Unmanned aerial vehicle tracking method based on movable multi-base station cooperative perception and model predictive control

Abstract

The application belongs to the field of flight control technology and provides a kind of movable multi-base station cooperative sensing and model predictive control unmanned aerial vehicle tracking method, comprising: constructing the system model containing unmanned aerial vehicle and multiple movable base stations and planning reference path, deriving the CRLB closed-form solution based on multi-base station arrival time, arrival angle and arrival frequency, then adopting the strategy combining grouping local search and global search, dynamically optimizing base station spatial layout to minimize CRLB, then unmanned aerial vehicle uses the base station signal after optimization to complete high-precision self-positioning, and inputs the state into model predictive controller, generates optimal control instruction by minimizing tracking error, finally predicts the next moment position of unmanned aerial vehicle based on dynamic model, and feeds back to base station position optimization step, forms "sensing-control-prediction" closed loop.The application realizes the integrated cooperative optimization of base station deployment, positioning and control, and significantly improves the positioning accuracy and autonomous tracking ability of unmanned aerial vehicle in complex environment.

Description

Technical Field

[0001] This application belongs to the field of flight control technology, and in particular relates to a mobile multi-base station cooperative sensing and model predictive control method, system, terminal equipment and storage medium for tracking unmanned aerial vehicles. Background Technology

[0002] With the booming development of the low-altitude economy, drones are increasingly being used in logistics delivery, urban patrols, and emergency rescue. To ensure their stable and reliable operation in complex environments, especially when satellite navigation signals are limited or interfered with, there is an urgent need for high-precision autonomous positioning and tracking capabilities. Currently, common solutions mainly rely on externally deployed positioning base station networks (such as ultra-wideband base stations), combined with the drone's onboard sensors and flight controllers (such as PID controllers) to achieve positioning and tracking. While these methods provide positioning support to some extent, their base stations are typically statically deployed, and the positioning and control systems are often designed independently.

[0003] However, current methods suffer from problems such as the inability to optimize positioning geometry due to fixed base station layouts, and error propagation and performance bottlenecks caused by the independence of the positioning system and the control system. Summary of the Invention

[0004] This application provides a mobile multi-base station collaborative sensing and model predictive control method, system, terminal device and storage medium for UAV tracking, which can solve the problems of the current method, such as the fixed base station layout leading to the inability to optimize the positioning geometry, and the error propagation and performance bottleneck caused by the independence of the positioning system and the control system.

[0005] In a first aspect, embodiments of this application provide a method for tracking unmanned aerial vehicles (UAVs) using mobile multi-base station cooperative sensing and model predictive control, comprising: S1, constructing a cooperative sensing system model including one UAV and at least three mobile cooperative base stations, dividing the distribution area of ​​the mobile cooperative base stations into uniform grids, and generating a UAV reference path using Bézier curves based on the UAV's starting point, UAV's ending point, and obstacles; S2, deriving a closed analytical expression for the UAV self-localization Cramer-Rao lower bound (CRLB) by fusing the Time of Arrival (TOA), Angle of Arrival (AOA), and Frequency of Arrival (FOA) based on the cooperative sensing system model; S3, using the UAV's estimated position at the current moment, evaluating each candidate grid point of each mobile cooperative base station within the distribution area of ​​the uniformly gridded mobile cooperative base stations using a grouped local search strategy, and calculating the CRLB value of the UAV at each candidate grid point while keeping the positions of other mobile cooperative base stations fixed, and selecting the top M candidate grid points that minimize the CRLB value as the preferred candidate grid points for each mobile cooperative base station. Set, M is a positive integer; S4, Perform a global search based on the preferred candidate grid set of each mobile cooperative base station, calculate all base station location combinations, calculate the CRLB value corresponding to each base station location combination, and select the base station location combination with the smallest CRLB value as the optimal base station location layout; S5, The UAV receives the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, performs fusion calculation based on TOA, AOA and FOA to obtain the current state estimate containing the UAV's real-time position and speed information, and inputs the current state estimate into the model predictive controller, constructs the tracking error weighted cost function and obtains the optimal control input through optimization solution; S6, The UAV adjusts its own flight state according to the optimal control input, and predicts the UAV position state of the next flight node based on the preset UAV dynamics model and the optimal control input, and uses the predicted UAV position state of the next flight node as the UAV's estimated position at the current moment in S3, and iteratively executes S3-S6 until the UAV flies to the UAV's destination.

[0006] In one possible implementation of the first aspect, S2 above, based on the cooperative sensing system model, derives a closed analytical expression for the Cramer-Rao lower bound (CRLB) of UAV self-localization by fusing the Time of Arrival (TOA), Angle of Arrival (AOA), and Frequency of Arrival (FOA), specifically including:

[0007] Construct observation vectors containing the TOA, AOA, and FOA of the l-th path of the k-th mobile cooperative base station. ,in, TOA for the propagation path, The azimuth angle of arrival of the incident signal. The elevation angle of the incident signal. The Doppler frequency shift of the propagation path;

[0008] Define the UAV state vector as , For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The velocity component in the direction, For drones The velocity component in the direction, For drones The velocity component in the direction; where the UAV's position vector is The velocity vector is Let the location vector of the k-th mobile cooperative base station be defined as... ,in For the first One base station Direction coordinates For the first One base station Direction coordinates For the first One base station Direction coordinates;

[0009] The frequency domain model of the multipath channel of the k-th base station is established as follows:

[0010] ;

[0011] Where L is the total number of propagation paths, The propagation path is the Loss path. The complex gain of the propagation path; The guiding vector for a uniform planar array UPA is expressed as:

[0012]

[0013]

[0014] ;

[0015] in, for The axial direction of the guide vector. for The axial direction steering vector, with a carrier wavelength of d is the spacing between antenna elements, N x and Nz These represent the number of units in the UPA along the x and z dimensions, respectively.

[0016] Let the subcarrier domain steering vector be:

[0017] ;

[0018] in, For the number of subcarriers, Subcarrier frequency spacing;

[0019] Let the steering vector of the OFDM symbol field be:

[0020] ;

[0021] in, In the time window The number of OFDM symbols continuously acquired within the unit;

[0022] based on ,in , To perform the operation of taking the real part, Let H be the channel vector, and H denote the conjugate transpose. Calculate the information of the observation vector in the Fisher information FIM matrix:

[0023]

[0024]

[0025]

[0026] ;

[0027] in, Noise power;

[0028] calculate and Mutual information between and :

[0029] ;

[0030] Establish observation vector and UAV state vector with the first Mapping relationship between the location vectors of mobile cooperative base stations:

[0031]

[0032] Where c is the speed of light, f c For transmission frequency; It is a drone and the first Euclidean distance between two mobile cooperative base stations:

[0033] ;

[0034] Calculate the Jacobian matrix of the observation vector with respect to the UAV state vector:

[0035]

[0036]

[0037] ;

[0038] in Indicates drones and the The Euclidean distance of a mobile cooperative base station projected onto the xoy plane:

[0039] ;

[0040] The partial derivative of the Doppler frequency shift with respect to the three-dimensional position is calculated as follows:

[0041]

[0042]

[0043]

[0044] Based on the information of the observation vector in the FIM matrix, mutual information, and the Jacobian matrix of the observation vector with respect to the UAV state vector, calculate the FIM matrix of the UAV state vector:

[0045]

[0046] The trace of the FIM matrix of the UAV state vector is used as a closed-form analytical expression for CRLB.

[0047] Optionally, in another possible implementation of the first aspect, S3 above, based on the estimated position of the UAV at the current moment, employs a grouped local search strategy to evaluate each candidate grid point of each mobile cooperative base station within the distribution area of ​​the uniformly gridded mobile cooperative base stations. While keeping the positions of other mobile cooperative base stations fixed, it calculates the CRLB value of the UAV at each candidate grid point and selects the top M candidate grid points that minimize the CRLB value as the preferred candidate grid point set for each mobile cooperative base station. Specifically, this includes:

[0048] For the One mobile cooperative base station, , Given the total number of mobile cooperative base stations, its candidate grid set is defined as follows:

[0049]

[0050] in, Indicates the first The mobile cooperative base station in the first The state at each candidate grid point Indicates the first The status of each mobile cooperative base station at the current grid point The maximum travel distance constraint for mobile cooperative base stations. The total number of candidate grid points for each mobile cooperative base station;

[0051] For the Each candidate grid point of a mobile cooperative base station While keeping the locations of other mobile cooperative base stations fixed, the self-localization CRLB value of the UAV at this candidate grid point is calculated based on the closed-form analytical expression of CRLB:

[0052] ;

[0053] in, For the trace operation of a matrix, Indicates the first The base station is located at the first There are 10 candidate grid points, while the remaining base stations are fixed. The total Fisher information matrix of each base station for the drone;

[0054] The top M candidate grid points that minimize the CRLB value are selected as the preferred candidate grid point set for each mobile cooperative base station.

[0055] Optionally, in another possible implementation of the first aspect, S4 above, based on the preferred candidate grid set of each mobile cooperative base station, performs a global search to calculate all base station location combinations, calculates the CRLB value corresponding to all base station location combinations, and selects the base station location combination with the smallest CRLB value as the optimal base station location layout, specifically including:

[0056] S41. Define a circular movable constraint area with radius R centered on the current location of each mobile cooperative base station. The radius R is determined based on the deployment environment, base station mobility, and energy consumption constraints. Grid points that fall into this area after uniform grid division constitute the candidate location grid point set of the base station.

[0057] S42. For the k-th base station, traverse all candidate grid points in its candidate location grid point set, fix the current positions of the other K-1 base stations at each candidate grid point, and calculate the CRLB value of the UAV under this specific base station layout based on the CRLB closed-form solution derived in S2, as the performance evaluation index of the candidate grid point.

[0058] S43. After completing the traversal, sort all candidate grid points according to the performance evaluation index, select the top M candidate grid points with the best performance, and form the preferred candidate location set of the kth base station.

[0059] S44. Perform steps S42-S43 sequentially on the K base stations to obtain the preferred candidate location set for each base station;

[0060] S45. A global search is performed based on the preferred candidate location set of each base station, resulting in a total of Possible combinations of base station locations;

[0061] S46. For each combination of base station locations, calculate the CRLB value of the UAV's positioning when all base stations are located at the specified locations of that combination.

[0062] S47. Compare the CRLB values ​​corresponding to all combinations, and determine the base station location combination with the smallest CRLB value as the optimal combination of multiple base station locations, which is used as the optimal base station location layout at the current moment.

[0063] Optionally, in another possible implementation of the first aspect, S5, the UAV receives the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, performs fusion calculation based on TOA, AOA, and FOA to obtain a current state estimate containing the UAV's real-time position and velocity information, and inputs the current state estimate into the model predictive controller. After constructing a tracking error weighted cost function, the optimal control input is obtained through optimization, specifically including:

[0064] The UAV receives cooperative signals transmitted by each mobile cooperative base station located at the optimal base station position, and performs fusion calculation based on TOA, AOA and FOA parameters to obtain a current state estimate including the UAV's real-time position and speed.

[0065] A prediction model for the Model Predictive Controller (MPC) is constructed. The prediction model is based on the dynamic model of the UAV, and its continuous-time expression is as follows:

[0066]

[0067]

[0068] in, Let be the rate of change of the system state. The vector is a 3×3 identity matrix, where m is the mass of the UAV, u is the control input vector, w is the process noise vector, and y is the observation vector. It is a 6×6 unit matrix;

[0069] Discretizing the continuous-time expression yields the discrete-time state transition equation:

[0070]

[0071] in, It is the first drone The state vector at any given time includes three-dimensional position and velocity. It is the first Control input for drones at all times Is The zero-mean Gaussian noise vector at time step A; A is the state transition matrix, B is the input matrix, and A and B are defined as follows:

[0072]

[0073]

[0074] In each control cycle, MPC solves a finite-time optimal control problem for the next N steps; a cost function Lmpc is defined to minimize the weighted sum of tracking errors:

[0075]

[0076] in, , indicating the first The drone's status can be monitored in real time. Indicates the first Time Prediction Real-time drone status Indicates the first The state vector of the drone that is always on the preset trajectory. , This represents the stage cost weight matrix. Represents the terminal cost weight matrix; the cost function L mpc Sorted as:

[0077]

[0078] in, , , ;

[0079] Based on discrete-time state transition equations and The relationship satisfies:

[0080]

[0081] in, , , , Indicates the first Time Prediction Real-time drone control input, ;

[0082] Will and Substituting the relation into the cost function L mpc :

[0083] ;

[0084] By combining the cost function and preset constraints, a system is constructed based on... The problem is to optimize the decision variables and solve the optimization problem to obtain the optimal control input; the preset constraints include system dynamic constraints, control input constraints and obstacle avoidance constraints.

[0085] Secondly, embodiments of this application provide a UAV tracking system with mobile multi-base station cooperative sensing and model predictive control, comprising: a system modeling and path planning module, used to construct a cooperative sensing system model including one UAV and at least three mobile cooperative base stations, dividing the distribution area of ​​the mobile cooperative base stations into uniform grid points, and generating a UAV reference path based on the UAV's starting point, ending point, and obstacles using Bézier curves; and a positioning performance lower bound modeling module, used to derive the UAV self-localization scale based on the cooperative sensing system model, which integrates the time of arrival (TOA), angle of arrival (AOA), and frequency of arrival (FOA). The closed-form analytical expression for the lower bound CRLB of the US-Russian coalescing base stations; the base station location cooperative optimization module, which, based on the estimated position of the UAV at the current moment, uses a grouped local search strategy to evaluate each candidate grid point of each mobile cooperative base station within the distribution area of ​​uniformly gridded mobile cooperative base stations, and calculates the CRLB value of the UAV at each candidate grid point while keeping the positions of other mobile cooperative base stations fixed, selects the top M candidate grid points that minimize the CRLB value as the preferred candidate grid point set for each mobile cooperative base station, where M is a positive integer; the UAV localization and state estimation module, used to optimize the location of each mobile cooperative base station within the distribution area of ​​uniformly gridded mobile cooperative base stations. Based on the preferred candidate grid set of cooperative base stations, a global search is performed to calculate all base station location combinations. The CRLB value corresponding to each base station location combination is calculated, and the base station location combination with the smallest CRLB value is selected as the optimal base station location layout. The model prediction tracking control module enables the UAV to receive cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout. It performs fusion calculation based on TOA, AOA, and FOA to obtain a current state estimate containing the UAV's real-time position and velocity information. This current state estimate is input to the model prediction controller, and after constructing a tracking error weighted cost function, the optimal control input is obtained through optimization. The state prediction and closed-loop feedback module is used for the UAV to adjust its flight state according to the optimal control input. Based on a preset UAV dynamics model and the optimal control input, it predicts the UAV's position state at the next flight node. The predicted UAV position state at the next flight node is used as the UAV's estimated position at the current moment required by the base station location cooperative optimization module. The methods corresponding to the base station location cooperative optimization module, UAV positioning and state estimation module, model prediction tracking control module, and state prediction and closed-loop feedback module are iteratively executed until the UAV reaches its destination.

[0086] Thirdly, embodiments of this application provide a terminal device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the aforementioned mobile multi-base station cooperative perception and model prediction control method for tracking unmanned aerial vehicles.

[0087] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the aforementioned mobile multi-base station cooperative sensing and model predictive control method for tracking unmanned aerial vehicles.

[0088] Beneficial Effects: This application first constructs a system model including a UAV and multiple mobile base stations and plans a reference path. Then, it derives a closed-form solution for CRLB based on the arrival time, angle of arrival, and frequency of arrival of multiple base stations. Next, it employs a strategy combining grouped local search and global search to dynamically optimize the spatial layout of base stations to minimize CRLB. The UAV then uses the optimized base station signals to achieve high-precision self-localization and inputs its state into a model predictive controller. This controller generates optimal control commands by minimizing tracking errors. Finally, it predicts the UAV's next position based on a dynamic model and feeds this prediction back to the base station position optimization step, forming a "perception-control-prediction" closed loop. This method achieves integrated and coordinated optimization of base station deployment, localization, and control, significantly improving the UAV's localization accuracy and autonomous tracking capability in complex environments. This application fundamentally improves positioning accuracy by dynamically optimizing base station layout, ensuring the system always maintains the optimal positioning geometry. It achieves synergistic optimization of perception and control, integrating base station layout optimization, high-precision positioning, and model predictive control into a virtuous cycle. It enhances the system's environmental adaptability and robustness, enabling it to proactively adapt to complex environments and avoid obstacles. It optimizes resource and energy efficiency; the grouped local search strategy reduces computational complexity, while smooth trajectory planning and MPC optimized control reduce overall energy consumption. This application provides an innovative solution for systematically addressing the problem of high-precision autonomous operation of UAVs in complex environments, which is of significant value in promoting the large-scale and automated application of UAVs in the low-altitude economy. Attached Figure Description

[0089] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art 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.

[0090] Figure 1 This is a flowchart illustrating a mobile multi-base station cooperative sensing and model predictive control method for tracking unmanned aerial vehicles (UAVs) according to an embodiment of this application.

[0091] Figure 2 This is a schematic diagram of the UPA antenna array distribution provided in one embodiment of this application;

[0092] Figure 3This is a comparison diagram of the actual trajectory of a drone in 3D space and a preset trajectory provided in an embodiment of this application;

[0093] Figure 4 This is a comparison diagram of the actual trajectory and estimated trajectory of a drone in 3D space provided in an embodiment of this application;

[0094] Figure 5 This is a schematic diagram of the position estimation error of a UAV in the X, Y, and Z coordinate axes provided in an embodiment of this application;

[0095] Figure 6 This is a schematic diagram comparing location CRLB in two scenarios: base station collaborative optimization and fixed base station layout, provided in an embodiment of this application.

[0096] Figure 7 This is a schematic diagram comparing the speed CRLB under two scenarios: base station collaborative optimization and fixed base station layout, provided in an embodiment of this application;

[0097] Figure 8 This is a schematic diagram of the dynamically optimized trajectories of four base stations within an elliptical region as the drone moves, and the flight trajectory of the drone itself, provided in an embodiment of this application.

[0098] Figure 9 This is a schematic diagram illustrating the evolution of the FIM eigenvalue orientation ratio and condition number according to an embodiment of this application;

[0099] Figure 10 This is a schematic diagram of the structure of a mobile multi-base station cooperative sensing and model predictive control UAV tracking system provided in an embodiment of this application;

[0100] Figure 11 This is a schematic diagram of the structure of the terminal device provided in the embodiments of this application. Detailed Implementation

[0101] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0102] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0103] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0104] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0105] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0106] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0107] The following description, with reference to the accompanying drawings, details a mobile multi-base station cooperative sensing and model predictive control method, system, terminal device, and storage medium for UAV tracking provided in this application.

[0108] Figure 1 The illustration shows a flowchart of a mobile multi-base station cooperative sensing and model predictive control method for tracking unmanned aerial vehicles (UAVs) provided in an embodiment of this application.

[0109] like Figure 1 As shown, the mobile multi-base station cooperative sensing and model predictive control drone tracking method includes the following steps:

[0110] S1. Construct a cooperative perception system model that includes one UAV and at least three mobile cooperative base stations. Divide the distribution area of ​​the mobile cooperative base stations into uniform grid points, and generate a UAV reference path using Bézier curves based on the UAV's starting point, UAV's ending point, and obstacles.

[0111] S2. Based on the cooperative sensing system model, derive the closed-form analytical expression of the Cramer-Rao lower bound (CRLB) for UAV self-localization by fusing the time of arrival (TOA), angle of arrival (AOA), and frequency of arrival (FOA).

[0112] Furthermore, in this embodiment of the application, step S2 includes:

[0113] Construct observation vectors containing the TOA, AOA, and FOA of the l-th path of the k-th mobile cooperative base station. ,in, TOA for the propagation path, The azimuth angle of arrival of the incident signal. The elevation angle of the incident signal. The Doppler frequency shift of the propagation path;

[0114] Define the UAV state vector as , For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The velocity component in the direction, For drones The velocity component in the direction, For drones The velocity component in the direction; where the UAV's position vector is The velocity vector is Let the location vector of the k-th mobile cooperative base station be defined as... ,in For the first One base station Direction coordinates For the first One base station Direction coordinates For the first One base station Direction coordinates;

[0115] The frequency domain model of the multipath channel of the k-th base station is established as follows:

[0116] ;

[0117] Where L is the total number of propagation paths, The propagation path is the Loss path. The complex gain of the propagation path; The guiding vector for a uniform planar array UPA is expressed as:

[0118]

[0119]

[0120] ;

[0121] in, for The axial direction of the guide vector. for The axial direction steering vector, with a carrier wavelength of d is the spacing between antenna elements, N x and N z These represent the number of units in the UPA along the x and z dimensions, respectively.

[0122] Let the subcarrier domain steering vector be:

[0123] ;

[0124] in, For the number of subcarriers, Subcarrier frequency spacing;

[0125] Let the steering vector of the OFDM symbol field be:

[0126] ;

[0127] in, In the time window The number of OFDM symbols continuously acquired within the unit;

[0128] based on ,in , To perform the operation of taking the real part, Let H be the channel vector, and H denote the conjugate transpose. Calculate the information of the observation vector in the Fisher information FIM matrix:

[0129]

[0130]

[0131]

[0132] ;

[0133] in, Noise power;

[0134] calculate and Mutual information between and :

[0135] ;

[0136] Establish observation vector and UAV state vector with the first Mapping relationship between the location vectors of mobile cooperative base stations:

[0137]

[0138] Where c is the speed of light, f c For transmission frequency; It is a drone and the first Euclidean distance between two mobile cooperative base stations:

[0139] ;

[0140] Calculate the Jacobian matrix of the observation vector with respect to the UAV state vector:

[0141]

[0142]

[0143] ;

[0144] in Indicates drones and the The Euclidean distance of a mobile cooperative base station projected onto the xoy plane:

[0145] ;

[0146] The partial derivative of the Doppler frequency shift with respect to the three-dimensional position is calculated as follows:

[0147]

[0148]

[0149]

[0150] Based on the information of the observation vector in the FIM matrix, mutual information, and the Jacobian matrix of the observation vector with respect to the UAV state vector, calculate the FIM matrix of the UAV state vector:

[0151]

[0152] The trace of the FIM matrix of the UAV state vector is used as a closed-form analytical expression for CRLB.

[0153] In one embodiment, such as Figure 2 The figure shows the uniform planar array (UPA) antenna structure used in this application. The array consists of 16 antenna elements (4×4), with a spacing of half a wavelength. The numbering and arrangement of the antenna elements are clearly shown in the figure, with the X and Y axes representing the two dimensions of the array. This UPA structure can simultaneously provide azimuth and elevation angle measurements. The azimuth angle is defined as the angle between the signal projection onto the xoy plane and the x-axis, and the elevation angle is the angle with the z-axis.

[0154] S3. Based on the estimated position of the UAV at the current moment, a grouped local search strategy is adopted to evaluate each candidate grid point of each mobile cooperative base station in the distribution area of ​​the mobile cooperative base station after uniform grid division. Under the condition of keeping the positions of other mobile cooperative base stations fixed, the CRLB value of the UAV at each candidate grid point is calculated, and the top M candidate grid points that make the CRLB value the smallest are selected as the preferred candidate grid point set of each mobile cooperative base station.

[0155] Furthermore, in this embodiment of the application, step S3 includes:

[0156] For the One mobile cooperative base station, , Given the total number of mobile cooperative base stations, its candidate grid set is defined as follows:

[0157]

[0158] in, Indicates the first The mobile cooperative base station in the first The state at each candidate grid point Indicates the first The status of each mobile cooperative base station at the current grid point The maximum travel distance constraint for mobile cooperative base stations. The total number of candidate grid points for each mobile cooperative base station;

[0159] For the Each candidate grid point of a mobile cooperative base station While keeping the locations of other mobile cooperative base stations fixed, the self-localization CRLB value of the UAV at this candidate grid point is calculated based on the closed-form analytical expression of CRLB:

[0160] ;

[0161] in, For the trace operation of a matrix, Indicates the first The base station is located at the first There are 10 candidate grid points, while the remaining base stations are fixed. The total Fisher information matrix of each base station for the drone;

[0162] The top M candidate grid points that minimize the CRLB value are selected as the preferred candidate grid point set for each mobile cooperative base station.

[0163] S4. Based on the preferred candidate grid set of each mobile cooperative base station, perform a global search, calculate all base station location combinations, calculate the CRLB value corresponding to all base station location combinations, and select the base station location combination with the smallest CRLB value as the optimal base station location layout.

[0164] Furthermore, in this embodiment of the application, step S4 includes:

[0165] S41. Define a circular movable constraint area with radius R centered on the current location of each mobile cooperative base station. The radius R is determined based on the deployment environment, base station mobility, and energy consumption constraints. Grid points that fall into this area after uniform grid division constitute the candidate location grid point set of the base station.

[0166] S42. For the k-th base station, traverse all candidate grid points in its candidate location grid point set, fix the current positions of the other K-1 base stations at each candidate grid point, and calculate the CRLB value of the UAV under this specific base station layout based on the CRLB closed-form solution derived in S2, as the performance evaluation index of the candidate grid point.

[0167] S43. After completing the traversal, sort all candidate grid points according to the performance evaluation index, select the top M candidate grid points with the best performance, and form the preferred candidate location set of the kth base station.

[0168] S44. Perform steps S42-S43 sequentially on the K base stations to obtain the preferred candidate location set for each base station;

[0169] S45. A global search is performed based on the preferred candidate location set of each base station, resulting in a total of Possible combinations of base station locations;

[0170] S46. For each combination of base station locations, calculate the CRLB value of the UAV's positioning when all base stations are located at the specified locations of that combination.

[0171] S47. Compare the CRLB values ​​corresponding to all combinations, and determine the base station location combination with the smallest CRLB value as the optimal combination of multiple base station locations, which is used as the optimal base station location layout at the current moment.

[0172] S5. The UAV receives the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, performs fusion calculation based on TOA, AOA and FOA to obtain the current state estimate containing the UAV's real-time position and speed information, and inputs the current state estimate into the model predictive controller. After constructing the tracking error weighted cost function, the optimal control input is obtained by optimization solution.

[0173] Furthermore, in this embodiment of the application, step S5 includes:

[0174] The UAV receives cooperative signals transmitted by each mobile cooperative base station located at the optimal base station position, and performs fusion calculation based on TOA, AOA and FOA parameters to obtain a current state estimate including the UAV's real-time position and speed.

[0175] A prediction model for the Model Predictive Controller (MPC) is constructed. The prediction model is based on the dynamic model of the UAV, and its continuous-time expression is as follows:

[0176]

[0177]

[0178] in, Let be the rate of change of the system state. The vector is a 3×3 identity matrix, where m is the mass of the UAV, u is the control input vector, w is the process noise vector, and y is the observation vector. It is a 6×6 unit matrix;

[0179] Discretizing the continuous-time expression yields the discrete-time state transition equation:

[0180]

[0181] in, It is the first drone The state vector at any given time includes three-dimensional position and velocity. It is the first Control input for drones at all times Is The zero-mean Gaussian noise vector at time step A; A is the state transition matrix, B is the input matrix, and A and B are defined as follows:

[0182]

[0183]

[0184] In each control cycle, MPC solves a finite-time optimal control problem for the next N steps; a cost function Lmpc is defined to minimize the weighted sum of tracking errors:

[0185]

[0186] in, , indicating the first The drone's status can be monitored in real time. Indicates the first Time Prediction Real-time drone status Indicates the first The state vector of the drone that is always on the preset trajectory. , This represents the stage cost weight matrix. Represents the terminal cost weight matrix; the cost function L mpc Sorted as:

[0187]

[0188] in, , , ;

[0189] Based on discrete-time state transition equations and The relationship satisfies:

[0190]

[0191] in, , , , Indicates the first Time Prediction Real-time drone control input, ;

[0192] Will and Substituting the relation into the cost function L mpc :

[0193] ;

[0194] By combining the cost function and preset constraints, a system is constructed based on... The problem is to optimize the decision variables and solve the optimization problem to obtain the optimal control input; the preset constraints include system dynamic constraints, control input constraints and obstacle avoidance constraints.

[0195] S6. The UAV adjusts its flight state according to the optimal control input, and predicts the UAV position state of the next flight node based on the preset UAV dynamics model and the optimal control input. The predicted UAV position state of the next flight node is used as the estimated position of the UAV at the current moment in S3. S3-S6 are executed iteratively until the UAV flies to the UAV endpoint.

[0196] This application provides a UAV tracking method based on mobile multi-base station collaborative sensing and model predictive control. First, a system model including the UAV and multiple mobile base stations is constructed and a reference path is planned. Then, a closed-form solution for CRLB based on the arrival time, angle of arrival, and frequency of arrival of multiple base stations is derived. Next, a strategy combining grouped local search and global search is used to dynamically optimize the spatial layout of base stations to minimize CRLB. Then, the UAV uses the signals from the optimized base station layout to achieve high-precision self-localization and inputs its state into the model predictive controller. Optimal control commands are generated by minimizing the tracking error. Finally, the UAV's position at the next moment is predicted based on a dynamic model and fed back to the base station position optimization step, forming a "sensing-control-prediction" closed loop. This method achieves integrated collaborative optimization of base station deployment, localization, and control, significantly improving the UAV's localization accuracy and autonomous tracking capability in complex environments. This application fundamentally improves positioning accuracy by dynamically optimizing base station layout, ensuring the system always maintains the optimal positioning geometry. It achieves synergistic optimization of perception and control, integrating base station layout optimization, high-precision positioning, and model predictive control into a virtuous cycle. It enhances the system's environmental adaptability and robustness, enabling it to proactively adapt to complex environments and avoid obstacles. It optimizes resource and energy efficiency; the grouped local search strategy reduces computational complexity, while smooth trajectory planning and MPC optimized control reduce overall energy consumption. This application provides an innovative solution for systematically addressing the problem of high-precision autonomous operation of UAVs in complex environments, which is of significant value in promoting the large-scale and automated application of UAVs in the low-altitude economy.

[0197] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0198] The advantages of this application are illustrated below with an example.

[0199] The simulation settings included a carrier frequency of 3.5 GHz, 600 OFDM subcarriers, a subcarrier frequency spacing of 15 kHz, a Doppler sampling time interval of 0.5 ms, and 50 sampling cycles. The signal-to-noise ratio (SNR) was calculated based on a free-space path loss model, incorporating transmit power. (Set to 1W), Antenna Gain , (Set to 1dBi), free space path loss, noise figure (Set to 5dB) and thermal noise power . Figure 3 and Figure 4 The comparison between the actual trajectory and the planned trajectory of the UAV in three-dimensional space, and between the actual trajectory and the estimated trajectory, are shown respectively. In terms of overall trend, the trajectories in the two figures are basically consistent and consistent, indicating that the UAV can track the preset path well. The estimation error is theoretically reduced by CRLB, which proves the rationality of this framework. The accurate correspondence between the start and end points verifies the reliability of system initialization and task execution. The continuity and smoothness of the trajectory reflect the superior performance of the model predictive controller in trajectory tracking. Figure 5 The paper demonstrates how the position estimation error of the UAV changes over time in the X, Y, and Z coordinate axes. Initially, because the base station was not in the optimal position, the UAV's self-localization error was relatively large. Subsequently, the base station moved to achieve relative position coordination with the UAV, and the error curves in the three directions did not show drastic fluctuations, indicating that the positioning estimation provided in this application has good stability and reliability.

[0200] Figure 6 and Figure 7 The changes in position CRLB and velocity CRLB were compared under two scenarios: base station cooperative optimization and fixed base station deployment. The figures show that the CRLB value using the dynamic base station optimization method of this application is significantly lower than that of the traditional fixed base station method. The CRLB value of the dynamic optimization method remains relatively stable throughout the flight, with the position CRLB fluctuation range within... arrive Between meters, the speed CRLB fluctuation range is within arrive Between meters and seconds, the CRLB value of the fixed base station method fluctuates significantly and peaks at multiple time points, indicating that the positioning accuracy fluctuates with the relative position of the base station and the unmanned personnel. This comparison verifies the theoretical lower bound of the proposed application, which can fundamentally improve the positioning accuracy by dynamically optimizing the base station layout.

[0201] Figure 8 The system intuitively demonstrates the coordinated movement of base stations and drones throughout the entire system: the green ellipse represents the feasible area boundary of the base station, the blue solid line is the planned trajectory of the drone, the red dashed line is the actual flight trajectory, and the movement trajectory of each base station is represented by dashed lines of different colors, showing the process of the base station dynamically adjusting according to the drone's position within the elliptical area. The starting point and the ending point are marked with red and blue dots, respectively. Figure 9The evolution of the Fisher Information Matrix (FIM) characteristics was analyzed, and the information ratios in the zx, zy, and xy directions were compared. These ratios were obtained by comparing the ratios of eigenvalues ​​in the corresponding directions using the FIM, reflecting the relative information content in these two directions. The FIM condition number reflects the ratio of the largest to the smallest eigenvalue in one direction. Since ground base stations are all on the same horizontal plane, the positioning information for the UAV in the z-axis direction is insufficient. Therefore, the z-axis of the information ellipsoid is longer than the x and y axes, resulting in relatively lower positioning accuracy.

[0202] A mobile multi-base station cooperative sensing and model predictive control method for UAV tracking, corresponding to the above embodiment, Figure 10 This diagram illustrates a structural block diagram of a mobile multi-base station cooperative sensing and model predictive control UAV tracking system provided in an embodiment of this application. For ease of explanation, only the parts related to the embodiments of this application are shown.

[0203] Reference Figure 10 The device 1000 includes:

[0204] The system modeling and path planning module 1001 is used to construct a cooperative perception system model containing one UAV and at least three mobile cooperative base stations. The distribution area of ​​the mobile cooperative base stations is divided into uniform grid points, and a reference path for the UAV is generated using Bézier curves based on the UAV's starting point, UAV's ending point, and obstacles.

[0205] The positioning performance lower bound modeling module 1002 is used to derive a closed analytical expression for the Cramer-Rao lower bound (CRLB) of UAV self-localization based on the cooperative sensing system model, which integrates the time of arrival (TOA), angle of arrival (AOA), and frequency of arrival (FOA).

[0206] The base station location coordination optimization module 1003 is used to evaluate each candidate grid point of each mobile cooperative base station in the distribution area of ​​the mobile cooperative base stations after uniform grid division, based on the estimated position of the UAV at the current moment and using a grouped local search strategy. Under the condition of keeping the positions of other mobile cooperative base stations fixed, it calculates the CRLB value of the UAV at each candidate grid point and selects the top M candidate grid points that minimize the CRLB value as the preferred candidate grid point set of each mobile cooperative base station.

[0207] The UAV positioning and state estimation module 1004 is used to perform a global search based on the preferred candidate grid point set of each mobile cooperative base station, calculate all base station location combinations, calculate the CRLB value corresponding to all base station location combinations, and select the base station location combination with the smallest CRLB value as the optimal base station location layout.

[0208] The model prediction tracking control module 1005 is used to enable the UAV to receive the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, perform fusion calculation based on TOA, AOA and FOA to obtain the current state estimate containing the real-time position and speed information of the UAV, and input the current state estimate into the model prediction controller. After constructing the tracking error weighted cost function, the optimal control input is obtained by optimization solution.

[0209] The state prediction and closed-loop feedback module 1006 is used for the UAV to adjust its own flight state according to the optimal control input, and predict the UAV position state at the next flight node based on the preset UAV dynamics model and the optimal control input. The predicted UAV position state at the next flight node is used as the estimated UAV position at the current moment required by the base station position cooperative optimization module. The corresponding methods of the base station position cooperative optimization module, UAV positioning and state estimation module, model prediction tracking control module and state prediction and closed-loop feedback module are executed iteratively until the UAV flies to the UAV destination.

[0210] In practical use, the mobile multi-base station cooperative sensing and model predictive control UAV tracking system provided in this application embodiment can be configured in any terminal device to execute the aforementioned mobile multi-base station cooperative sensing and model predictive control UAV tracking method.

[0211] This application provides a mobile multi-base station collaborative sensing and model predictive control (MRC) UAV tracking system. First, a system model including the UAV and multiple mobile base stations is constructed and a reference path is planned. Then, a closed-form solution for CRLB based on the arrival time, angle of arrival, and frequency of arrival of multiple base stations is derived. Next, a strategy combining grouped local search and global search is used to dynamically optimize the spatial layout of base stations to minimize CRLB. Then, the UAV uses the signals from the optimized base station layout to achieve high-precision self-localization and inputs its state into the MRC. The MRC generates optimal control commands by minimizing the tracking error. Finally, the system predicts the UAV's position at the next moment based on a dynamic model and feeds it back to the base station position optimization step, forming a "perception-control-prediction" closed loop. This method achieves integrated collaborative optimization of base station deployment, localization, and control, significantly improving the UAV's localization accuracy and autonomous tracking capability in complex environments. This application fundamentally improves positioning accuracy by dynamically optimizing base station layout, ensuring the system always maintains the optimal positioning geometry. It achieves synergistic optimization of perception and control, integrating base station layout optimization, high-precision positioning, and model predictive control into a virtuous cycle. It enhances the system's environmental adaptability and robustness, enabling it to proactively adapt to complex environments and avoid obstacles. It optimizes resource and energy efficiency; the grouped local search strategy reduces computational complexity, while smooth trajectory planning and MPC optimized control reduce overall energy consumption. This application provides an innovative solution for systematically addressing the problem of high-precision autonomous operation of UAVs in complex environments, which is of significant value in promoting the large-scale and automated application of UAVs in the low-altitude economy.

[0212] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0213] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments 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. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0214] To implement the above embodiments, this application also proposes a terminal device.

[0215] Figure 11 This is a schematic diagram of the structure of a terminal device according to an embodiment of this application.

[0216] like Figure 11 As shown, the terminal device 200 includes:

[0217] The system includes a memory 210 and at least one processor 220, and a bus 230 connecting different components (including the memory 210 and the processor 220). The memory 210 stores a computer program, which, when executed by the processor 220, implements a mobile multi-base station cooperative sensing and model predictive control UAV tracking method as described in the embodiments of this application.

[0218] Bus 230 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0219] Terminal device 200 typically includes various electronically readable media. These media can be any available media that can be accessed by terminal device 200, including volatile and non-volatile media, removable and non-removable media.

[0220] Memory 210 may also include computer system readable media in the form of volatile memory, such as random access memory (RAM) 240 and / or cache memory 250. Terminal device 200 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 260 may be used to read and write non-removable, non-volatile magnetic media (… Figure 11 Not shown; usually referred to as a "hard drive"). Although Figure 11 As not shown, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 230 via one or more data media interfaces. Memory 210 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of this application.

[0221] A program / utility 280 having a set (at least one) of program modules 270 may be stored in, for example, memory 210. Such program modules 270 include—but are not limited to—an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 270 typically perform the functions and / or methods described in the embodiments of this application.

[0222] Terminal device 200 can also communicate with one or more external devices 290 (e.g., keyboard, pointing device, display 291, etc.), and with one or more devices that enable a user to interact with terminal device 200, and / or with any device that enables terminal device 200 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed via input / output (I / O) interface 292. Furthermore, terminal device 200 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 293. As shown, network adapter 293 communicates with other modules of terminal device 200 via bus 230. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with terminal device 200, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0223] The processor 220 performs various functional applications and data processing by running programs stored in the memory 210.

[0224] It should be noted that the implementation process and technical principles of the terminal device in this embodiment are explained in the foregoing description of a mobile multi-base station cooperative sensing and model predictive control method for UAV tracking according to an embodiment of this application, and will not be repeated here.

[0225] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0226] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0227] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a photographing device / terminal device, a recording medium, a computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0228] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0229] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0230] In the embodiments provided in this application, it should be understood that the disclosed devices / terminal equipment and methods can be implemented in other ways. For example, the device / terminal equipment embodiments described above are merely illustrative. For instance, the division of modules or 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 displayed or discussed mutual coupling or direct coupling or communication connection may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0231] 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.

[0232] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A mobile multi-base station cooperative sensing and model predictive control method for tracking unmanned aerial vehicles (UAVs), characterized in that, Includes the following steps: S1. Construct a cooperative perception system model that includes one UAV and at least three mobile cooperative base stations. Divide the distribution area of ​​the mobile cooperative base stations into uniform grid points, and generate a UAV reference path using Bézier curves based on the UAV's starting point, UAV's ending point, and obstacles. S2. Based on the cooperative sensing system model, derive the closed-form analytical expression of the Cramer-Rao lower bound (CRLB) for UAV self-localization by fusing the time of arrival (TOA), angle of arrival (AOA), and frequency of arrival (FOA). S3. Based on the estimated position of the UAV at the current moment, a grouped local search strategy is adopted to evaluate each candidate grid point of each mobile cooperative base station in the distribution area of ​​the mobile cooperative base station after uniform grid division. Under the condition of keeping the positions of other mobile cooperative base stations fixed, the CRLB value of the UAV at each candidate grid point is calculated. The top M candidate grid points that make the CRLB value the smallest are selected as the preferred candidate grid point set of each mobile cooperative base station, where M is a positive integer. S4. Based on the preferred candidate grid set of each mobile cooperative base station, perform a global search, calculate all base station location combinations, calculate the CRLB value corresponding to all base station location combinations, and select the base station location combination with the smallest CRLB value as the optimal base station location layout. S5. The UAV receives the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, performs fusion calculation based on TOA, AOA and FOA to obtain the current state estimate containing the UAV's real-time position and speed information, and inputs the current state estimate into the model prediction controller. After constructing the tracking error weighted cost function, the optimal control input is obtained by optimization solution. S6. The UAV adjusts its flight state according to the optimal control input, and predicts the UAV position state at the next flight node based on the preset UAV dynamics model and the optimal control input. The predicted UAV position state at the next flight node is used as the estimated UAV position at the current moment in S3. S3-S6 are executed iteratively until the UAV flies to the UAV endpoint.

2. The method according to claim 1, characterized in that, S2, based on the cooperative sensing system model, derives a closed-form analytical expression for the Cramer-Rao lower bound (CRLB) of UAV self-localization by fusing Time of Arrival (TOA), Angle of Arrival (AOA), and Frequency of Arrival (FOA), specifically including: Construct observation vectors containing the TOA, AOA, and FOA of the l-th path of the k-th mobile cooperative base station. ,in, TOA for the propagation path, The azimuth angle of arrival of the incident signal. The elevation angle of the incident signal. The Doppler frequency shift of the propagation path; Define the UAV state vector as , For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The position coordinates of the direction, For drones The velocity component in the direction, For drones The velocity component in the direction, For drones The velocity component in the direction; where the UAV's position vector is The velocity vector is Let the location vector of the k-th mobile cooperative base station be defined as... ,in For the first One base station Direction coordinates For the first One base station Direction coordinates For the first One base station Direction coordinates; The frequency domain model of the multipath channel of the k-th base station is established as follows: ； Where L is the total number of propagation paths, The propagation path is the Loss path. The complex gain of the propagation path; The guiding vector for a uniform planar array UPA is expressed as: ； ； ； in, for The axial direction of the guide vector. for The axial direction steering vector, with a carrier wavelength of d is the spacing between antenna elements, N x and N z These represent the number of units in the UPA along the x and z dimensions, respectively. Let the subcarrier domain steering vector be: ； in, For the number of subcarriers, Subcarrier frequency spacing; Let the steering vector of the OFDM symbol field be: ； in, In the time window The number of OFDM symbols continuously acquired within the unit; based on ,in , To perform the operation of taking the real part, Let H be the channel vector, and H denote the conjugate transpose. Calculate the information of the observation vector in the Fisher information FIM matrix: ； ； ； ； in, Noise power; calculate and Mutual information between and : ； Establish the observation vector and the UAV state vector with the first Mapping relationship between the location vectors of mobile cooperative base stations: ； Where c is the speed of light, f c For transmission frequency; It is a drone and the first Euclidean distance between two mobile cooperative base stations: ； Calculate the Jacobian matrix of the observation vector with respect to the UAV state vector: ； ； ； in Indicates drones and the The Euclidean distance of a mobile cooperative base station projected onto the xoy plane: ； The partial derivative of the Doppler frequency shift with respect to the three-dimensional position is calculated as follows: ； ； ； Based on the information of the observation vector in the FIM matrix, the mutual information, and the Jacobian matrix of the observation vector with respect to the UAV state vector, calculate the FIM matrix of the UAV state vector: ； The trace of the FIM matrix of the UAV state vector is used as a closed-form analytical expression for CRLB.

3. The method according to claim 2, characterized in that, S3, based on the estimated location of the UAV at the current moment, employs a grouped local search strategy within the distribution area of ​​the mobile cooperative base stations after uniform grid division to evaluate each candidate grid point of each mobile cooperative base station. While keeping the locations of other mobile cooperative base stations fixed, it calculates the CRLB value of the UAV at each candidate grid point and selects the top M candidate grid points that minimize the CRLB value as the preferred candidate grid point set for each mobile cooperative base station. Specifically, this includes: For the One mobile cooperative base station, , Given the total number of mobile cooperative base stations, its candidate grid set is defined as follows: ； in, Indicates the first The mobile cooperative base station in the first The state at each candidate grid point Indicates the first The status of each mobile cooperative base station at the current grid point The maximum travel distance constraint for mobile cooperative base stations. The total number of candidate grid points for each mobile cooperative base station; For the Each candidate grid point of a mobile cooperative base station While keeping the positions of other mobile cooperative base stations fixed, the self-localization CRLB value of the UAV at the candidate grid point is calculated based on the closed-form analytical expression of the CRLB: ； in, For the trace operation of a matrix, Indicates the first The base station is located at the first There are 10 candidate grid points, while the remaining base stations are fixed. The total Fisher information matrix of each base station for the drone; The top M candidate grid points that minimize the CRLB value are selected as the preferred candidate grid point set for each mobile cooperative base station.

4. The method according to claim 3, characterized in that, S4 involves performing a global search based on the preferred candidate grid set of each mobile cooperative base station, calculating all base station location combinations, calculating the CRLB value corresponding to each base station location combination, and selecting the base station location combination with the smallest CRLB value as the optimal base station location layout. Specifically, this includes: S41. Define a circular movable constraint region with radius R centered on the current location for each mobile cooperative base station. The radius R is determined based on the deployment environment, base station mobility, and energy consumption constraints. The grid points that fall into this region after the uniform grid division constitute the candidate location grid point set for the base station. S42. For the k-th base station, traverse all candidate grid points in its candidate location grid point set, fix the current positions of the other K-1 base stations at each candidate grid point, and calculate the CRLB value of the UAV under this specific base station layout based on the CRLB closed-form solution derived in S2, as the performance evaluation index of the candidate grid point. S43. After completing the traversal, sort all candidate grid points according to the performance evaluation index, and select the top M candidate grid points with the best performance to form the preferred candidate location set of the kth base station. S44. Perform steps S42-S43 sequentially on the K base stations to obtain the preferred candidate location set for each base station; S45. A global search is performed based on the preferred candidate location set of each base station to form a total of Possible combinations of base station locations; S46. For each combination of base station locations, calculate the CRLB value of the UAV's positioning when all base stations are located at the specified locations of that combination. S47. Compare the CRLB values ​​corresponding to all combinations, and determine the base station location combination with the smallest CRLB value as the optimal combination of multiple base station locations, which is used as the optimal base station location layout at the current moment.

5. The method according to claim 4, characterized in that, S5: The UAV receives the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, performs fusion calculation based on TOA, AOA, and FOA to obtain a current state estimate containing the UAV's real-time position and speed information, and inputs the current state estimate into the model predictive controller. After constructing a tracking error weighted cost function, it obtains the optimal control input through optimization, specifically including: The UAV receives cooperative signals transmitted by each mobile cooperative base station located at the optimal base station position, and performs fusion calculation based on TOA, AOA and FOA parameters to obtain a current state estimate including the UAV's real-time position and speed. A prediction model for the Model Predictive Controller (MPC) is constructed. This prediction model is based on the dynamics model of the UAV, and its continuous-time expression is as follows: ； ； in, Let be the rate of change of the system state. The vector is a 3×3 identity matrix, where m is the mass of the UAV, u is the control input vector, w is the process noise vector, and y is the observation vector. It is a 6×6 unit matrix; Discretizing the continuous-time expression yields the discrete-time state transition equation: ； in, It is the first drone The state vector at any given time includes three-dimensional position and velocity. It is the first Control input for drones at all times Is The zero-mean Gaussian noise vector at time step A; A is the state transition matrix, B is the input matrix, and A and B are defined as follows: ； ； In each control cycle, the MPC solves a finite-time optimal control problem for the next N steps; the cost function L is defined. mpc The weighted sum used to minimize the tracking error: ； in, , indicating the first The drone's status can be monitored in real time. Indicates the first Time Prediction Real-time drone status Indicates the first The state vector of the drone that is always on the preset trajectory. , This represents the stage cost weight matrix. Represents the terminal cost weight matrix; the cost function L mpc Sorted as: ； in, , , ; Based on the aforementioned discrete-time state transition equation and The relationship satisfies: ； in, , , , Indicates the first Time Prediction Real-time drone control input, ; The and Substituting the relationship into the cost function L mpc : ； By combining the cost function with preset constraints, a system is constructed based on... The optimization problem is a decision variable problem, and the optimal control input is obtained by solving the optimization problem; the preset constraints include system dynamic constraints, control input constraints and obstacle avoidance constraints.

6. A mobile multi-base station cooperative sensing and model predictive control unmanned aerial vehicle (UAV) tracking system, characterized in that, include: The system modeling and path planning module is used to construct a cooperative perception system model that includes one UAV and at least three mobile cooperative base stations. The distribution area of ​​the mobile cooperative base stations is divided into uniform grid points, and a reference path for the UAV is generated using Bézier curves based on the UAV's starting point, UAV's ending point, and obstacles. The positioning performance lower bound modeling module is used to derive a closed analytical expression for the UAV self-localization Cramer-Rao lower bound CRLB that integrates the time of arrival (TOA), angle of arrival (AOA), and frequency of arrival (FOA) based on the cooperative sensing system model. The base station location coordination optimization module is used to evaluate each candidate grid point of each mobile cooperative base station in the distribution area of ​​the mobile cooperative base stations after uniform grid division, based on the estimated position of the UAV at the current moment and using a grouped local search strategy. Under the condition of keeping the positions of other mobile cooperative base stations fixed, it calculates the CRLB value of the UAV at each candidate grid point and selects the top M candidate grid points that minimize the CRLB value as the preferred candidate grid point set of each mobile cooperative base station, where M is a positive integer. The UAV positioning and state estimation module is used to perform a global search based on the preferred candidate grid set of each mobile cooperative base station, calculate all base station location combinations, calculate the CRLB value corresponding to all base station location combinations, and select the base station location combination with the smallest CRLB value as the optimal base station location layout. The model prediction tracking control module is used to enable the UAV to receive the cooperative signals transmitted by each mobile cooperative base station under the optimal base station location layout, perform fusion calculation based on TOA, AOA and FOA to obtain the current state estimate containing the real-time position and speed information of the UAV, and input the current state estimate into the model prediction controller. After constructing the tracking error weighted cost function, the optimal control input is obtained by optimization solution. The state prediction and closed-loop feedback module is used to adjust the UAV's flight state according to the optimal control input, and predict the UAV's position state at the next flight node based on the preset UAV dynamics model and the optimal control input. The predicted UAV position state at the next flight node is used as the UAV's estimated position at the current moment required by the base station position collaborative optimization module. The corresponding methods of the base station position collaborative optimization module, UAV positioning and state estimation module, model prediction tracking control module and state prediction and closed-loop feedback module are executed iteratively until the UAV flies to the UAV's destination.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.

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