Multi-uav low-cost aided positioning method and device based on wireless communication link

Abstract

This invention proposes a low-cost assisted positioning method and device for multiple unmanned aerial vehicles (UAVs) based on a wireless communication link, comprising: an initial step of constructing an agricultural machinery positioning system including multiple agricultural machines and at least three UAVs; an analysis step where, during agricultural machinery operation, the actual position is obtained based on GPS signals emitted by a base station, and simultaneously, the agricultural machine receives electromagnetic wave signals emitted by the UAVs through its own onboard sensors, analyzes the electromagnetic wave signals, and executes a DOA (Demand of Allocation) position estimation algorithm to obtain an estimated position; when the agricultural machine travels outside the coverage area of ​​the base station and fails to receive GPS signals, the estimated position is used as its positioning result; and a compensation step where, after the agricultural machine travels within the coverage area of ​​the base station and obtains its actual position, a system-level angle error is calculated using the deviation between its estimated position and its actual position; and the estimated position of the agricultural machine that failed to receive GPS signals in the agricultural machinery positioning system is compensated based on this system-level angle error.

Description

Technical Field

[0001] This invention relates to the fields of agricultural machinery automation and wireless communication positioning technology, and particularly to a low-cost assisted positioning method, device, electronic device, computer-readable storage medium, and computer program product based on a wireless communication link for multiple unmanned aerial vehicles (UAVs). This invention falls under the category of target positioning and navigation technology in the context of vehicle-to-everything (V2X) and space-air-ground integrated network (SAGIN) environments, specifically involving the use of UAVs and agricultural machinery to construct a local area network for assisted positioning, and signal processing technology for direction of arrival (DOA) estimation based on an improved Stochastic Maximum Likelihood (SML) algorithm. Background Technology

[0002] Currently, autonomous driving technology is widely used in public transportation, agriculture, logistics, and other fields, becoming an important way to improve work efficiency and save manpower. In the agricultural sector, autonomous driving technology is mainly applied to agricultural machinery and equipment, such as driverless tractors. The key to achieving driverless tractor operation lies in its ability to quickly and accurately determine its position and attitude. However, in large-scale farmland scenarios, the number of auxiliary positioning facilities such as base stations is relatively small. Uneven terrain (non-line-of-sight) and poor network conditions lead to large communication delays and poor quality between base stations and tractors, resulting in low positioning accuracy for driverless tractors and affecting the quality of tractor-operated agricultural operations.

[0003] To address the aforementioned issues, multi-sensor fusion technology can combine the technological advantages of different sensors for joint vehicle localization, achieving higher positioning accuracy and stability compared to independent localization methods. A multi-sensor fusion localization strategy for intelligent vehicles based on global pose graph optimization has been proposed, improving positioning accuracy and environmental adaptability by employing a GPS / NRTK / IMU / visual multi-sensor fusion localization method in unknown environments. A tightly coupled stereo camera and IMU fusion localization architecture has also been proposed, enabling localization in unknown environments. To improve positioning accuracy and robustness, a GNSS / UWB / DR / VMM fusion localization strategy has been proposed, incorporating UWB for localization and relying on GNSS to maintain global consistency. However, while multi-sensor fusion algorithms offer high positioning accuracy, the sensors used for auxiliary localization are generally expensive, heavy, and power-intensive. Furthermore, to achieve the same positioning accuracy, each vehicle must be equipped with multiple positioning sensors, leading to a significant increase in cost as the number of vehicles increases.

[0004] Based on the above issues, Internet of Things (IoT) technology can enable communication between vehicles in the field of vehicle-assisted positioning, reducing positioning costs and improving positioning accuracy, and is now widely used.

[0005] Generally, existing IoT-based assisted positioning scenarios refer to adding relay devices to perform multi-hop positioning of vehicle positioning signals in order to achieve real-time and accurate positioning. Based on the type of relay device, they can be divided into two categories: fixed-point relays and mobile-point relays.

[0006] The first category is assisted positioning architecture based on fixed-point relays, such as base stations (BS), access points (AP), and roadside units (RSU). In smart city scenarios, an assisted positioning algorithm based on MIMO arrays and cooperative base stations has been proposed. Leveraging the dense base station density in cities, multiple base station cooperative nodes are established to jointly locate vehicles. Additionally, an assisted vehicle positioning system based on AP and cloud platforms has been proposed, enabling joint vehicle positioning in areas with a high AP density. A vehicle positioning system based on MIMO arrays and distributed mobile edge computing (MEC) for noncoherent distributed (ID) source direction of arrival (DOA) estimation has been proposed. An assisted positioning architecture based on deep unfolded networks has been proposed, with roadside units (RSU) responsible for signal transmission and reception, and DOA estimation performed using deep unfolded networks and MEC. However, in situations where complex surrounding environments obstruct the view of vehicles and base stations (i.e., non-line-of-sight (NLOS), the positioning performance of the above algorithms is poor. Therefore, various assisted positioning frameworks for NLOS environments have been proposed. Based on the construction of surrounding environmental occlusion conditions, vehicle-assisted localization is achieved through base stations (BS), intelligent reflectors (IRS), and some active sensors (referred to as semi-passive IRS). A virtual station-assisted DOA estimation localization algorithm is proposed for typical non-line-of-sight (NLOS) environments. All the above algorithms rely on fixed relay points for vehicle-assisted localization; however, in large-scale farmland scenarios, the number of BS, AP, and IRS devices is relatively small, resulting in limited coverage of farmland areas (e.g., ...). Figure 1 In areas where coverage is lacking, vehicle positioning errors will increase significantly. Furthermore, the construction cost of fixed-point relays is relatively high; therefore, fixed-point relay-based assisted positioning frameworks cannot be applied to large-scale agricultural scenarios.

[0007] The second category is assisted positioning architecture based on mobile point relays, such as drones. As an indispensable part of the Internet of Vehicles (IOV), a target localization framework based on multi-UAV (UAV) collaboration can be used for assisted target localization and navigation in a space-air-ground integrated network (SAGIN) environment. For smart city scenarios, this paper proposes a vehicle location-assisted analysis framework using technologies such as multi-UAVs, IoT, and distributed mobile edge computing (MEC) to implement vehicle location resolution in industrial areas. A deep learning-based architecture for non-coherent source DOA vehicle localization was constructed, achieving sub-meter positioning errors when the number of signal snapshots is 600. Since urban vehicles cannot be equipped with edge computing devices, excessive reliance on 5G / 6G links is necessary. In large-scale agricultural scenarios, poor network signals and slow information transmission lead to positioning delays. For maritime scenarios, a marine target localization (MUC-WSF) algorithm based on multi-UAV signal transmission and reception strategies was proposed for real-time position analysis of enemy ships at sea. This scenario typically requires UAVs equipped with MIMO arrays to handle signal transmission and reception. When there are many targets or the information transmission frequency is high, the drone's transmission and reception delay will be large, and the positioning frequency and error will not meet the requirements.

[0008] Furthermore, DOA estimation algorithms, as the core algorithms of assisted localization architectures, are being applied in an increasing number of scenarios. Generally, DOA estimation algorithms are divided into two categories: those based on mathematical models and those based on trained models. DOA estimation algorithms based on trained models mainly rely on extensive training of signal covariance matrix data to construct a nonlinear fitting relationship, thereby quickly estimating the DOA of unknown signals. Representative algorithms include BPNN, CNN, and DCNN. DOA estimation algorithms based on mathematical models mainly rely on constructing accurate mathematical models for DOA estimation. Beamforming and Capon's method are the most basic mathematical model-based DOA estimation algorithms; however, their estimation accuracy is relatively low. Based on this, subspace decomposition algorithms have been proposed, such as Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). However, this algorithm cannot directly process coherent signals.

[0009] Compressed sensing (CS) is a DOA estimation algorithm used when the number of snapshots is limited. CS algorithms mainly consist of three aspects: sparse representation, compressed sampling, and signal reconstruction. The sparse representation stage can be divided into three types: on-network, off-network, and unnetworked. In the signal reconstruction stage, matching pursuit (MP) and its optimized algorithms are commonly used for signal reconstruction in gridded environments, such as OMP, Hybrid Array OMP, and MSCM-OMP. However, these algorithms primarily rely on reconstructing incoming wave information for DOA estimation, resulting in poor environmental robustness.

[0010] To address the aforementioned drawbacks, subspace fitting algorithms have been proposed, with Stochastic Maximum Likelihood (SML) and Weighted Subspace Fitting (WSF) being the main representatives. Among these, SML is one of the most accurate DOA estimation algorithms currently available. Applying SML to vehicle-assisted positioning architectures can significantly improve vehicle-assisted positioning accuracy, and this algorithm is the focus of this invention. However, traditional SML algorithms involve multi-dimensional nonlinear optimization steps during DOA estimation, resulting in high computational complexity and a tendency to get trapped in local optima. Based on this, a coarse-fine DOA estimation algorithm is proposed to address local optima. First, it utilizes multi-target decoupling and target detection to obtain the targets' range bin indexes set. Then, it uses the amplitude information of each antenna for coarse DOA estimation, calculates the Cramer-Rao bound (CRLB) to obtain the value range, and finally performs fine DOA estimation using the SML algorithm. A subspace decomposition optimization-based SML algorithm is also proposed. First, a rough estimate of DOA is made using the MUSIC algorithm, and the range of values ​​is obtained based on CRLB. In the next stage, the SML algorithm is used for a finer DOA estimate. However, in large-scale farmland operations, the high noise level leads to a low signal-to-noise ratio (SNR), resulting in a small solution space limited by the above algorithms and excluding true DOA estimates. To statistically and efficiently locate as many irrelevant sources as possible, a maximum likelihood estimation algorithm (MESA) based on sequential ADMM is proposed. It employs the stochastic maximum likelihood (SML) criterion and proposes an efficient algorithm based on sophisticated problem reconstruction and the alternating direction multiplier method (ADMM). However, this algorithm is a local optimization algorithm and may get stuck in local extrema, leading to estimation bias.

[0011] To address the high computational complexity of the SML algorithm, an efficient Alternating Minimization (EAM) SML algorithm for DOA estimation is proposed. An irreducible form of the EAM criterion, IAM, is proposed for uniform linear arrays. Simulation results show that the IAM algorithm significantly reduces the computational complexity of SML estimation and avoids the numerical instability problems that may occur in AM and EAM algorithms when multiple parameters converge to the same value. A robust and statistically efficient DOA estimation algorithm for sparse linear array SML is proposed. The SML algorithm is optimized based on elegant problem reconstruction and the Alternating Direction Multiplier Method (ADMM) to reduce computational complexity. A signal subspace reconstruction and DOA estimation algorithm based on quantum particle swarm optimization is proposed. Utilizing the orthogonality between the signal space and the noise subspace, a cost function containing the required DOA information is designed. The orthogonality error is minimized using the quantum particle swarm optimization algorithm (QPSO) to determine the optimal signal subspace, thereby obtaining the DOA estimate. While the above algorithms can solve the problem of high computational complexity of the SML algorithm to some extent, the optimized SML algorithm is still not applicable to practical systems.

[0012] In summary, the existing technology has the following problems:

[0013] Question 1: Existing assisted positioning frameworks cannot be directly applied to agricultural field scenarios due to their over-reliance on high-quality network links, unmanned aerial vehicle signal transmission and reception performance, and unsuitable selection of IoT node carriers.

[0014] Question 2: Due to the limitations of the algorithm principle that restricts the solution space formation, the existing algorithm cannot effectively alleviate the drawback of SML being prone to getting trapped in local optima. Therefore, the current optimized SML algorithm cannot be directly applied to large-scale farmland operation scenarios.

[0015] Question 3: Due to the limited and singular optimization methods, the existing optimized SML algorithm still cannot be applied to practical systems. There is an urgent need to explore a new algorithm to further reduce the overall computational complexity of the DOA estimation system based on the latest optimization algorithm.

[0016] In studying the problem of agricultural machinery positioning in large-scale farmland operations, the inventors discovered the following key challenges in existing technologies:

[0017] (1) The difficulty of adapting existing auxiliary positioning architectures to agricultural field environments:

[0018] Existing assisted positioning frameworks cannot be directly applied to agricultural field scenarios due to their over-reliance on high-quality network links (such as 5G / 6G), the signal transmission and reception performance of drones, and the unsuitability of IoT node carrier selection. Specifically:

[0019] 1) Strong network dependence: Existing solutions based on mobile point relay (drones) usually rely on 5G / 6G links to transmit data, but the network environment in large-scale farmland is poor, resulting in slow information transmission and large positioning delays.

[0020] 2) Conflict between drone payload and endurance: Existing solutions often require drones to carry MIMO arrays to handle signal transmission and reception. When there are many targets, this can lead to large transmission and reception delays and high power consumption, which seriously affects endurance and makes it difficult to meet the requirements of long-term operation.

[0021] 3) Cost and coverage conflict: Fixed-point relay (base station, AP, etc.) solutions have high construction costs and limited coverage, which cannot meet the needs of wide-area farmland.

[0022] (2) The difficulty of traditional SML algorithm failing in farmland environment:

[0023] Although the SML algorithm is one of the most accurate algorithms for DOA estimation, it has serious shortcomings in large-scale farmland operation scenarios:

[0024] 1) Prone to getting trapped in local optima: Traditional SML algorithms involve multidimensional nonlinear optimization, which makes them very prone to getting trapped in local optima, leading to positioning errors.

[0025] 2) High computational complexity: Traditional algorithms involve a large amount of computation, making it difficult to meet the real-time requirements of unmanned agricultural machinery.

[0026] 3) Existing optimization algorithms fail: Existing optimization algorithms (such as those based on CRLB to limit the solution space) often have too small a solution space in the high noise and low signal-to-noise ratio environment of farmland, which can easily exclude the true DOA estimate and cause the algorithm to fail.

[0027] (3) The challenges of improving positioning accuracy by utilizing cluster characteristics:

[0028] In complex farmland environments, single positioning methods are insufficient to eliminate systematic errors. The inventors discovered that how to utilize the characteristics of agricultural machinery cluster operations to correct global errors through local high-precision information (such as GPS information of agricultural machinery within the base station coverage area) is a technical problem that urgently needs to be solved. Summary of the Invention

[0029] The purpose of this invention is to address the problems that existing assisted positioning architectures are difficult to adapt to agricultural field environments and that traditional SML algorithms fail in agricultural environments. This invention proposes a low-cost intelligent agricultural machinery assisted positioning architecture based on wireless communication links for large-scale agricultural field scenarios.

[0030] Specifically, such as Figure 6As shown, this invention proposes a low-cost assisted positioning method for multiple UAVs based on a wireless communication link, including:

[0031] The initial step involves constructing an agricultural machinery positioning system that includes multiple agricultural machines and at least three drones;

[0032] The analysis steps are as follows: when the agricultural machinery is operating, it obtains its true location based on the GPS signal emitted by the base station. At the same time, the agricultural machinery receives the electromagnetic wave signal emitted by the drone through its own onboard sensors, analyzes the electromagnetic wave signal and executes the DOA position estimation algorithm to obtain the estimated location. When the agricultural machinery moves outside the coverage area of ​​the base station and fails to receive the GPS signal, the estimated location is used as its positioning result.

[0033] The compensation step involves obtaining the actual location of the agricultural machinery after it has traveled within the coverage area of ​​the base station. The system-level angle error is calculated by using the deviation between the estimated location and the actual location. The estimated location of the agricultural machinery that failed to receive GPS signals in the positioning system is then compensated based on this system-level angle error.

[0034] The aforementioned low-cost assisted localization method for multiple UAVs based on wireless communication links includes the following parsing step:

[0035] The agricultural machinery carries sensors with an array element number of The agricultural machinery positioning system consists of a uniform linear array of M drones, each of which transmits an electromagnetic wave signal from different directions. The incident light falls onto the uniform linear array;

[0036] The array-received signal of the r-th agricultural machine is represented in complex envelope form as follows:

[0037] (1)

[0038] in express Time of the first The first agricultural machinery received by Taiwan An electromagnetic wave signal; express Time of the first The noise vector of the agricultural machinery; Indicates the first Taiwanese agricultural machinery array pointing direction The guide vector,

[0039] (2)

[0040] in c represents the speed of light, and f represents the frequency of the electromagnetic wave signal. Indicates wavelength. Represents the transpose of a matrix;

[0041] The electromagnetic wave signals received by the array of all agricultural machinery are represented as follows:

[0042] (3)

[0043] (4)

[0044] (5)

[0045] (6)

[0046] (7)

[0047] in This indicates the total number of agricultural machines in the vehicle auxiliary positioning frame;

[0048] Assuming the electromagnetic wave signal is received It is a far-field narrowband signal; and the data receiving matrix At any moment Perform sampling to form a sampling matrix:

[0049] (8)

[0050] Where K is the number of snapshots, B is the signal bandwidth, and the sample covariance matrix of the array output vector is... for:

[0051] (9)

[0052] The DOA location estimation algorithm is based on given sampled data. This yields a set of estimated positions containing the estimated directions:

[0053] (10)

[0054] Far-field narrowband signal It can be represented as:

[0055] (11)

[0056] in:

[0057] Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors; The orthogonal matrix representing the noise subspace of the r-th agricultural machine; yes Signal components in the signal subspace yes Noise components in the noise subspace;

[0058] Using the square root matrix of a nonnegative definite matrix, Represented as:

[0059] (12)

[0060] (13)

[0061] (14)

[0062] (15)

[0063] (16)

[0064] (17)

[0065] (18)

[0066] (19)

[0067] in, It is receiving signals The covariance matrix in the signal subspace, It is receiving signals The covariance matrix in the noise subspace;

[0068] covariance matrix of the signal It can be represented as:

[0069] (20)

[0070] in It is a Hermitian matrix;

[0071] Therefore, the constraints of the solution space of this DOA location estimation algorithm are:

[0072] (twenty one)

[0073] in This represents a positive semidefinite ordering; the constraint solution space is obtained based on this constraint condition. :

[0074]

[0075] (twenty two).

[0076] The aforementioned low-cost assisted localization method for multiple unmanned aerial vehicles (UAVs) based on wireless communication links includes a DOA (Domain of Arrival) estimation algorithm comprising:

[0077] enter: ;

[0078] initialization: The solution space is ;

[0079] The array received signal is obtained according to Formula 9. covariance matrix ;

[0080] Construct the constraint solution space according to Formula 31;

[0081] when At that time, random initialization is performed within the global solution space. ;if ;

[0082] ;

[0083] when and hour, ;

[0084] Calculate the Jacobian matrix ;

[0085] For signal steering vector Formula 5 is expanded using a first-order Taylor series.

[0086] Calculate the residual vector using formulas 25 and 26. ;

[0087] The parameter increment is calculated using formula 27. ;

[0088] Update the DOA parameter estimate according to Formula 28. ;

[0089] if ;

[0090] Record A convergence angle ;

[0091] Choose the solution that minimizes the SML cost function according to the following formula 30. As the final estimated location;

[0092] Output: Optimized particle position

[0093] The guidance matrix is ​​estimated with respect to the current parameter. Jacobian matrix for:

[0094] (twenty three)

[0095] The first-order Taylor expansion is:

[0096] (twenty four)

[0097] Substituting the linearized steering matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector:

[0098] (25)

[0099] (26)

[0100] Solving for parameter increments using the normal equations :

[0101] (27)

[0102] Update DOA parameter estimation:

[0103] (28)

[0104] Record A convergence angle :

[0105] (29)

[0106] Choose the solution that minimizes the SML cost function. As the final DOA estimate:

[0107] (30)

[0108] Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration.

[0109] and The definition is as follows:

[0110] (31)

[0111] (32)

[0112] By substituting the linearized guiding matrix into the residual function, expanding and deleting... The second-order term in the equation yields:

[0113] (33)

[0114] Find the increment that minimizes the residual. :

[0115] (34)

[0116] The solution to the above least squares problem is given by the normal equations:

[0117] (35).

[0118] like Figure 7 As shown, this invention also proposes a low-cost assisted positioning device for multiple UAVs based on a wireless communication link, including:

[0119] The initial module constructs an agricultural machinery positioning system that includes multiple agricultural machines and at least three drones;

[0120] The analysis module obtains the actual location of the agricultural machinery based on the GPS signal emitted by the base station during operation. At the same time, the agricultural machinery receives the electromagnetic wave signal emitted by the drone through its own onboard sensors, analyzes the electromagnetic wave signal and executes the DOA position estimation algorithm to obtain the estimated location. When the agricultural machinery moves outside the coverage area of ​​the base station and fails to receive the GPS signal, the estimated location is used as its positioning result.

[0121] The compensation module calculates the system-level angle error by using the deviation between the estimated position and the actual position after the agricultural machinery has traveled into the coverage area of ​​the base station. Based on this system-level angle error, it compensates for the estimated position of the agricultural machinery that failed to receive GPS signals in the agricultural machinery positioning system.

[0122] The aforementioned low-cost assisted positioning device for multiple unmanned aerial vehicles based on a wireless communication link, wherein the parsing module includes:

[0123] The agricultural machinery carries sensors with an array element number of The agricultural machinery positioning system consists of a uniform linear array of M drones, each of which transmits an electromagnetic wave signal from different directions. The incident light falls onto the uniform linear array;

[0124] The array-received signal of the r-th agricultural machine is represented in complex envelope form as follows:

[0125] (1)

[0126] in express Time of the first The first agricultural machinery received by Taiwan An electromagnetic wave signal; express Time of the first The noise vector of the agricultural machinery; Indicates the first Taiwanese agricultural machinery array pointing direction The guide vector,

[0127] (2)

[0128] in c represents the speed of light, and f represents the frequency of the electromagnetic wave signal. Indicates wavelength. Represents the transpose of a matrix;

[0129] The electromagnetic wave signals received by the array of all agricultural machinery are represented as follows:

[0130] (3)

[0131] (4)

[0132] (5)

[0133] (6)

[0134] (7)

[0135] in This indicates the total number of agricultural machines in the vehicle auxiliary positioning frame;

[0136] Assuming the electromagnetic wave signal is received It is a far-field narrowband signal; and the data receiving matrix At any moment Perform sampling to form a sampling matrix:

[0137] (8)

[0138] Where K is the number of snapshots, B is the signal bandwidth, and the sample covariance matrix of the array output vector is... for:

[0139] (9)

[0140] The DOA location estimation algorithm is based on given sampled data. This yields a set of estimated positions containing the estimated directions:

[0141] (10)

[0142] Far-field narrowband signal It can be represented as:

[0143] (11)

[0144] in:

[0145] Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors; The orthogonal matrix representing the noise subspace of the r-th agricultural machine; yes Signal components in the signal subspace yes Noise components in the noise subspace;

[0146] Using the square root matrix of a nonnegative definite matrix, Represented as:

[0147] (12)

[0148] (13)

[0149] (14)

[0150] (15)

[0151] (16)

[0152] (17)

[0153] (18)

[0154] (19)

[0155] in, It is receiving signals The covariance matrix in the signal subspace, It is receiving signals The covariance matrix in the noise subspace;

[0156] covariance matrix of the signal It can be represented as:

[0157] (20)

[0158] in It is a Hermitian matrix;

[0159] Therefore, the constraints of the solution space of this DOA location estimation algorithm are:

[0160] (twenty one)

[0161] in This represents a positive semidefinite ordering; the constraint solution space is obtained based on this constraint condition. :

[0162]

[0163] (twenty two).

[0164] The aforementioned low-cost assisted positioning device for multiple unmanned aerial vehicles (UAVs) based on a wireless communication link, wherein the DOA (Domain of Arrival) estimation algorithm includes:

[0165] enter: ;

[0166] initialization: The solution space is ;

[0167] The array received signal is obtained according to Formula 9. covariance matrix ;

[0168] Construct the constraint solution space according to Formula 31;

[0169] when At that time, random initialization is performed within the global solution space. ;if ;

[0170] ;

[0171] when and hour, ;

[0172] Calculate the Jacobian matrix ;

[0173] For signal steering vector Formula 5 is expanded using a first-order Taylor series.

[0174] Calculate the residual vector using formulas 25 and 26. ;

[0175] The parameter increment is calculated using formula 27. ;

[0176] Update the DOA parameter estimate according to Formula 28. ;

[0177] if ;

[0178] Record A convergence angle ;

[0179] Choose the solution that minimizes the SML cost function according to the following formula 30. As the final estimated location;

[0180] Output: Optimized particle position

[0181] The guidance matrix is ​​estimated with respect to the current parameter. Jacobian matrix for:

[0182] (twenty three)

[0183] The first-order Taylor expansion is:

[0184] (twenty four)

[0185] Substituting the linearized steering matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector:

[0186] (25)

[0187] (26)

[0188] Solving for parameter increments using the normal equations :

[0189] (27)

[0190] Update DOA parameter estimation:

[0191] (28)

[0192] Record A convergence angle :

[0193] (29)

[0194] Choose the solution that minimizes the SML cost function. As the final DOA estimate:

[0195] (30)

[0196] Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration.

[0197] and The definition is as follows:

[0198] (31)

[0199] (32)

[0200] By substituting the linearized guiding matrix into the residual function, expanding and deleting... The second-order term in the equation yields:

[0201] (33)

[0202] Find the increment that minimizes the residual. :

[0203] (34)

[0204] The solution to the above least squares problem is given by the normal equations:

[0205] (35).

[0206] The present invention also proposes a client for implementing any of the aforementioned low-cost assisted positioning devices for multiple unmanned aerial vehicles based on wireless communication links.

[0207] The present invention also proposes an electronic device, including the aforementioned low-cost assisted positioning device for multiple unmanned aerial vehicles based on a wireless communication link. The electronic device may be connected to an information display device, which is used to display the positioning result using user-set display parameters, attributes, or through an artificial intelligence model.

[0208] The present invention also proposes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the low-cost assisted positioning method for multiple unmanned aerial vehicles based on a wireless communication link.

[0209] The present invention also proposes a computer program product, comprising a computer program, wherein when the computer program is executed by a processor, it implements the steps of the low-cost assisted positioning method for multiple unmanned aerial vehicles based on a wireless communication link.

[0210] As can be seen from the above solutions, the advantages of the present invention are:

[0211] This invention first proposes a low-cost, multi-UAV assisted positioning architecture based on wireless communication links for large-scale farmland operations. Secondly, addressing the limited number of signal snapshots in practical positioning architectures for Direction of Arrival (DOA) estimation, we employ a DOA estimation model based on the Stochastic Maximum Likelihood (SML) algorithm. Furthermore, to address the issues of the SML algorithm's susceptibility to local optima and high computational complexity, we derive and construct a "constrained solution space" based on the SML algorithm, and combine it with a heuristically optimized Gauss-Newton SML-DOA estimation algorithm, named CHG-SML. Finally, simulation experiments compare the performance of the proposed algorithm with existing algorithms, demonstrating the significant advantages of the proposed algorithm. Attached Figure Description

[0212] Figure 1 This is a diagram of the multi-UAV assisted positioning architecture based on wireless communication links of the present invention;

[0213] Figure 2 This is the solution space model of the present invention;

[0214] Figure 3 is a schematic diagram of the constrained solution space for incoherent signals;

[0215] Figure 3a , Figure 3b and Figure 3c These are enlarged views of Figure 3 from left to right;

[0216] Figure 4 is a schematic diagram of the limited solution space in the case of coherent signals;

[0217] Figure 4a , Figure 4b and Figure 4c These are enlarged views of Figure 4 from left to right;

[0218] Figure 5 This is a simplified schematic diagram of the auxiliary positioning architecture of the present invention;

[0219] Figure 6 This is a flowchart of the method of the present invention;

[0220] Figure 7 This is a block diagram of the device of the present invention;

[0221] Figure 8 This is a schematic diagram of the structure of the first electronic device of the present invention;

[0222] Figure 9 This is a schematic diagram of the application environment structure of the first electronic device of the present invention;

[0223] Figure 10 This is a schematic diagram of the structure of the second electronic device of the present invention.

[0224] Figure label:

[0225] A - First electronic device;

[0226] B-Low-cost assisted positioning device for multiple UAVs based on wireless communication links;

[0227] C-Data acquisition equipment;

[0228] D-Information display device;

[0229] 1000 - Second electronic device;

[0230] Ⅰ-Computational Unit;

[0231] II-ROM;

[0232] III-RAM;

[0233] N-bus;

[0234] V-Interface;

[0235] VI - Input Unit;

[0236] VII - Output Unit;

[0237] VIII - Storage medium;

[0238] IX - Communication Unit. Detailed Implementation

[0239] It should be noted that, in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0240] Without further restrictions, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0241] The processor described in this invention is the control center of an electronic device. It can be a single processor or a collective term for multiple processing elements. For example, it can be one or more central processing units (CPUs), application-specific integrated circuits (ASICs), or one or more integrated circuits configured to implement embodiments of this invention, such as one or more digital signal processors (DSPs), or one or more field-programmable gate arrays (FPGAs).

[0242] Alternatively, the processor can perform various functions of the electronic device by running or executing software programs stored in memory and by calling data stored in memory.

[0243] In a specific implementation, as one example, the processor may include one or more CPUs. Each of these processors may be a single-core processor or a multi-core processor. Here, "processor" can refer to one or more devices, circuits, and / or processing cores for processing data (e.g., computer program instructions). Electronic devices may include servers, desktop computers, laptops, smartphones, tablets, embedded computers, etc., where the embedded computer includes vehicles and robots, etc.

[0244] The memory is used to store the software program that executes the solution of the present invention, and the execution is controlled by the processor. For specific implementation methods, please refer to the above method embodiments, which will not be repeated here.

[0245] It should be noted that the structure of the electronic device shown in the accompanying drawings of this invention does not constitute a limitation thereof. The actual knowledge structure recognition device may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0246] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0247] It should also be understood that the term "and / or" in this invention is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. A and B can be singular or plural. Furthermore, the character " / " in this invention generally indicates an "or" relationship between the preceding and following related objects, but it may also indicate an "and / or" relationship. Please refer to the preceding and following text for a more detailed understanding.

[0248] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0249] It should also be understood that, in various embodiments of the present invention, the order of the above-mentioned processes 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 the present invention.

[0250] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0251] 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.

[0252] In addition, the functional units in the various embodiments of the present invention 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.

[0253] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0254] After in-depth research, the inventors proposed the following key technical points:

[0255] (1) To address the challenges of architecture and improving positioning accuracy, an innovative low-cost intelligent agricultural machinery assisted positioning architecture based on wireless communication links for large-scale farmland scenarios is proposed. In this architecture, each agricultural machine is equipped with a uniform linear array, and the UAVs only need to perform signal transmission tasks. In addition, the local area network constructed avoids the drawbacks of over-reliance on 5G / 6G links for information transmission. The DOA estimation model proposed in this invention is used for real-time target orientation analysis, and the orientation information of the agricultural machinery is calculated through joint estimation. Three UAVs can locate all agricultural machines within the coverage area, reducing positioning costs. In addition, a system-level error compensation mechanism is designed. When some agricultural machines are within the coverage area of ​​the base station, the deviation between their actual GPS position and the DOA estimated position is used to calculate the system-level angle error, and the DOA estimation results of other agricultural machines with weaker GPS signals are compensated in real time through the communication links between agricultural machines, further approximating the actual coordinates and significantly improving the overall positioning accuracy.

[0256] (2) To address the challenges of the algorithm, the properties of the received signal were redefined and a "constrained solution space" model was proposed. This model avoids the limitations of the traditional SML algorithm in getting trapped in local optima and the constraints of the traditional constrained solution space algorithm. Furthermore, by constraining the solution space, the computational complexity of the overall algorithm model is reduced.

[0257] (3) To address the difficulties of the algorithm, based on the idea of ​​heuristic algorithms (such as PSO, GA algorithm, etc.), an SML-DOA estimation model optimized by heuristic Gauss-Newton algorithm is proposed. This model can quickly converge to the optimal solution in the "constrained solution space", which greatly reduces the positioning error and improves the real-time performance of the positioning system.

[0258] To make the above-mentioned features and effects of the present invention clearer and easier to understand, specific embodiments are described below in conjunction with the accompanying drawings. This specification discloses one or more embodiments incorporating the features of the present invention. The disclosed embodiments are merely illustrative. The scope of protection of the present invention is not limited to the disclosed embodiments, but is defined by the appended claims.

[0259] 1. System Architecture

[0260] In large-scale farmland operations, the number of base stations is relatively small, resulting in limited coverage of the farmland. Figure 1 (Medium gray area). Agricultural machinery in the base station coverage area uses GPS positioning via the base station as a relay point, achieving high positioning accuracy. Conversely, in uncovered areas, vehicle positioning errors increase significantly. Benefiting from the excellent collaborative target positioning capabilities of UAVs in the SAGIN environment, this invention proposes a multi-UAV assisted positioning architecture based on a wireless communication link, such as... Figure 1As shown, taking an agricultural machinery positioning scenario as an example, unlike existing assisted positioning frameworks, the drone in this invention does not carry array elements; it only needs to transmit electromagnetic wave signals (signal transmission node). This avoids the drawbacks of short flight time caused by drones carrying array elements and information transmission congestion caused by repeated receiving and transmitting information when there are many positioning targets. Furthermore, since unmanned agricultural machinery can carry hardware devices such as local data processing systems and signal receiving systems, in the positioning framework proposed in this invention, the agricultural machinery, as an IoT node in the SAGIN environment, can perform data processing itself, and each node is equipped with a uniform linear array (ULA). Figure 1 The drone remains stationary relative to the agricultural machinery, meaning its position remains unchanged even as the machinery moves. Furthermore, within the drone's coverage area, this auxiliary positioning architecture can support cluster positioning of multiple agricultural machines, significantly reducing positioning costs.

[0261] In terms of wireless communication link construction, a local area network (LAN) was built between the drone and the tractor, avoiding the problem of positioning delay or failure caused by communication failure or large communication latency between UVAs and MEC due to the unstable performance of 4G / 5G networks in large-scale farmland. Figure 1 In the diagram, the red line represents the drone signal transmission link, the yellow line represents the LAN link connecting the drone and the intelligent agricultural machine, and the blue line represents the ZigBee wireless communication link connecting the intelligent agricultural machines. In the signal transmission link, the drone sends electromagnetic signals to the tractor; in the LAN link, the drone sends its own GPS and battery information to the tractor; and in the ZigBee link, the intelligent agricultural machines transmit their own GPS, battery information, and DOA estimation errors to each other. During unmanned operation, the intelligent agricultural machine's onboard array continuously receives electromagnetic signals from the drone and synchronizes the clocks between multiple signals. Then, using a DOA estimation algorithm, the phase difference and intensity changes of the received signals are analyzed to obtain the azimuth angle information of the intelligent agricultural machine relative to the drone at the same moment. Furthermore, since the intelligent agricultural machines in the positioning architecture operate in clusters, when the machine enters the base station coverage area at time t, the deviation between its DOA estimated position and its actual GPS position can be used to calculate the system-level angle error. When the environmental noise satisfies zero-mean ergodicity and the noise covariance matrix of the received signals from each agricultural machine is consistent (the noise carried by each signal is basically the same), the system-level angle error can be used to compensate for the DOA estimation results of other agricultural machines with weaker GPS signals. This process has a significant statistical gain on positioning accuracy. By combining the DOA estimation information obtained from multiple UAVs with the system-level angle error, the relative position of the intelligent agricultural machine (position in the UAV coordinate system) is jointly solved. Finally, based on the GPS position of the UAV, the current GPS position of the tractor (position in the world coordinate system) is analyzed.

[0262] It is worth noting that in the wireless communication link, UVAs and agricultural machinery communicate using the Wi-Fi 6 (IEEE 802.11ax) protocol at 5GHz with 40 channels. This method has strong anti-interference capabilities and is suitable for short-distance, high-bandwidth transmission. The electromagnetic waves transmitted and received between the agricultural machinery and the drone use the 24GHz band, which has good penetration and is less affected by weather. Communication between agricultural machinery uses ZigBee (IEEE 802.15.4) at 868MHz, employing the ZigBee local area network communication protocol. Because these three types of electromagnetic waves differ in modulation methods, spatial attenuation characteristics, and power, they are frequency-isolated. Therefore, it can be said that interference between the information communication links in this architecture is minimal.

[0263] Based on the above discussion, a simplified diagram of the assisted positioning architecture is shown below. Figure 5 As shown. Considering the overall cost of the positioning architecture, this embodiment deploys three drones, and randomly selects one of them as the coordinate origin, for example, choosing... As the origin. In addition, to ensure that the drones can fully cover the operation path of agricultural machinery, the relative positions of the three drones usually form a triangular layout, and the selection of drone positions has a certain degree of local randomness.

[0264] in, Indicates agricultural machinery The path trajectory; Indicates agricultural machinery The path trajectory; Indicates agricultural machinery At any moment GPS location information; Indicates agricultural machinery At any moment GPS location information; , and They represent the times at time 1 and 2 respectively. Depend on and , and , and Predicted location points of intelligent agricultural machinery obtained through joint estimation of DOA.

[0265] Assume at time... Agricultural machinery The GPS signal quality is relatively high, that is... If it is known, then it can be calculated. and , and The relative positional relationship between any two predicted locations, i.e. , or Determine system-level angle error , and .

[0266] This invention is based on and For example, the system-level angle error can be expressed as:

[0267]

[0268]

[0269]

[0270] Consider intelligent agricultural machinery The received GPS signal at time In cases of degradation, pose recovery requires UAV-assisted DOA joint estimation. For clarity, without loss of generality, we will use UAV-assisted DOA joint estimation. Taking one example as an illustration, the other drone pairs can be handled in a symmetrical manner.

[0271] set up Indicates at time Depend on and Agricultural machinery obtained through joint estimation The position. To characterize the effect caused by hardware bias, maintain The azimuth angle remains unchanged, and towards Inject system-level angular perturbations into the azimuth angle Thus, the perturbed DOA is obtained:

[0272]

[0273] Among them, the positive and negative signs are determined by The direction determines the position. This yields two candidate positions. and Both share a coordinate system. and corresponding azimuth angles respectively .

[0274] because It only indicates the magnitude of the deviation, not its direction. Therefore, to achieve precise positioning, it is necessary to distinguish between two candidate positions. To this end, this method utilizes readily available prior information, namely, agricultural machinery... Pre-planned operation trajectory By calculating the Euclidean distances from the two candidate locations to the pre-planned job trajectory:

[0275]

[0276] And retain the candidate positions with smaller residuals as the final correction positions, that is:

[0277]

[0278] Since normally operating agricultural machinery typically deviates only slightly from its pre-planned path, a discrimination criterion based on trajectory priors can make the estimated position closer to the agricultural machinery. The true coordinates. Compared with the DOA positioning reference method without introducing disturbance compensation, this method can achieve a consistent improvement in positioning accuracy.

[0279] Extending the above rules to all drone assemblies and agricultural machinery The three azimuth angles relative to the three drones can be expressed as follows:

[0280]

[0281]

[0282]

[0283] Each of the three UAV pairs independently generates a relative position estimate, which is calculated locally by the tractor. The final pose is obtained by averaging the estimates from all UAV pairs, thereby suppressing the bias effect of a single UAV pair and enhancing the stability of the positioning output under non-line-of-sight propagation conditions.

[0284] Assuming that after error compensation, the final position of the agricultural machinery is .according to and The location and corresponding DOA information, the first set of positioning positions for agricultural machinery. It can be represented as:

[0285]

[0286] Similarly, the other two sets of location results can be represented as follows:

[0287]

[0288]

[0289]

[0290] Finally, the current position of the agricultural machinery can be calculated as follows:

[0291]

[0292] The constraints are as follows:

[0293] (1) The angle formed between any two drones and intelligent agricultural machinery shall not be equal to the angle between them at the same time. That is, satisfying:

[0294]

[0295]

[0296]

[0297] To meet the above conditions, all three drones were deployed outside the work site.

[0298] (2) In the second set of positioning formulas above, the following should be satisfied:

[0299]

[0300] Right now:

[0301]

[0302] Alternatively, in the third set of positioning formulas above, the following should be satisfied:

[0303]

[0304] Right now:

[0305]

[0306] In large-scale farmland operations, various agricultural tasks, such as sowing, land preparation, and spraying, all focus on the lateral errors generated by agricultural machinery operations. Therefore, this invention focuses on the horizontal angular error of the assisted positioning architecture. In the aforementioned intelligent agricultural machinery assisted positioning architecture, DOA estimation is a core component. The more accurate the DOA estimation, the higher the accuracy of the agricultural machinery assisted positioning. The SML algorithm is one of the most accurate DOA estimation algorithms currently available. Applying the SML algorithm to the vehicle assisted positioning architecture can significantly improve the vehicle assisted positioning accuracy. Therefore, the following mainly introduces the SML-DOA algorithm.

[0307] 2. DOA estimation model based on SML algorithm

[0308] The number of array elements is set to In theory, any array manifold is allowed; however, implementations of DOA estimation typically employ predefined array configurations, including uniform linear arrays (ULAs). Furthermore, with M drones each transmitting one signal, the model contains M far-field narrowband signals originating from different directions at a known common center frequency. The signal is incident on the sensor array. It is modeled under the far-field narrowband assumption, with the condition N > M.

[0309] The array elements are isotropic and independent. By randomly selecting the r-th agricultural machine from the vehicle-assisted positioning architecture described in the system architecture description, the array received signal of the r-th agricultural machine can be represented in complex envelope form as follows:

[0310] (36)

[0311] in express Time of the first The first agricultural machinery received by Taiwan One signal. express Time of the first The noise vector of the agricultural machinery. Indicates the first Taiwanese agricultural machinery array pointing direction The “guide vector” can be represented as:

[0312] (37)

[0313] in c represents the speed of light. f represents the signal frequency. Indicates wavelength. This represents the transpose of a matrix.

[0314] The array-received signals of all agricultural machinery in the vehicle-assisted positioning architecture can be represented as:

[0315] (38)

[0316] (39)

[0317] (40)

[0318] (41)

[0319] (42)

[0320] in This represents the total number of agricultural machines in the vehicle-assisted positioning frame. In actual large-scale farmland operation scenarios, it is assumed that the noise environment at each agricultural machine is additive white Gaussian noise (AWGN), and the noise satisfies the "statistically identical distribution characteristic", that is, only the noise power (or variance) exhibits different amplitudes due to factors such as the position of the agricultural machine, surrounding electromagnetic obstacles, and differences in the electronic components of each agricultural machine, while the probability distribution characteristics of the noise (such as mean and autocorrelation function) remain consistent.

[0321] Assuming the received signal It is a far-field narrowband signal, i.e. In the formula Let f be the signal wavelength and f be the signal frequency. And the data receiving matrix... At any moment Perform sampling to form a sampling matrix:

[0322] (43)

[0323] Where K is the number of snapshots and B is the signal bandwidth. The sample covariance matrix of the array output vector. for:

[0324] (44)

[0325] The DOA estimation problem is described below. Given sampled data... We can obtain a set of estimated directions:

[0326] (45)

[0327] Far-field narrowband signal It can be represented as:

[0328] (46)

[0329] The evaluation criteria for the SML algorithm are:

[0330] (47)

[0331] In the above formula:

[0332] (48)

[0333] (49)

[0334] (50)

[0335] (51)

[0336] This represents the steering vector of the signal received by the r-th agricultural machine; This represents the noise covariance.

[0337] Solving the DOA estimation problem using the SML algorithm is transformed into finding a unique set of solutions such that... Minimize. However, in practical implementations of the SML algorithm, there are problems such as being prone to getting trapped in local optima (inaccuracy) and high computational complexity (non-real-time). Being prone to getting trapped in local optima specifically refers to the use of... During the solution process, multiple optimal solutions may emerge, while only one solution may closely approximate the true value, yet these may be difficult to distinguish. High computational complexity specifically refers to the fact that the SML algorithm involves nonlinear function optimization during the solution process, and its computational complexity increases significantly with increasing dimensionality. In view of the problems existing in the traditional SML algorithm, a series of optimization methods will be proposed in the following sections.

[0338] 3. SML DOA estimation model optimized by multi-heuristic Gauss-Newton algorithm based on constraint solution space

[0339] 3.1 Definition of Constraint Solution Space

[0340] According to the evaluation criteria of the SML algorithm, when the array is a uniform linear array (ULA) with two independent incident angles, the entire solution space... Indicates each angle of incidence The set of all possible angles, i.e. In the presence of noise, the global search of the traditional SML algorithm may sometimes identify a solution that is far from the true direction of arrival (DOA), even though a local solution that is closer to the true DOA exists.

[0341] In addition, such as Figure 2 As shown, in practical DOA estimation, we found that we only need to optimize the SML algorithm near the true solution (the red area in the figure), which is also called the efficient computation region. The inefficient computation region contains local optima of the SML algorithm, i.e., interference solutions, and significantly increases the computational complexity of the SML algorithm. The next step is how to identify these in practical DOA estimation. Figure 2 The effective calculation area is shown (the red area in the figure).

[0342] Inspired by the assumption that signals must be non-negative definite, the concept of a "constrained solution space" is proposed for the first time. This invention first provides a constrained solution space, and then uses a heuristic Gauss-Newton improved SML algorithm within this constrained solution space to perform DOA estimation. All of these are aimed at achieving faster and more accurate DOA estimation. The constrained solution space is used to limit the range of the solution space, which helps the subsequent heuristic Gauss-Newton improved SML algorithm to find the optimal DOA estimate.

[0343] Formula 11 can be rewritten as follows:

[0344] (52)

[0345] in Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors. Let represent the orthogonal matrix of the noise subspace of the r-th agricultural machine, which is the orthogonal complement of the signal subspace. yes Signal components in the signal subspace yes Noise components in the noise subspace.

[0346] Using the square root matrix of a nonnegative definite matrix, It can be represented as:

[0347] (53)

[0348] (54)

[0349] From the above definition, we can conclude that:

[0350] (55)

[0351] (56)

[0352] (57)

[0353] (58)

[0354] Through formula 20 and the definition and We can conclude that:

[0355] (59)

[0356] (60)

[0357] in, It is receiving signals The covariance matrix in the signal subspace, It is receiving signals The covariance matrix in the noise subspace.

[0358] covariance matrix of the signal It can be represented as:

[0359] (61)

[0360] in It is a Hermitian matrix. This is due to the covariance matrix of the signal component. The condition that a non-negative definite matrix must be satisfied can be deduced. The matrix is ​​also nonnegative definite. Therefore, the conditions for the solution space become:

[0361] (62)

[0362] in This represents a positive semidefinite ordering. We call the region obtained based on this constraint the constraint solution space of SML, as shown below:

[0363]

[0364] (63)

[0365] Equivalently, the constraint in Formula 31 can be expressed as:

[0366] (64)

[0367] in This represents the smallest eigenvalue of the matrix.

[0368] Based on the above derivation, the constraint solution space is shown in Figures 3 and 4. Experimental conditions are as follows: In the solution space In the middle, two angle values ​​are randomly generated. To determine the constrained solution space under incoherent and coherent source scenarios. The angle search step size for each iteration is... .

[0369] Figures 3(a) and 4(a) show the global solution space distribution of the SML algorithm. The red areas in the figures represent the proposed constraint solution space. Figures 3(b) and 4(b) show the spatial distribution of the proposed constraint solution space, which also includes the true solution. Furthermore, the three-dimensional constraint solution space is projected onto an angular plane, and the ratio of the constraint solution space to the global solution space is calculated. Under uncorrelated and coherent signal conditions, the constraint solution space occupies [percentage] of the global solution space, respectively. and It is worth noting that the constrained solution space of coherent signals is smaller than that of uncorrelated signals. This is mainly because the correlation between signals introduces strong structural prior information (i.e., low-rank characteristics) into the signal covariance matrix, which significantly tightens the boundaries of the solution space. The gray area in the figure represents the redundant solution space, where the local optimum of the SML algorithm resides. This area also increases the computational complexity of the SML algorithm. Figures 3(c) and 4(c) show the three-dimensional surface plots of Equation 32 over the angular combination interval. The green plane corresponds to the condition. The regions of the surface above the green plane represent angle combinations that satisfy the physical constraints and belong to the feasible solution space, while the regions below the green plane do not satisfy the constraints and should be excluded. In summary, as can be observed from the figure, the proposed constraint solution space significantly reduces the solution space of the SML algorithm, thereby avoiding the possibility of the SML algorithm getting trapped in local optima.

[0370] 3.2 SML-DOA Estimation Model Based on Heuristic Gauss-Newton Algorithm Optimized by Constrained Solution Space

[0371] Due to the limited and singular nature of optimization methods, existing optimization SML algorithms exhibit high computational complexity and remain unsuitable for practical systems. There is an urgent need to explore a new algorithm that further reduces the computational complexity of SML algorithms compared to existing DOA estimation algorithms, such as the State of the Origin (SOTA) algorithm.

[0372] The Gauss-Newton algorithm approximates the objective function of the SML algorithm using a Taylor series expansion, and then iteratively updates the parameters, gradually converging to the optimal solution of the nonlinear optimization problem. Its goal is to minimize the sum of squared residuals of the original model (i.e., the cost function of the SML algorithm), ultimately obtaining the DOA estimate. The main advantage of this algorithm is that, given a good initial guess, it exhibits fast convergence and high accuracy, thus becoming one of the main methods for solving nonlinear optimization problems.

[0373] Although the traditional Gauss-Newton algorithm has low computational complexity, its convergence result is overly dependent on the choice of initial value and the nonlinearity of the objective function. When the selected initial value is close enough to the optimal solution, the algorithm can achieve a high linear convergence speed, and even guarantee quadratic convergence. However, when the selected initial value is far from the optimal solution, the convergence performance will significantly decrease, and in severe cases, the algorithm may fail to converge.

[0374] Based on the above discussion, this invention, combining the definition of "constrained solution space" and utilizing heuristic principles, proposes an SML-DOA estimation model optimized by a heuristic Gauss-Newton algorithm based on constrained solution space. The core idea of ​​this model is to constrain the solution space based on the constrained solution space, thereby narrowing the range of initial values ​​to be selected for the Gauss-Newton algorithm. Furthermore, using heuristic principles, multiple initial points are selected within the constrained solution space, and parallel computation is employed for simultaneous convergence iteration. This method, while maintaining sufficiently low computational complexity, further reduces the risk of the Gauss-Newton algorithm converging to local optima, thus improving the overall accuracy of the DOA estimation algorithm. The main process of this model is shown in Algorithm 1.

[0375] enter:

[0376] initialization: The solution space is

[0377] The array received signal is obtained according to Formula 9. covariance matrix ;

[0378] Construct the constraint solution space according to Formula 31;

[0379] While do;

[0380] Random initialization within the global solution space ;

[0381] if ;

[0382] ;

[0383] While do;

[0384] While ( do;

[0385] ;

[0386] Calculate the Jacobian matrix ;

[0387] right Perform a first-order Taylor expansion;

[0388] Calculate the residual vector ;

[0389] Solving for parameter increments ;

[0390] Update DOA parameter estimation ;

[0391] if ;

[0392] Record A convergence angle ;

[0393] Choose the solution that minimizes the SML cost function. As the final DOA estimate;

[0394] Output: Optimized particle position

[0395] In Algorithm 1, the guiding matrix is ​​estimated with respect to the current parameter. Jacobian matrix for:

[0396] (65)

[0397] The first-order Taylor expansion is:

[0398] (66)

[0399] It achieves the linearization of the nonlinear guidance matrix. Substituting the linearized guidance matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector:

[0400] (67)

[0401] (68)

[0402] Solving for parameter increments using the normal equations :

[0403] (69)

[0404] Update DOA parameter estimation:

[0405] (70)

[0406] Record A convergence angle :

[0407] (71)

[0408] Choose the solution that minimizes the SML cost function. As the final DOA estimate:

[0409] (72)

[0410] Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration.

[0411] and The definition is as follows:

[0412] (73)

[0413] (74)

[0414] By substituting the linearized guiding matrix into the residual function, expanding and ignoring... From the second-order terms in the equation, we obtain:

[0415] (75)

[0416] Our goal is to find the increment that minimizes the residual. :

[0417] (76)

[0418] The solution to the above least squares problem is given by the normal equations:

[0419] (77)

[0420] Furthermore, steps 1-6 constitute the process of constructing the constraint solution space. Steps 7-17 constitute the process of optimizing the SML-DOA estimation model based on the heuristic Gauss-Newton algorithm.

[0421] Simulation Experiment

[0422] This section compares the proposed CHG-SML algorithm with QPSO-SML, ss-MUSIC, MSCM-OMP, MUC-WSF, and MESA through multiple experiments. QPSO-SML uses the QPSO algorithm for global optimization in the SML solution space. ss-MUSIC applies spatial smoothing techniques to the MUSIC algorithm. MSCM-OMP, MUC-WSF, and MESA represent state-of-the-art methods in compressed sensing (CS) and subspace fitting, respectively.

[0423] The array model was selected as a uniform linear array (ULA). In addition, the distance between two adjacent sensors It is the signal wavelength 1 / 2. The angle search step size for all algorithms is set to 1 / 2. All results are based on 100 Monte Carlo (MC) trials. The root mean square error (RMSE) was used to assess the accuracy of the estimation, defined as follows:

[0424] (78)

[0425] Where M represents the number of information sources. and Let represent the estimated angle value of DOA for the m-th source in the i-th iteration and the actual angle value for the m-th source, respectively.

[0426] 4.1 Comparison of DOA estimation accuracy

[0427] Figure 5 The results of DOA estimation for each algorithm under incoherent signal conditions obtained through Monte Carlo simulation are presented. The experimental parameters are set as follows: the angle search range is... .from Randomly select a set of angle values As real DOAs, DOAs were estimated and recorded using the proposed CHG-SML algorithm, as well as QPSO-SML, ss-MUSIC, MESA, MUC-WSF, and MSCM-OMP algorithms, for comparison. A total of MC = 100 estimated DOAs were recorded for each algorithm.

[0428] As can be observed from the figure, algorithms whose estimated values ​​exhibit significant fluctuations around the true DOA value have weaker estimation performance. Conversely, algorithms whose estimated values ​​exhibit minimal dispersion around the true value have stronger estimation performance. Compared to state-of-the-art algorithms, the proposed CHG-SML algorithm produces estimated values ​​closer to the true DOA, demonstrating higher estimation accuracy and superior robustness.

[0429] Figure 6 and Figure 7 The incoherent signals were shown respectively. Figure 6 ) and coherent signals ( Figure 7 The figure shows the RMSE versus SNR curves under low SNR conditions. As shown, ss-MUSIC, MSCM-OMP, and QPSO-SML exhibit large DOA estimation errors under low SNR conditions. In contrast, the proposed CHG-SML algorithm maintains superior DOA estimation performance even under low SNR conditions. It is worth noting that due to multipath propagation effects, the overall RMSE of coherent signals is higher than that of incoherent signals. Nevertheless, this algorithm still exhibits excellent DOA estimation performance under coherent signal conditions.

[0430] Furthermore, for incoherent signals, in At that time, the RMSE of CHG-SML were QPSO-SML, ss-MUSIC, MESA, MUC-WSF, and MSCM-OMP, respectively. and For coherent signals, in At that time, the RMSE of CHG-SML were QPSO-SML, ss-MUSIC, MESA, MUC-WSF, and MSCM-OMP, respectively. and These results demonstrate that CHG-SML achieves higher DOA estimation accuracy compared to existing state-of-the-art algorithms.

[0431] Figure 7 Curve of RMSE as a function of SNR under coherent signal conditions

[0432] 4.2 Comparison of Position Errors

[0433] The positioning accuracy of autonomous agricultural vehicles is mainly controlled by two error sources: the compensated DOA estimation error and the time delay error.

[0434] DOA estimation after system-level error compensation: Individual agricultural machinery units are randomly distributed within the drone's coverage area, forming a set. ,in Indicates the first The actual position of the agricultural machinery in the drone's reference frame, while the drone remains stationary throughout the experiment. In the drone's reference frame, assume the drone... , and The positions are respectively and Furthermore, during the positioning process, at least one agricultural machine within the drone's coverage area must have available GPS positioning information.

[0435] In the experiment, the signal source is coherent. The signal-to-noise ratio (SNR) is set to... and The CHG-SML, QPSO-SML, ss-MUSIC, MESA, MUC-WSF, and MSCM-OMP algorithms were used to... DOA estimation is performed on the location of each agricultural machine to obtain angle information, i.e. , , .in , and They represent drones , and agricultural machinery The DOA estimate obtained after system-level error compensation is 67. Using these angle estimates, the following calculations are performed. The average positioning error of the test for:

[0436] (79)

[0437] in and Let x and y represent the actual x and y coordinates of the j-th agricultural machine in the UAV coordinate system, respectively. and

[0438] Let x and y represent the estimated x and y coordinates of the j-th agricultural machine in the UAV coordinate system during the i-th experiment, respectively. Furthermore, This represents the estimated position of the agricultural machinery without systematic error compensation, while The subscript indicates the positioning error after system-level error compensation.

[0439] Time delay error: This refers to the mismatch between discrete positioning updates and the continuous movement of the agricultural machinery. During field operations, the machinery moves continuously, while the vehicle-assisted positioning architecture provides discrete positioning points, resulting in a trajectory composed of positioning points separated by time intervals t. In continuous positioning points... and The time interval between Within this area, the agricultural machinery has not received a positioning update, which may cause navigation errors to increase proportionally with the machinery's speed. Therefore, reducing... This can reduce latency errors, but it increases the computational burden on the positioning algorithm. Therefore, we compared... The average computation time required for DOA estimation using the CHG-SML, QPSO-SML, ss-MUSIC, MESA, MUC-WSF, and MSCM-OMP algorithms. The average operating speed of the agricultural machinery is set to... The time delay error is calculated based on the speed of the agricultural machinery as follows: The experiments were conducted on a personal computer equipped with an Intel R7-4800H CPU and 16 GB of RAM using MATLAB R2023b, where $K=16$. It was assumed that the differences in propagation delay between algorithms due to electromagnetic wave propagation in the air and hardware-related factors were negligible. Furthermore, although the maximum update rate of GPS is 10 Hz (corresponding to an update interval of 0.1 s), the proposed CHG-SML algorithm achieves... Therefore, the CHG-SML algorithm synchronizes with the UAV's GPS data transmission, enabling the proposed vehicle-assisted positioning architecture to update the agricultural machinery's position with negligible delay, thereby achieving a higher update rate and higher positioning accuracy.

[0440] The overall navigation error of the agricultural machinery is shown in Table 1. Regarding positioning error, the CHG-SML algorithm shows lower positioning errors than existing algorithms at all signal-to-noise ratio levels (shown in bold). Time error is Regarding latency error, compared to existing algorithms, the CHG-SML algorithm achieves the lowest computation time and latency error across all signal-to-noise ratio levels (shown in bold). The total navigation error is calculated as follows: These results demonstrate that, compared to existing algorithms, the CHG-SML algorithm achieves higher positioning accuracy while reducing computational complexity. Furthermore, after system-level error compensation, the algorithm exhibits even stronger practical performance.

[0441] Table 1. Comparison of Overall Navigation Errors of Agricultural Machinery

[0442]

[0443] The following are system embodiments corresponding to the above method embodiments. This embodiment can be implemented in conjunction with the above embodiments. The relevant technical details mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0444] like Figure 7 As shown, this invention also proposes a low-cost assisted positioning device for multiple UAVs based on a wireless communication link, including:

[0445] The initial module constructs an agricultural machinery positioning system that includes multiple agricultural machines and at least three drones;

[0446] The analysis module obtains the actual location of the agricultural machinery based on the GPS signal emitted by the base station during operation. At the same time, the agricultural machinery receives the electromagnetic wave signal emitted by the drone through its own onboard sensors, analyzes the electromagnetic wave signal and executes the DOA position estimation algorithm to obtain the estimated location. When the agricultural machinery moves outside the coverage area of ​​the base station and fails to receive the GPS signal, the estimated location is used as its positioning result.

[0447] The compensation module calculates the system-level angle error by using the deviation between the estimated position and the actual position after the agricultural machinery has traveled into the coverage area of ​​the base station. Based on this system-level angle error, it compensates for the estimated position of the agricultural machinery that failed to receive GPS signals in the agricultural machinery positioning system.

[0448] The aforementioned low-cost assisted positioning device for multiple unmanned aerial vehicles based on a wireless communication link, wherein the parsing module includes:

[0449] The agricultural machinery carries sensors with an array element number of The agricultural machinery positioning system consists of a uniform linear array of M drones, each of which transmits an electromagnetic wave signal from different directions. The incident light falls onto the uniform linear array;

[0450] The array-received signal of the r-th agricultural machine is represented in complex envelope form as follows:

[0451] Formula 1

[0452] in express Time of the first The first agricultural machinery received by Taiwan An electromagnetic wave signal; express Time of the first The noise vector of the agricultural machinery; Indicates the first Taiwanese agricultural machinery array pointing direction The guide vector,

[0453] Formula 2

[0454] in c represents the speed of light, and f represents the frequency of the electromagnetic wave signal. Indicates wavelength. Represents the transpose of a matrix;

[0455] The electromagnetic wave signals received by the array of all agricultural machinery are represented as follows:

[0456] Formula 3

[0457] Formula 4

[0458] Formula 5

[0459] Formula 6

[0460] Formula 7

[0461] in This indicates the total number of agricultural machines in the vehicle auxiliary positioning frame;

[0462] Assuming the electromagnetic wave signal is received It is a far-field narrowband signal; and the data receiving matrix At any moment Perform sampling to form a sampling matrix:

[0463] Formula 8

[0464] Where K is the number of snapshots, B is the signal bandwidth, and the sample covariance matrix of the array output vector is... for:

[0465] Formula 9

[0466] The DOA location estimation algorithm is based on given sampled data. This yields a set of estimated positions containing the estimated directions:

[0467] Formula 10

[0468] Far-field narrowband signal It can be represented as:

[0469] Formula 11

[0470] in:

[0471] Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors; The orthogonal matrix representing the noise subspace of the r-th agricultural machine; yes Signal components in the signal subspace yes Noise components in the noise subspace;

[0472] Using the square root matrix of a nonnegative definite matrix, Represented as:

[0473] Formula 12

[0474] Formula 13

[0475] Formula 14

[0476] Formula 15

[0477] Formula 16

[0478] Formula 17

[0479] Formula 18

[0480] Formula 19

[0481] in, It is receiving signals The covariance matrix in the signal subspace, It is receiving signals The covariance matrix in the noise subspace;

[0482] covariance matrix of the signal It can be represented as:

[0483] Formula 20

[0484] in It is a Hermitian matrix;

[0485] Therefore, the constraints of the solution space of this DOA location estimation algorithm are:

[0486] Formula 21

[0487] in This represents a positive semidefinite ordering; the constraint solution space is obtained based on this constraint condition. :

[0488]

[0489] Formula 22.

[0490] The aforementioned low-cost assisted positioning device for multiple unmanned aerial vehicles (UAVs) based on a wireless communication link, wherein the DOA (Domain of Arrival) estimation algorithm includes:

[0491] enter: ;

[0492] initialization: The solution space is ;

[0493] The array received signal is obtained according to Formula 9. covariance matrix ;

[0494] Construct the constraint solution space according to Formula 31;

[0495] when At that time, random initialization is performed within the global solution space. ;if ;

[0496] ;

[0497] when and hour, ;

[0498] Calculate the Jacobian matrix ;

[0499] For signal steering vector Formula 5 is expanded using a first-order Taylor series.

[0500] Calculate the residual vector using formulas 25 and 26. ;

[0501] The parameter increment is calculated using formula 27. ;

[0502] Update the DOA parameter estimate according to Formula 28. ;

[0503] if ;

[0504] Record A convergence angle ;

[0505] Choose the solution that minimizes the SML cost function according to the following formula 30. As the final estimated location;

[0506] Output: Optimized particle position

[0507] The guidance matrix is ​​estimated with respect to the current parameter. Jacobian matrix for:

[0508] Formula 23

[0509] The first-order Taylor expansion is:

[0510] Formula 24

[0511] Substituting the linearized steering matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector:

[0512] Formula 25

[0513] Formula 26

[0514] Solving for parameter increments using the normal equations :

[0515] Formula 27

[0516] Update DOA parameter estimation:

[0517] Formula 28

[0518] Record A convergence angle :

[0519] Formula 29

[0520] Choose the solution that minimizes the SML cost function. As the final DOA estimate:

[0521] Formula 30

[0522] Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration.

[0523] and The definition is as follows:

[0524] Formula 31

[0525] Formula 32

[0526] By substituting the linearized guiding matrix into the residual function, expanding and deleting... The second-order term in the equation yields:

[0527] Formula 33

[0528] Find the increment that minimizes the residual. :

[0529] Formula 34

[0530] The solution to the above least squares problem is given by the normal equations:

[0531] Formula 35.

[0532] The present invention also proposes a client for implementing any of the aforementioned low-cost assisted positioning devices for multiple unmanned aerial vehicles based on wireless communication links.

[0533] like Figure 8 As shown, in another embodiment of the present invention, a first electronic device A is also proposed, which includes the aforementioned low-cost assisted positioning device B for multiple unmanned aerial vehicles based on a wireless communication link.

[0534] like Figure 9 As shown, the first electronic device A can also be connected to the data acquisition device C and the information display device D through a wired or wireless information transmission scheme. The data acquisition device C is used to acquire signals, and the information display device D is used to display the position obtained by the analysis of the present invention.

[0535] The information display device D can process and organize the data output by the first electronic device A based on an information display mechanism to improve the readability of the data. This information display mechanism can be manually preset, for example, visualizing the data output by the first electronic device A. It can present the user with the specified key information based on user-defined display parameters and / or attributes, such as the data range and font, color, and scrolling options. Users can access this information more quickly without needing to navigate to secondary pages or scroll through pages, saving them time and effort. Alternatively, the information display mechanism can be an artificial intelligence (AI) display model that learns the user's key information interests based on past usage habits, such as viewing time, click count, and edit count, and automatically presents rich and necessary key information.

[0536] The present invention also provides a computer program product, which includes a computer program that can be stored on a readable storage medium. When the computer program is executed by a processor, the computer is able to execute the low-cost assisted positioning method for multiple UAVs based on wireless communication links provided by the above methods.

[0537] In another embodiment, the present invention also proposes a storage medium VIII for storing a computer program that executes the aforementioned low-cost assisted positioning method for multiple unmanned aerial vehicles based on a wireless communication link. It should be understood that the storage medium in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which serves as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0538] Figure 10 A schematic block diagram of a second electronic device 1000 that can be used to implement embodiments of the present invention is shown. The second electronic device 1000 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The second electronic device 1000 can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown in this invention, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein. The second electronic device 1000 may be the same as or different from the first electronic device A.

[0539] The second electronic device 1000 includes a computing unit I, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory II (ROM) or a computer program loaded from storage medium VIII into random access memory (RAM) III. The RAM III may also store various programs and data required for the operation of the device 1000. The computing unit I, ROM II, and RAM III are interconnected via bus IV. An input / output (I / O) interface V is also connected to bus IV.

[0540] Multiple components in the second electronic device 1000 are connected to I / O interface V, including: input unit VI, such as a keyboard, mouse, etc.; output unit VII, such as various types of displays, speakers, etc.; storage medium VIII, such as a disk, optical disk, etc.; and communication unit IX, such as a network card, modem, wireless transceiver, etc. Communication unit IX allows the second electronic device 1000 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0541] The computing unit I can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of computing unit I include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit I performs the various methods and processes described above, such as method steps S1-S3. For example, in some embodiments, the methods can be implemented as computer software programs tangibly contained in a machine-readable medium, such as storage medium VIII. In some embodiments, part or all of the computer program can be loaded and / or installed on device 1000 via ROM II and / or communication unit IX. When the computer program is loaded into RAM III and executed by computing unit I, one or more steps of the methods described above can be performed. Alternatively, in other embodiments, computing unit I can be configured to perform methods by any other suitable means (e.g., by means of firmware).

[0542] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A low-cost assisted positioning method for multiple unmanned aerial vehicles (UAVs) based on a wireless communication link, characterized in that, include: The initial step involves constructing an agricultural machinery positioning system that includes multiple agricultural machines and at least three drones; The analysis steps are as follows: when the agricultural machinery is operating, it obtains the real location based on the GPS signal emitted by the base station. At the same time, the agricultural machinery receives the electromagnetic wave signal emitted by the drone through its own onboard sensors, analyzes the electromagnetic wave signal and executes the DOA position estimation algorithm to obtain the estimated position. When agricultural machinery travels outside the coverage area of ​​a base station and fails to receive GPS signals, the estimated location is used as its positioning result. The compensation step involves obtaining the actual location of the agricultural machinery after it has traveled within the coverage area of ​​the base station, and then calculating the system-level angle error by using the deviation between its estimated location and the actual location. The estimated position of agricultural machinery that fails to receive GPS signals in the agricultural machinery positioning system is compensated based on the system-level angle error.

2. The low-cost assisted positioning method for multiple UAVs based on wireless communication links as described in claim 1, characterized in that, The parsing steps include: The agricultural machinery carries sensors with an array element number of The agricultural machinery positioning system consists of a uniform linear array of M drones, each transmitting an electromagnetic wave signal from different directions. The incident light falls onto the uniform linear array; The array-received signal of the r-th agricultural machine is represented in complex envelope form as follows: （1） in express Time of the first The first agricultural machinery received by Taiwan An electromagnetic wave signal; express Time of the first The noise vector of the agricultural machinery; Indicates the first Taiwanese agricultural machinery array pointing direction The guide vector, （2） in c represents the speed of light, and f represents the frequency of the electromagnetic wave signal. Indicates wavelength. Represents the transpose of a matrix; The electromagnetic wave signals received by the array of all agricultural machinery are represented as follows: （3） （4） （5） （6） （7） wherein represents the total number of agricultural machines in the vehicle-assisted positioning framework; Assuming the received electromagnetic wave signal is a far field narrow band signal; and the data receiving matrix At time Sampling is performed, forming a sampling matrix: （8） where K is the number of snapshots, B is the signal bandwidth; the sample covariance matrix of the array output vector is: （9） The DOA position estimation algorithm obtains a set of estimated positions containing estimated directions from given sample data , obtaining a set of estimated positions containing estimated directions （10） Far-field narrowband signal It can be represented as: （11） in: Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors; The orthogonal matrix representing the noise subspace of the r-th agricultural machine; yes Signal components in the signal subspace yes Noise components in the noise subspace; Utilizing the square root matrix of a non-negative definite matrix, is expressed as: （12） （13） （14） （15） （16） （17） （18） （19） wherein is the received signal covariance matrix in the signal subspace, is the received signal covariance matrix in the noise subspace; Covariance matrix of signals may be expressed as: （20） in It is a Hermitian matrix; Therefore, the constraints of the solution space of this DOA location estimation algorithm are: （21） wherein denotes a positive semi-definite ordering; the constrained solution space is obtained according to this constraint : （22）。 3.The low-cost assisted positioning method based on wireless communication link of multiple UAVs according to claim 2, wherein, The DOA location estimation algorithm includes: Output: ; Initialization: solution space is ; The array received signal is calculated according to equation 9 covariance matrix of the array received signal ; Construct the constraint solution space according to Formula 31; when At that time, random initialization is performed within the global solution space. ;if ; ； When and , ; Computing the Jacobian matrix ; Signal steering vector Equation 5 is first order Taylor expanded; The residual vector is calculated according to equations 25 and 26 ; Solve for parameter increments according to equation 27 ; Update the DOA parameter estimation according to equation 28 ; If ; Record Convergence angle ; The solution that minimizes the SML cost function is chosen according to equation 30 below as the final estimated position; Output: Optimized particle positions where the steering matrix is about the current parameter estimate the Jacobian matrix of is: （23） The first-order Taylor expansion is: （24） Substituting the linearized guidance matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector: （25） （26） Solving for parameter increments by normal equations : （27） Update DOA parameter estimation: （28） Record Convergence angle : （29） selecting a solution that minimizes the SML cost function as a final DOA estimate: （30） Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration. and The definition is as follows: （31） （32） By substituting the linearized steering matrix into the residual function, expanding and deleting... The second-order term in the equation yields: （33） Find the increment that minimizes the residual. : （34） The solution to the above least squares problem is given by the normal equations: （35）。 4. A low-cost assisted positioning device for multiple unmanned aerial vehicles (UAVs) based on a wireless communication link, characterized in that, include: The initial module constructs an agricultural machinery positioning system that includes multiple agricultural machines and at least three drones; The analysis module obtains the real location of the agricultural machinery based on the GPS signal emitted by the base station during operation. At the same time, the agricultural machinery receives the electromagnetic wave signal emitted by the drone through its own onboard sensors, analyzes the electromagnetic wave signal and executes the DOA position estimation algorithm to obtain the estimated position. When agricultural machinery travels outside the coverage area of ​​a base station and fails to receive GPS signals, the estimated location is used as its positioning result. The compensation module calculates the system-level angle error by using the deviation between the estimated position and the actual position after the agricultural machinery has traveled into the coverage area of ​​the base station and obtained its true position. The estimated position of agricultural machinery that fails to receive GPS signals in the agricultural machinery positioning system is compensated based on the system-level angle error.

5. The low-cost assisted positioning device for multiple UAVs based on a wireless communication link as described in claim 4, characterized in that, This parsing module includes: The agricultural machinery carries sensors with an array element number of The agricultural machinery positioning system consists of a uniform linear array of M drones, each of which transmits an electromagnetic wave signal from different directions. The incident light falls onto the uniform linear array; The array-received signal of the r-th agricultural machine is represented in complex envelope form as follows: （1） in express Time of the first The first agricultural machinery received by Taiwan An electromagnetic wave signal; express Time of the first The noise vector of the agricultural machinery; Indicates the first Taiwanese agricultural machinery array pointing direction The guide vector, （2） in c represents the speed of light, and f represents the frequency of the electromagnetic wave signal. Indicates wavelength. Represents the transpose of a matrix; The electromagnetic wave signals received by the array of all agricultural machinery are represented as follows: （3） （4） （5） （6） （7） in This indicates the total number of agricultural machines in the vehicle auxiliary positioning frame; Assuming the electromagnetic wave signal is received It is a far-field narrowband signal; and the data receiving matrix At any moment Perform sampling to form a sampling matrix: （8） Where K is the number of snapshots, B is the signal bandwidth, and the sample covariance matrix of the array output vector is... for: （9） The DOA location estimation algorithm is based on given sampled data. This yields a set of estimated positions containing the estimated directions: （10） Far-field narrowband signal It can be represented as: （11） in: Let the orthogonal matrix of the signal subspace of the r-th agricultural machine be represented by Zhang Cheng. It consists of column vectors; The orthogonal matrix representing the noise subspace of the r-th agricultural machine; yes Signal components in the signal subspace yes Noise components in the noise subspace; Using the square root matrix of a nonnegative definite matrix, Represented as: （12） （13） （14） （15） （16） （17） （18） （19） in, It is receiving signals The covariance matrix in the signal subspace, It is receiving signals The covariance matrix in the noise subspace; covariance matrix of the signal It can be represented as: （20） in It is a Hermitian matrix; Therefore, the constraints of the solution space of this DOA location estimation algorithm are: （21） in This represents a positive semidefinite ordering; the constraint solution space is obtained based on this constraint condition. : （22）。 6. The low-cost assisted positioning device for multiple UAVs based on a wireless communication link as described in claim 5, characterized in that, The DOA location estimation algorithm includes: enter: ; initialization: The solution space is ; The array received signal is obtained according to Formula 9. covariance matrix ; Construct the constraint solution space according to Formula 31; when At that time, random initialization is performed within the global solution space. ;if ; ； when and hour, ; Calculate the Jacobian matrix ; For signal steering vector Formula 5 is expanded using a first-order Taylor series. Calculate the residual vector using formulas 25 and 26. ; The parameter increment is calculated using formula 27. ; Update the DOA parameter estimate according to Formula 28. ; if ; Record A convergence angle ; Choose the solution that minimizes the SML cost function according to the following formula 30. As the final estimated location; Output: Optimized particle position The guidance matrix is ​​estimated with respect to the current parameter. Jacobian matrix for: （23） The first-order Taylor expansion is: （24） Substituting the linearized guidance matrix into the SML cost function constructs a linear least squares problem, thus forming the residual vector: （25） （26） Solving for parameter increments using the normal equations : （27） Update DOA parameter estimation: （28） Record A convergence angle : （29） Choose the solution that minimizes the SML cost function. As the final DOA estimate: （30） Where i represents the i-th particle. Indicates the maximum number of initial particles; typically . and These represent the current iteration number and the maximum iteration number, respectively. This represents the iteration error threshold. This represents the angle information of the r-th agricultural machine when the i-th particle is in the k-th iteration. and The definition is as follows: （31） （32） By substituting the linearized steering matrix into the residual function, expanding and deleting... The second-order term in the equation yields: （33） Find the increment that minimizes the residual. : （34） The solution to the above least squares problem is given by the normal equations: （35）。 7. A client for implementing any of the low-cost assisted positioning devices for multiple unmanned aerial vehicles based on wireless communication links as described in claims 4-6.

8. An electronic device, characterized in that, The invention includes a low-cost assisted positioning device for multiple unmanned aerial vehicles based on a wireless communication link as described in claims 4-6. The electronic device may be connected to an information display device, which is used to display the positioning result using user-set display parameters, attributes, or through an artificial intelligence model.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the low-cost assisted positioning method for multiple unmanned aerial vehicles based on a wireless communication link as described in any one of claims 1-3.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the low-cost assisted positioning method for multiple unmanned aerial vehicles based on wireless communication links as described in any of claims 1-3.

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