;

[0086] ;

[0087] The Doppler frequency shift of the channel caused by the direct trajectory velocity is modeled as follows:

[0088] ;

[0089] in, and These are the velocities of the receiving and transmitting ends, respectively, and u is a unit vector representing the signal propagation direction. The specific formula is as follows:

[0090] ;

[0091] The Doppler frequency shift formula for the channel caused by non-direct path velocity is modeled as follows:

[0092] ;

[0093] ;

[0094] in, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: Similarly, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: , The angle between the signal propagation direction and the velocity direction of the transmitting end. It is the angle between the signal propagation direction and the reference direction of the receiving antenna array.

[0095] Another objective of this invention is to provide an air-to-ground channel dynamic modeling system for highly maneuverable unmanned aerial vehicles (UAVs), used to implement the aforementioned air-to-ground channel dynamic modeling method, comprising:

[0096] The dynamics model building module is used to build the dynamics model of the UAV and quantify the antenna position offset caused by changes in the UAV's attitude.

[0097] The scene model building module is used to build a 3D digital scene model that recreates the real scene based on the collected terrain and obstacle data.

[0098] The channel statistical characteristic parameter extraction module is used to simulate multipath propagation based on a three-dimensional digital scene model using the ray tracing method and extract channel statistical characteristic parameters.

[0099] The statistical model building module is used to build a statistical model of the drone's jitter characteristics and quantify the drone's positional offset under jitter.

[0100] The channel model construction module is used to construct a channel model that integrates attitude dynamics and jitter effects using analytical methods, based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics.

[0101] This invention provides a dynamic air-to-ground channel modeling method for highly maneuverable unmanned aerial vehicles (UAVs). This method is based on the UAV attitude-jitter coupling effect. The overall approach establishes a UAV dynamic model and a 3D scene digitization platform, extracts channel statistical characteristics using ray tracing, and statistically models UAV jitter characteristics to construct a channel model combining attitude and jitter effects. It then uses analytical methods to derive the analytical expression for the time-varying channel characteristics and quantifies the key channel parameters including the attitude-jitter coupling effect. This method solves the problem of how to fully consider attitude dynamics and jitter effects in UAV communication to accurately model channel characteristics and quantify key parameters, and it has high applicability to complex and ever-changing UAV communication scenarios. Attached Figure Description

[0102] Figure 1 This is a flowchart illustrating the air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles (UAVs) provided in an embodiment of the present invention.

[0103] Figure 2 A schematic diagram of a channel model for highly maneuverable unmanned aerial vehicles provided in an embodiment of the present invention.

[0104] Figure 3 This is a schematic diagram of the air-to-ground channel dynamic modeling system architecture for highly maneuverable unmanned aerial vehicles (UAVs) provided in an embodiment of the present invention.

[0105] Figure 4 This is a channel impulse response diagram obtained through simulation in an embodiment of the present invention. Detailed Implementation

[0106] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0107] like Figure 1 and Figure 2 As shown, in one embodiment of the present invention, a method for dynamic modeling of air-to-ground channels for highly maneuverable unmanned aerial vehicles (UAVs) is provided, which includes the following steps:

[0108] S100. Construct a dynamic model of the UAV and quantify the antenna position offset caused by changes in UAV attitude.

[0109] S200: Based on the collected terrain and obstacle data, construct a three-dimensional digital scene model that recreates the real scene;

[0110] S300: Based on a three-dimensional digital scene model, the ray tracing method is used to simulate multipath propagation and extract channel statistical characteristic parameters.

[0111] S400, construct a statistical model of the drone's shaking characteristics, and quantify the drone's positional shift under shaking effects;

[0112] S500: Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, an analytical method is used to construct a channel model that integrates attitude dynamics and jitter effects.

[0113] In this embodiment of the invention, the channel modeling process is as follows: First, the basic physical parameters of the UAV are set and the antenna parameters are configured. A UAV dynamic model based on Newtonian mechanics is constructed, and the three-dimensional displacement caused by attitude angle changes is quantified through Euler angle decomposition and coordinate transformation. Then, ray tracing simulation is carried out for typical urban scenarios. Based on geometric optics and uniform diffraction theory, statistical characteristics such as time delay spread and angle spread of multipath components are extracted. Subsequently, the jitter displacement of the UAV is statistically modeled based on stochastic process theory. Finally, the attitude offset output by the dynamic model, the scene statistical characteristics extracted by ray tracing, and the time-varying parameters of jitter modeling are integrated. The analytical expression of the time-varying characteristics of the channel is derived using analytical methods. A channel model that integrates UAV attitude dynamics and jitter effects is constructed. Finally, the full-link mapping from physical scene to mathematical model is completed, realizing the air-to-ground channel modeling of highly maneuverable UAVs.

[0114] The air-to-ground channel modeling method for highly maneuverable UAVs proposed in this invention reduces computational overhead during the modeling process by dynamically modeling attitude changes and statistically modeling the time-varying characteristics of the channel caused by jitter effects, thus providing accurate channel model support for evaluating system transmission performance and optimizing transmission quality.

[0115] In a preferred embodiment of the present invention, the step of constructing a UAV dynamics model and quantifying the antenna position offset caused by changes in UAV attitude, i.e., step S100, specifically includes:

[0116] S110. Set the basic physical parameters of the UAV as physical constraints, input the physical constraints, combine the real-time data collected by the inertial measurement unit (IMU), establish the dynamic equation using the discretized Euler integral method, use the rotation matrix to realize the force and torque conversion between the machine system and the inertial system, iteratively update the dynamic equation, thereby completing the complete mapping from control input to global motion trajectory, realizing the UAV dynamic modeling that combines hard constraints of physical parameters with soft feedback of real-time state, and obtaining the UAV dynamic model;

[0117] S120. Based on the attitude data output by the UAV dynamics model, establish a position offset model caused by the UAV attitude. Convert the position offset caused by the attitude angle into pitch and azimuth angles in the ground coordinate system through the attitude matrix, and quantify the antenna position offset.

[0118] In step S110, the UAV dynamics model is achieved by using physical constraints such as the actual mass of the UAV, the moment of inertia matrix of the airframe, the propeller thrust coefficient and the propeller torque coefficient, as well as data such as the airframe angular velocity and initial attitude angle acquired in real time by the IMU, as input variables for UAV dynamics modeling.

[0119] Specifically, the dynamic equations used in the modeling are:

[0120] ;

[0121] In the formula, This represents the angular velocity of the UAV at time t in the body coordinate system. Let J represent the roll, pitch, and yaw angles of the body coordinate system relative to the inertial coordinate system at time t, where J is the moment of inertia matrix and W is the angular velocity transformation matrix. This represents the velocity of the UAV at time t in the ground coordinate system. This represents the position of the UAV at time t in the ground coordinate system; and These represent the control torque and total tension in the body coordinate system, respectively. The matrix represents the rotation of the body coordinate system, and m and g represent the mass and gravitational acceleration of the UAV.

[0122] In step S120, based on the above UAV dynamics model, the position offset caused by the UAV attitude angle is converted into pitch and azimuth angles in the ground coordinate system using the attitude matrix. The position offset model caused by the UAV attitude is as follows:

[0123] ;

[0124] In the formula, This represents the position offset caused by the drone's attitude. and These are the azimuth and elevation angles, respectively. and This represents the displacement caused by the swaying at that angle; the azimuth and pitch angle models are as follows:

[0125] ;

[0126] In the formula, , and These are the pitch angle, roll angle, and yaw angle output by the UAV dynamics model, respectively.

[0127] In a preferred embodiment of the present invention, the step of constructing a three-dimensional digital scene model that recreates the real scene based on the collected terrain data and obstacle data, namely step S200, specifically includes:

[0128] S210. Perform digital analysis on real-world scenes; among them, for elevation maps of typical urban scenes, extract key information through algorithms: convert elevation values ​​into vertex heights in three-dimensional space, map geographic coordinates into position parameters in a digital coordinate system, transform the physical characteristics of real terrain into computable geometric data, form an initial terrain framework, and obtain a terrain grid.

[0129] S220. Classify, model, and fuse the parsed real-world scene data to obtain obstacle models. For static obstacles, construct geometric models using their size and coordinate data. For dynamic obstacles, associate positional change parameters with time dimension to form digital volumes with temporal information. Align these obstacle models with the terrain grid according to their real-world spatial locations and use collision detection algorithms to ensure that their spatial relationships conform to physical logic and avoid spatial conflicts in the digital scene.

[0130] S230. Achieve model standardization and scene integration: Convert terrain meshes and obstacle models into a universal OBJ format, unify their coordinate system and data structure, use vertex coordinates to record spatial positions, use texture mapping to restore surface materials, use normal vectors to define surface orientation, and finally achieve digital mapping of real scenes to obtain three-dimensional digital scene models.

[0131] In a preferred embodiment of the present invention, the step of simulating multipath propagation using ray tracing based on a three-dimensional digital scene model and extracting channel statistical characteristic parameters, namely step S300, specifically includes:

[0132] S310. Configure ray emission and scene association: Set the three-dimensional coordinates of the signal source and receiver in the three-dimensional digital scene model, set the basic parameters, and define the ray propagation angle range and maximum tracking distance based on the distribution characteristics of scatterers in the scene to ensure that the ray can cover the area where all potential scatterers are located; the above basic parameters include, but are not limited to, the frequency of the transmitted signal, the initial power, and the antenna type.

[0133] S320. Begin ray tracing algorithm: Based on the geometric properties of the terrain mesh, obstacles, and scatterers in the 3D digital scene model, and the physical properties of their corresponding materials, locate the interaction point between the ray and the scatterer using a collision detection algorithm; combine the scattering angle, incident power, and scatterer material characteristics, derive the power attenuation of each scattering path according to scattering theory formulas; simultaneously record the propagation time of the ray from the emission source to the scatterer and then to the receiving point to determine the time delay parameter of the scattering path; extract the azimuth and elevation angles of the ray incident on the scatterer and the exit angle after scattering through vector calculation to form a complete set of angle parameters; the aforementioned geometric properties include, but are not limited to, dimensions, spatial coordinates, and surface normal vectors; the aforementioned physical properties of the material include, but are not limited to, scattering coefficient and dielectric constant;

[0134] S330. Aggregate channel statistical characteristic parameters: First, systematically classify and organize the loss power, delay, and angle data collected from all scattering paths. After obtaining the statistical sample set, first organize the parameters such as pitch angle, yaw angle, scatterer loss, and delay in the sample set, and remove outliers with too low energy or invalid values ​​to ensure data validity. Calculate the mean and variance of each parameter using statistical tools. For delay, the root mean square delay extension parameter also needs to be calculated. At the same time, draw the frequency histogram of each parameter. Based on the histogram, use the maximum likelihood estimation method to fit the probability density function (PDF), and obtain the cumulative distribution function (CDF) by integrating the probability density function. Finally, compare and verify the fitted probability density function and cumulative distribution function with typical channel models to determine the optimal fitting parameters, thereby obtaining the final channel statistical characteristics.

[0135] In this embodiment of the invention, based on the three-dimensional digital scene model constructed in step S200, the electromagnetic wave propagation path in the scene is simulated and calculated using the ray tracing method to construct a ray tracing model (i.e., RT model), and then the statistical characteristics of the channel (i.e., channel statistical features) are extracted; wherein, the channel statistical features include key parameters such as the power distribution of multipath components, time delay spread, and angle spread.

[0136] In practical applications, a 3D digital scene model constructed based on real urban scenarios includes 3D geometric structures such as high-rise buildings, streets, green belts, streetlights, and billboards, as well as dielectric constants, conductivity, and roughness parameters of materials such as concrete walls, glass curtain walls, asphalt pavements, and vegetation. When simulating the propagation path of electromagnetic waves using the ray tracing method, an initial ray beam is first generated from the UAV's antenna at preset angular intervals, while simultaneously setting the termination condition for ray propagation: the maximum number of reflections, diffractions, and scatterings is three. Subsequently, the propagation process of each ray in the scene is tracked: when specular reflection occurs on the high-rise building wall, the power loss is calculated based on the Fresnel reflection coefficient; when diffraction occurs at building corners and streetlight pole edges, the uniform diffraction theory (UTD) is used to calculate diffraction loss; when scattering occurs at green belt vegetation and rough walls, rays are generated in conjunction with the surface roughness model, and their power attenuates according to the scattering angle distribution. Then, based on the effective multipath components obtained from the above simulation, key parameters are extracted to calculate statistical characteristics: the scattered power distribution is calculated by statistically analyzing the received power of all multipaths, and the cumulative power distribution function is plotted; the delay spread is calculated by first calculating the propagation delay of each multipath, and then calculating the average delay and root mean square delay spread with the power of each multipath as the weight; the angle spread is calculated by decomposing the azimuth and elevation angles of each ray for the angle of arrival at the receiver, statistically analyzing the probability density function of the angle samples, and finally obtaining the root mean square angle spread through the second moment calculation, thus completing the extraction of channel statistical characteristics in urban scenarios.

[0137] In a preferred embodiment of the present invention, the step of constructing a statistical model of the drone's jitter characteristics and quantifying the drone's positional offset under jitter, specifically step S400, includes:

[0138] Statistical models are used to quantify the azimuth and pitch angle shifts caused by UAV jitter, and then the position change caused by the UAV is calculated based on geometric relationships. UAV jitter includes internal jitter caused by rotor vibration and external jitter caused by external factors. The position shift of the UAV under jitter is modeled as follows:

[0139] ;

[0140] In the formula, The positional offset of the drone under jitter. This refers to the positional offset of the drone due to internal jitter. This represents the positional offset of the drone under external jitter.

[0141] Specifically, regarding internal vibration, based on the structural parameters and dynamic characteristics of the UAV, and combined with historical vibration data, the periodic variation law of azimuth and pitch angles caused by mechanical motion such as rotors is described by the amplitude, frequency, and phase of a sine function. The specific model is as follows:

[0142] ;

[0143] In the formula, and These are the azimuth and pitch angles generated by the drone's shaking due to internal jitter. and This is the displacement caused by the swaying at that angle;

[0144] ;

[0145] In the formula, It is the internal jitter frequency.

[0146] In addition, external jitter factors include wind speed fluctuations and airflow disturbances. These factors are complex and independent, and wind speed fluctuations and airflow disturbances generally exhibit random distributions. However, the real-time compensation mechanism of the UAV flight control system ensures that the changes in azimuth and pitch angles statistically follow a normal distribution with zero mean and stable variance. The specific model is as follows:

[0147] ;

[0148] In the formula, and These are the azimuth and pitch angles generated by the drone's shaking under external vibrations. and This represents the displacement caused by the shaking at that angle.

[0149] like Figure 3 As shown, in a preferred embodiment of the present invention, the step of constructing a channel model that integrates attitude dynamics and jitter effects using an analytical method based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, i.e., step S500, specifically includes:

[0150] S510. Using analytical methods, derive the analytical expression for the time-varying characteristics of the channel. The channel impulse response formula is as follows:

[0151] ;

[0152] In the formula, H LoS and H NLoS These are the impulse response matrices for the direct and indirect beam paths, respectively. The transmitter uses a P-row, Q-column two-dimensional antenna array containing P*Q transmitting antennas; the receiver uses an A-row, B-column two-dimensional antenna array containing A*B receiving antennas. Therefore, each matrix contains P*Q*A*B elements, as detailed below:

[0153] ;

[0154] ;

[0155] In the formula, and Let be the channel impulse responses of the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively, expressed by the following formulas:

[0156] ;

[0157] ;

[0158] In the formula, and , respectively, are the antenna gains along the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna; and Let be the direct and indirect large-scale fading from the qp-th transmitting antenna to the ab-th receiving antenna, respectively. and These are the signal phase change factors for the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively.

[0159] S520. Next, the parameters constituting the channel impulse response will be described separately. In the UAV air-to-ground communication system, the modeling of antenna gain needs to comprehensively consider the influence of platform dynamic characteristics and hardware losses. The effective aperture of the antenna is the equivalent area that the antenna can actually receive or transmit electromagnetic waves. Its actual effectiveness will be directionally attenuated due to UAV attitude deviations and high-frequency random jitter. When the antenna main lobe deviates from the target direction, the equivalent effective aperture can be regarded as the projection of the antenna physical aperture on the signal pointing direction, forming a gain attenuation factor related to the attitude error angle. At the same time, hardware losses correct the antenna gain through a loss factor independent of spatial pointing. The aforementioned attitude deviations include, but are not limited to, roll, pitch, and yaw angle changes.

[0160] ;

[0161] ;

[0162] The total antenna gain can be expressed as the product of the ideal gain, the effective aperture efficiency correction factor caused by attitude and jitter, and the hardware loss factor. The specific model is as follows:

[0163] ;

[0164] in, Indicates the wavelength of electromagnetic waves. and These are the time delays for direct and indirect beams, respectively. and It is the hardware loss of the transmitting antenna qp and the receiving antenna ab, which follows a chi-square distribution; and The effective apertures of the transmitting and receiving antennas under direct illumination conditions are given by the following formula:

[0165] ;

[0166] ;

[0167] in, and Let qp and ab be the normal directions of the antenna, respectively. Here is the attitude transformation matrix for the UAV. and They are time t and t+ respectively. Consider the distance of antenna qp-ab after jitter offset;

[0168] ;

[0169] ;

[0170] In the formula, It is the position of the transmitter at time t. It is the position of the receiver at time t. Indicates the spacing between the antenna elements at the transmitting end. Indicates the spacing between antenna elements at the receiving end;

[0171] Immediately afterwards, and The effective apertures of the transmitting and receiving antennas under non-direct illumination conditions are given by the following formula:

[0172] ;

[0173] in, The physical area of ​​the transmitting QP antenna. This represents the mutual coupling matrix of the transmitting antenna. The physical area of ​​the receiver's ab antenna. This represents the mutual coupling matrix of the receiving antenna. and They are time t and t+ respectively. Consider the non-direct path distance of antenna qp-ab after jitter offset;

[0174] ;

[0175] ;

[0176] in, and Representing t and scattering body at time Location;

[0177] Large-scale fading is used to characterize the slowly varying characteristics of signal strength in wireless communication over a large spatial and environmental range, including path loss and shadow fading (SH). The formulas for direct-path large-scale fading and indirect-path large-scale fading are as follows:

[0178] ;

[0179] ;

[0180] Path loss originates from the signal propagation distance and the propagation environment, causing energy to attenuate with distance or complex scenarios. It determines the basic signal coverage and received strength. Quantized attitude and jitter offsets are incorporated into the path loss calculation, specifically the path loss of the direct path. Path loss of non-direct path The formula is expressed as follows:

[0181]

[0182] ;

[0183] Where c=2 is the free space loss model; c=3~5 is the urban environment; and These are the direct and indirect trajectory lengths after incorporating quantized attitude and jitter parameters, respectively, expressed by the following formulas:

[0184] ;

[0185] ;

[0186] In the formula, This represents the position offset caused by the drone's attitude.

[0187] When radio waves encounter obstacles such as rolling hills, buildings, and forests, forming a shadow region and causing a slow change in the median signal strength, this phenomenon is called the shadowing effect. Statistically, it follows a log-normal distribution, and its probability density function can be expressed as:

[0188] ;

[0189] in, and These are the mean and variance of shadow fading, respectively.

[0190] S540. Next, the small-scale parameters of the channel are modeled. The small-scale parameters caused by jitter and attitude are represented by the position offsets modeled in the above statistical model. Here, only the influence caused by velocity is described. Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the small-scale parameter model of the UAV is obtained as follows:

[0191] ;

[0192] ;

[0193] The Doppler frequency shift of the channel caused by the direct trajectory velocity is modeled as follows:

[0194] ;

[0195] in, and These are the velocities of the receiving and transmitting ends, respectively, and u is a unit vector representing the signal propagation direction. The specific formula is as follows:

[0196] ;

[0197] The Doppler frequency shift formula for the channel caused by non-direct path velocity is modeled as follows:

[0198] ;

[0199] ;

[0200] in, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: Similarly, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: , The angle between the signal propagation direction and the velocity direction of the transmitting end. It is the angle between the signal propagation direction and the reference direction of the receiving antenna array.

[0201] The time-domain graph of the channel impulse response (CIR) of the channel model obtained in practical applications according to the embodiments of the present invention is shown below. Figure 4 As shown, this channel is a time-varying fading channel, with prominent multipath effects and deep fading problems.

[0202] In another embodiment of the present invention, an air-to-ground channel dynamic modeling system for highly maneuverable unmanned aerial vehicles is also provided, for implementing the above-mentioned air-to-ground channel dynamic modeling method, comprising:

[0203] The dynamics model building module is used to build the dynamics model of the UAV and quantify the antenna position offset caused by changes in the UAV's attitude.

[0204] The scene model building module is used to build a 3D digital scene model that recreates the real scene based on the collected terrain and obstacle data.

[0205] The channel statistical characteristic parameter extraction module is used to simulate multipath propagation based on a three-dimensional digital scene model using the ray tracing method and extract channel statistical characteristic parameters.

[0206] The statistical model building module is used to build a statistical model of the drone's jitter characteristics and quantify the drone's positional offset under jitter.

[0207] The channel model construction module is used to construct a channel model that integrates attitude dynamics and jitter effects using analytical methods, based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics.

[0208] It should be noted that each of the above modules can be implemented as a computer program, which can run on a computer device. The computer device's memory can store the computer program that makes up each module, enabling the processor to execute each step of the above method.

[0209] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0210] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Furthermore, any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0211] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for dynamic modeling of air-to-ground communication channels for highly maneuverable unmanned aerial vehicles (UAVs), characterized in that, Includes the following steps: Construct a dynamic model of the UAV and quantify the antenna position offset caused by changes in UAV attitude; Based on the collected terrain and obstacle data, a three-dimensional digital scene model that recreates the real scene is constructed. Based on a three-dimensional digital scene model, ray tracing is used to simulate multipath propagation and extract channel statistical characteristic parameters. Construct a statistical model of the drone's jitter characteristics and quantify the drone's positional shift under jitter. Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, an analytical method is used to construct a channel model that integrates attitude dynamics and jitter effects. Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the steps for constructing a channel model that integrates attitude dynamics and jitter effects using analytical methods include: The analytical expression for the time-varying characteristics of the channel is derived using analytical methods. The channel impulse response formula is as follows: ； In the formula, H LoS and H NLoS These are the impulse response matrices for the direct and indirect beam paths, respectively. The transmitter uses a P-row, Q-column two-dimensional antenna array, containing P*Q transmitting antennas; the receiver uses an A-row, B-column two-dimensional antenna array, containing A*B receiving antennas. Therefore, each matrix contains P*Q*A*B elements, as detailed below: ； ； In the formula, and Let be the channel impulse responses of the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively, expressed by the following formulas: ； ； In the formula, and , respectively, are the antenna gains along the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna; and Let be the direct and indirect large-scale fading from the qp-th transmitting antenna to the ab-th receiving antenna, respectively. and These are the signal phase change factors for the direct and indirect paths from the qp-th transmitting antenna to the ab-th receiving antenna, respectively. The formulas for direct and indirect beam lengths are as follows: ； ； In the formula, and These are the direct and indirect trajectory lengths after adding quantized attitude and jitter parameters, respectively; The positional offset of the drone under jitter. It is the position of the transmitter at time t. It is the position of the receiver at time t. Indicates the spacing between the antenna elements at the transmitting end. Indicates the spacing between antenna elements at the receiving end; Represents the scattering body at time t Location; This represents the position offset caused by the drone's attitude.

2. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 1, characterized in that, The steps for constructing a UAV dynamics model and quantifying the antenna position offset caused by changes in UAV attitude include: The basic physical parameters of the UAV are set as physical constraints. The physical constraints are input and combined with real-time IMU data. The discretized Euler integral method is used to establish the dynamic equations. The rotation matrix is ​​used to realize the force and torque conversion between the machine system and the inertial frame. The dynamic equations are iteratively updated to complete the complete mapping from control input to global motion trajectory. This realizes the UAV dynamic modeling that combines hard constraints of physical parameters with soft feedback of real-time state, and obtains the UAV dynamic model. Based on the attitude data output by the UAV dynamics model, a position offset model caused by the UAV attitude is established. The position offset caused by the attitude angle is converted into pitch and azimuth angles in the ground coordinate system through the attitude matrix, and the antenna position offset is quantified.

3. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 2, characterized in that, The dynamic equation is: ； In the formula, This represents the angular velocity of the UAV at time t in the body coordinate system. Let J represent the roll, pitch, and yaw angles of the body coordinate system relative to the inertial coordinate system at time t, where J is the moment of inertia matrix and W is the angular velocity transformation matrix. This represents the velocity of the UAV at time t in the ground coordinate system. This represents the position of the UAV at time t in the ground coordinate system; and These represent the control torque and total tension in the body coordinate system, respectively. The matrix represents the rotation of the body coordinate system, and m and g represent the mass and gravitational acceleration of the UAV. The position offset model caused by the drone's attitude is as follows: ； In the formula, This represents the position offset caused by the drone's attitude. and These are the azimuth and elevation angles, respectively. and This represents the displacement caused by the swaying at that angle; the models for the azimuth and pitch angles are as follows: ； In the formula, , and These are the pitch angle, roll angle, and yaw angle output by the UAV dynamics model, respectively.

4. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 1, characterized in that, The steps for constructing a 3D digital scene model that recreates the real scene based on the collected terrain and obstacle data specifically include: Digital analysis of real-world scenes is performed; specifically, for elevation maps, key information is extracted through algorithms: elevation values ​​are converted into vertex heights in three-dimensional space, geographic coordinates are mapped into position parameters in a digital coordinate system, and the physical characteristics of real terrain are transformed into computable geometric data to form an initial terrain framework and obtain a terrain grid. The parsed real-world scene data is classified, modeled, and fused to obtain obstacle models. For static obstacles, geometric models are constructed using their size and coordinate data. For dynamic obstacles, positional change parameters over time are associated to form digital volumes with temporal information. These obstacle models are aligned with the terrain grid according to their real-world spatial locations, and collision detection algorithms are used to ensure that their spatial relationships conform to physical logic, thus avoiding spatial conflicts in the digital scene. Achieving model standardization and scene integration: Converting terrain meshes and obstacle models into the universal OBJ format, unifying their coordinate system and data structure, using vertex coordinates to record spatial positions, using texture mapping to restore surface materials, and using normal vectors to define surface orientation, ultimately achieving digital mapping of the real scene and obtaining a 3D digital scene model.

5. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 1, characterized in that, Based on a 3D digital scene model, the steps for simulating multipath propagation using ray tracing and extracting channel statistical characteristic parameters include: Configure ray emission and scene association: Set the three-dimensional coordinates of the signal source and receiver in the three-dimensional digital scene model, set the basic parameters, and define the ray propagation angle range and maximum tracking distance based on the distribution characteristics of scatterers in the scene to ensure that the ray can cover the area where all potential scatterers are located; the basic parameters include the frequency of the transmitted signal, the initial power, and the antenna type. The ray tracing algorithm is initiated: Based on the geometric properties of the terrain mesh, obstacles, and scatterers in the 3D digital scene model, and the corresponding physical properties of their materials, the interaction point between the ray and the scatterer is located using a collision detection algorithm. Combining the scattering angle, incident power, and scatterer material characteristics, the power attenuation of each scattering path is derived using scattering theory formulas. The propagation time of the ray from the emission source to the scatterer and then to the receiving point is recorded simultaneously to determine the time delay parameters of the scattering path. The azimuth and elevation angles of the ray incident on the scatterer, as well as the scattering exit angle, are extracted through vector calculations to form a complete set of angle parameters. The geometric properties include dimensions, spatial coordinates, and surface normal vectors; the corresponding physical properties of the material include the scattering coefficient and dielectric constant. Channel statistical characteristic parameters are aggregated as follows: First, the loss power, delay, and angle data collected from all scattering paths are systematically classified and organized. After obtaining the statistical sample set, the pitch angle, yaw angle, scatterer loss, and delay parameters in the sample set are first organized, and outliers with too low energy or invalidity are removed to ensure data validity. The mean and variance of each of the above parameters are calculated using statistical tools. For delay, the root mean square delay spread parameter is also calculated. At the same time, frequency histograms of each parameter are plotted. Based on the histograms, the probability density function is fitted using the maximum likelihood estimation method, and the cumulative distribution function is obtained by integrating the probability density function. Finally, the fitted probability density function and cumulative distribution function are compared and verified with typical channel models to determine the optimal fitting parameters, thereby obtaining the final channel statistical characteristics.

6. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 1, characterized in that, The steps for constructing a statistical model of the drone's jitter characteristics and quantifying the drone's positional shift under jitter include: Statistical models are used to quantify the azimuth and pitch angle shifts caused by UAV jitter, and then the position change caused by the UAV is calculated based on geometric relationships. UAV jitter includes internal jitter caused by rotor vibration and external jitter caused by external factors. The position shift of the UAV under jitter is modeled as follows: ； In the formula, The positional offset of the drone under jitter. This refers to the positional offset of the drone due to internal jitter. This represents the positional offset of the drone under external jitter.

7. The method for dynamic air-to-ground channel modeling for highly maneuverable unmanned aerial vehicles according to claim 6, characterized in that, To address internal vibration, based on the UAV's structural parameters and dynamic characteristics, and combined with historical vibration data, the periodic variation patterns of azimuth and pitch angles caused by rotor mechanical motion are described using the amplitude, frequency, and phase of a sine function. The specific model is as follows: ； In the formula, and These are the azimuth and pitch angles generated by the drone's shaking due to internal jitter. and This is the displacement caused by the swaying at that angle; ； In the formula, It is the internal jitter frequency.

8. The method for dynamic modeling of air-to-ground channels for highly maneuverable unmanned aerial vehicles according to claim 6, characterized in that, Regarding external jitter, influencing factors include wind speed fluctuations and airflow disturbances. These factors exhibit a random distribution, while the real-time compensation mechanism of the UAV flight control system ensures that the changes in azimuth and pitch angles statistically follow a normal distribution with zero mean and stable variance. The specific model is as follows: ； In the formula, and These are the azimuth and pitch angles generated by the drone's shaking under external vibrations. and This represents the displacement caused by the shaking at that angle.

9. The air-to-ground channel dynamic modeling method for highly maneuverable unmanned aerial vehicles according to claim 1, characterized in that, Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the steps of constructing a channel model that integrates attitude dynamics and jitter effects using analytical methods also include: The parameters constituting the channel impulse response are described separately. In the UAV air-to-ground communication system, the modeling of antenna gain needs to comprehensively consider the influence of platform dynamic characteristics and hardware losses. The effective aperture of the antenna is the equivalent area that the antenna can actually receive or transmit electromagnetic waves. Its actual effectiveness will be directionally attenuated due to UAV attitude deviations and high-frequency random jitter. When the antenna main lobe deviates from the target direction, the equivalent effective aperture is regarded as the projection of the antenna physical aperture on the signal pointing direction, forming a gain attenuation factor related to the attitude error angle. At the same time, hardware losses correct the antenna gain through a loss factor independent of spatial pointing. The attitude deviations include roll, pitch, and yaw angle changes. ； ； The total antenna gain is expressed as the product of the ideal gain, the effective aperture efficiency correction factor caused by attitude and jitter, and the hardware loss factor. The specific model is as follows: ； in, Indicates the wavelength of electromagnetic waves. and These are the time delays for direct and indirect beams, respectively. and It is the hardware loss of the transmitting antenna qp and the receiving antenna ab, which follows a chi-square distribution; and The effective apertures of the transmitting and receiving antennas under direct illumination conditions are given by the following formula: ； ； in, and Let qp and ab be the normal directions of the antenna, respectively. Here is the attitude transformation matrix for the UAV. and They are time t and t+ respectively. Consider the distance of antenna qp-ab after jitter offset; ； ； Immediately afterwards, and The effective apertures of the transmitting and receiving antennas under non-direct illumination conditions are given by the following formula: ； in, The physical area of ​​the transmitting QP antenna. This represents the mutual coupling matrix of the transmitting antenna. The physical area of ​​the receiver's ab antenna. This represents the mutual coupling matrix of the receiving antenna. and They are time t and t+ respectively. Consider the non-direct path distance of antenna qp-ab after jitter offset; ； ； in, express scattering body at time Location; Large-scale fading is used to characterize the slowly varying characteristics of signal strength in wireless communication over a large spatial and environmental range, including path loss and shadow fading (SH). The formulas for direct-path large-scale fading and indirect-path large-scale fading are as follows: ； ； Path loss originates from the signal propagation distance and the propagation environment, causing energy to attenuate with distance or complex scenarios. It determines the basic signal coverage and received strength. Quantized attitude and jitter offsets are incorporated into the path loss calculation, specifically the path loss of the direct path. Path loss of non-direct path The formula is expressed as follows: ； ； Where c=2 is the free space loss model; c=3~5 is the urban environment; When radio waves encounter obstacles in their propagation path, a shadow is formed, causing a slow change in the median signal strength. This phenomenon is known as the shadowing effect. Statistically, it follows a log-normal distribution, and its probability density function can be expressed as: ； in, and These are the mean and variance of shadow fading, respectively. Next, we model the small-scale parameters of the channel. The small-scale parameters caused by jitter and attitude are represented by the position offsets modeled in the above statistical model. Here, we only describe the influence caused by velocity. Based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics, the small-scale parameter model of the UAV is obtained as follows: ； ； The Doppler frequency shift of the channel caused by the direct trajectory velocity is modeled as follows: ； in, and These are the velocities of the receiving and transmitting ends, respectively, and u is a unit vector representing the signal propagation direction. The specific formula is as follows: ； The Doppler frequency shift formula for the channel caused by non-direct path velocity is modeled as follows: ； ； in, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: Similarly, It is the speed of the transmitting end. The relative velocity between the transmitter and the scatterer It is the velocity of the scatterer n, expressed by the formula: ; The angle between the signal propagation direction and the velocity direction of the transmitting end. It is the angle between the signal propagation direction and the reference direction of the receiving antenna array.

10. A dynamic air-to-ground channel modeling system for highly maneuverable unmanned aerial vehicles (UAVs), used to implement the dynamic air-to-ground channel modeling method according to any one of claims 1-9, characterized in that, include: The dynamics model building module is used to build the dynamics model of the UAV and quantify the antenna position offset caused by changes in the UAV's attitude. The scene model building module is used to build a 3D digital scene model that recreates the real scene based on the collected terrain and obstacle data. The channel statistical characteristic parameter extraction module is used to simulate multipath propagation based on a three-dimensional digital scene model using the ray tracing method and extract channel statistical characteristic parameters. The statistical model building module is used to build a statistical model of the drone's jitter characteristics and quantify the drone's positional offset under jitter. The channel model construction module is used to construct a channel model that integrates attitude dynamics and jitter effects using analytical methods, based on the UAV dynamics model, channel statistical characteristic parameters, and statistical model of UAV jitter characteristics.

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