Multi-dimensional parameter joint estimation method and system for unmanned aerial vehicle target detection

Abstract

The invention discloses a multi-dimensional parameter joint estimation method and system for unmanned aerial vehicle (UAV) target detection, and the method comprises the steps: a receiver receives echo signals reflected by a multi-path UAV through an antenna array, processes the echo signals and extracts signal parameters, and the signal parameters comprise an angle of arrival, time delay and Doppler frequency shift; constructing a receiving signal model according to the attributes and the signal parameters of the antenna array, estimating the state of the UAV by using the receiving signal model, and obtaining a non-convex optimization target according to a set condition; the characteristic that low-altitude millimeter wave channel parameters are sparsely distributed is utilized, an optimization target of an SOCP parameter estimation method based on sparse recovery and convex optimization is designed, and meanwhile, the global search capability is improved by utilizing a complete matrix dimensionality reduction method based on a grey wolf optimization algorithm and heavy tail distribution. According to the invention, for the key parameter estimation problem of UAV detection, sparse signal processing and convex optimization technologies are combined, and the precision and robustness of angle-time delay-Doppler joint estimation are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radio communication, and particularly relates to a multi-dimensional parameter joint estimation method and system for UAV target detection. Background Art

[0002] In recent years, the low-altitude economy has been emerging as a new economic development form, opening up a brand-new application scenario for the next-generation communication technology. In response to the increasing number of new low-altitude services, ground base stations can provide wireless coverage services in the air for UAVs by adjusting the transmission angle, power, etc. of antennas. Therefore, the research on communication technology for low-altitude scenarios has become one of the current hot directions. As the carrier of airborne equipment, UAVs are a key component of the low-altitude network. Thanks to the remarkable progress made in recent years, UAVs have been widely used in many fields such as agricultural plant protection, power inspection, express delivery logistics, film shooting, and disaster relief. However, the rapid popularization of UAVs has also brought a series of safety hazards, including problems such as illegal flight, privacy infringement, and security threats to important facilities. Especially in the context of the rapid development of the low-altitude economy, the number of UAVs deployed in various scenarios has increased explosively, and traditional manual supervision means are difficult to meet the requirements. There is an urgent need to develop efficient and reliable UAV detection and trajectory tracking technologies to provide technical support for UAV safety supervision.

[0003] The existing UAV detection methods mainly include optical detection, acoustic detection, radio detection, etc. Optical detection relies on visible light or infrared cameras to obtain UAV images and uses computer vision algorithms for target recognition. However, this method is easily affected by environmental factors, and the detection performance significantly decreases in bad weather or complex backgrounds. Acoustic detection identifies UAVs by analyzing their unique sound characteristics, but the detection distance is relatively limited, and it is easily interfered in a noisy environment, resulting in a decrease in detection performance. Radio detection realizes target recognition by listening to and analyzing the communication signals between UAVs and remote controllers. However, this method has relatively weak detection capabilities for UAVs in communication silent mode or autonomous flight, and there are relatively large limitations.

[0004] On the other hand, as one of the candidate technologies for 6G, the ISAC technology has attracted great attention from the industry in recent years and has developed rapidly. Using ISAC communication signals for UAV detection has become a new research direction. The ISAC technology integrates communication and sensing functions, enabling the wireless network to have environmental sensing capabilities while transmitting information. Compared with traditional detection means such as optics, acoustics, and radar, UAV detection based on communication signals has advantages such as passive detection capabilities, low-cost deployment, joint Doppler and angle sensing, and all-weather adaptability, and is particularly suitable for UAV parameter detection in complex environments.

[0005] In view of the above development trends of technologies and applications, and aiming at low-altitude scenarios, the present invention proposes a high-precision UAV parameter detection method. It uses millimeter-wave OFDM signals for environmental perception, combines optimization methods to enhance the joint angle-delay-Doppler estimation ability, and integrates trajectory prediction and beam dynamic optimization technologies to achieve accurate detection of UAV parameters, providing an effective technical reference for the problem of UAV supervision in low-altitude scenarios. Summary of the Invention

[0006] The main objective of the present invention is to overcome the drawbacks and deficiencies of the prior art, and provide a multi-dimensional parameter joint estimation method and system for UAV target detection. It uses millimeter-wave OFDM signals for environmental perception, combines optimization methods to enhance the joint angle-delay-Doppler estimation ability, and integrates trajectory prediction and beam dynamic optimization technologies to achieve accurate detection of UAV parameters, providing an effective technical reference for the problem of UAV supervision in low-altitude scenarios.

[0007] To achieve the above objective, the present invention adopts the following technical solutions:

[0008] In the first aspect, the present invention provides a multi-dimensional parameter joint estimation method for UAV target detection, including the following steps:

[0009] The receiver receives the echo signals reflected by the multi-path UAV through the antenna array, processes the echo signals to extract signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift.

[0010] According to the attributes of the antenna array and the signal parameters, a received signal model is constructed, the state of the UAV is estimated using the received signal model, and a non-convex optimization objective is obtained according to the set conditions.

[0011] The echo signals are modeled for sparsity using an over-complete dictionary matrix to obtain a sparsity matrix. By relaxing the non-convex norm to an equivalent convex norm form, a convex optimization objective is obtained; a Lagrange operator is introduced to transform the convex optimization objective to obtain an unconstrained optimization objective; an auxiliary variable is introduced to transform and marginally constrain the unconstrained optimization objective to obtain a second-order cone programming optimization objective.

[0012] The gray wolf optimization algorithm is used to process the sparsity matrix, and at the same time, a perturbation mechanism based on heavy-tailed distribution is used to update the strategy of the gray wolf optimization algorithm to obtain a dynamic complete matrix; the dynamic complete matrix is solved using a solver according to the second-order cone programming optimization objective to obtain a parameter estimation result; the dynamic complete matrix is iteratively solved, and when the set number of times or set conditions are reached, the final UAV multi-dimensional parameter estimation value is obtained.

[0013] As a preferred technical solution, the construction of the received signal model according to the attributes of the antenna array and the signal parameters includes:

[0014] The angle of arrival is obtained by calculating the relative phase shift when the echo signal of a single antenna element is incident on the wavefront of the l-th path, as shown in the following formula:

[0015]

[0016] where d(m x -1) represents the abscissa of the antenna element, and d(m y -1) represents the ordinate of the antenna element, φ l is the elevation angle, θ l is the azimuth angle, and λ is the wavelength of the echo signal;

[0017] For the l-th path, the phase shift caused by the time delay τ l on the n-th subcarrier is as shown in the following formula:

[0018]

[0019] The known transmitted sequence of the sensing OFDM symbol, and the time interval between the same sampling points in two sensing OFDM symbols is T p , then the phase difference between the corresponding sampling points of the two sensing OFDM symbols is as shown in the following formula:

[0020] ρ p (f D ) = arg(x(t)[p]) - arg(x(t)[p - 1]);

[0021] where [p] represents the p-th sensing OFDM symbol, and f D represents the set of Doppler frequency shifts of all paths;

[0022] Taking all paths into account, a received signal model is constructed.

[0023] As a preferred technical solution, the received signal model is as shown in the following formula:

[0024] X = A(φ, θ, f D , τ)s + n;

[0025] A(φ, θ, f D , τ) = [Ω(φ1, θ1)ρ p (f D,1 )Γ(τ1), …, Ω(φ L , θ L )ρ p (f D,L )Γ(τ L )];

[0026] φ = [φ1, …, φ L, θ = [θ1, …, θ L , τ = [τ1, …, τ L , f D = [f D,1 , …, f D,L ;

[0027] where s is a vector of the superposition of the L×1 transmitted signal and the UAV echo signal, n is additive Gaussian noise, and A(φ, θ, f D , τ) represents the transposed matrix of multi-dimensional parameters, with dimensions (MN)×L.

[0028] As a preferred technical solution, estimating the state of the UAV using the received signal model and obtaining a non-convex optimization objective according to set conditions includes:

[0029] Estimating the state of the UAV using the received signal model and obtaining a non-convex optimization objective according to a given constraint tolerance or error upper bound, as follows:

[0030]

[0031] where s is a vector of the superposition of the L×1 transmitted signal and the UAV echo signal, X represents the received signal model, A represents the transposed matrix of multi-dimensional parameters, ε is a given constraint tolerance or error upper bound, and the state of the UAV includes azimuth, distance, and speed.

[0032] As a preferred technical solution, sparsity modeling of the echo signal using an overcomplete dictionary matrix to obtain a sparsity matrix Obtaining a convex optimization objective by relaxing the non-convex norm to an equivalent convex norm form, including:

[0033] Within a given search range, traversing the signal parameters according to a certain step size and setting the value of dimension K according to the traversed signal parameters, and inputting the traversed signal parameters and the K value into the overcomplete dictionary matrix to obtain a sparsity matrix As follows:

[0034]

[0035] a k = a(φ k , θ k , f D k , τ k ) = [Ω(φ k , θ k )ρ p (f D k )Γ(τ k )], k = 1, …, K;

[0036] Among them, Ω(φ k , θ k ) represents the arrival angles of the pitch angle φ k and the azimuth angle θ l , ρ p (f D k ) represents the phase difference of the sampling points of the Doppler shift f D k , Γ(τ k ) represents the phase shift caused by the time delay τ k ;

[0037] By relaxing the non-convex canonical optimization problem of the non-convex optimization objective into an equivalent convex canonical form, as follows:

[0038]

[0039] Among them, is the signal source symbol corresponding to , including the transmitted signal and the echo signal, with a dimension of K×1, and X represents the received signal model.

[0040] As a preferred technical solution, the Lagrange operator is introduced to transform the convex optimization objective, as follows:

[0041] <�

[0042] Among them, X represents the received signal model, is the sparsity matrix, is the signal source symbol corresponding to , and μ is the regularization parameter for enhancing sparsity.

[0043] As a preferred technical solution, the introduction of auxiliary variables is used to transform and marginally constrain the unconstrained optimization objective to obtain the second-order cone programming optimization objective, including:

[0044] The auxiliary variables w and q are introduced to transform the unconstrained optimization objective into a linear form, as follows:

[0045] P4: min w + μq;

[0046]

[0047] Among them, X represents the received signal model, is the signal source symbol corresponding to the sparsity matrix ;

[0048] A set of auxiliary variables Upper bound constraint is imposed on the optimization objective, where r k satisfies:

[0049] Define z l = X l - As l , and the second-order cone programming optimization objective is obtained as follows:

[0050]

[0051] where, X l represents the received signal in the l-th path, s l is the vector signal obtained by superimposing the transmitted signal and the UAV echo signal, represents the k-th element, (·) T represents the transpose operator, 1 represents a column vector with all elements being 1, r = (r1,..., r K ) T .

[0052] As a preferred technical solution, the gray wolf optimization algorithm is used to process the sparsity matrix, and at the same time, the strategy of the gray wolf optimization algorithm is updated by using a perturbation mechanism based on the heavy-tailed distribution, including:

[0053] Initialize the wolf pack uniformly. Let the number of gray wolf individuals be G, and randomly select individuals from the sparsity matrix with a sampling interval of to obtain a new complete matrix

[0054] Calculate the vector signal strength of the transmitted signal and the UAV echo signal superimposed corresponding to each individual according to the second-order cone programming optimization objective, and arrange the vector signal strengths from large to small, and select the first ψ h individuals with the largest values; use the selected individuals as the leaders of the gray wolf optimization algorithm to update the individuals;

[0055] When updating the individuals, additional perturbations are added through a perturbation mechanism based on the heavy-tailed distribution to explore the individuals globally.

[0056] As a preferred technical solution, the update of the individuals is specifically:

[0057] Update the pitch angle as follows

[0058]

[0059] where, ξ represents the iteration index, ξ max represents the maximum number of iterations, represents in the ξ-th iteration the g-th pitch angle element in is based on exponentially decaying jump amplitude control, where Levy(ι) represents a heavy-tailed distribution;

[0060] Update the azimuth angle as follows:

[0061]

[0062] Update the time delay as follows:

[0063]

[0064] Update the Doppler frequency shift as follows:

[0065]

[0066] In a second aspect, the present invention also provides a multi-dimensional parameter joint estimation system for UAV target detection, which is applied to the multi-dimensional parameter joint estimation method for UAV target detection, and includes a millimeter-wave transmitter, a millimeter-wave receiver, a UAV target, a channel, and a parameter estimation module; both the millimeter-wave transmitter and the millimeter-wave receiver include an antenna array and a power unit;

[0067] The parameter estimation module includes a signal processing module, a target decision module, a decision optimization module, and a task execution module;

[0068] The signal processing module is used for the receiver to receive the echo signals reflected by the multi-path or multi-channel UAV through the antenna array, process the echo signals to extract signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift;

[0069] The target decision module is used to construct a received signal model according to the attributes of the antenna array and the signal parameters, estimate the state of the UAV using the received signal model, and obtain a non-convex optimization target according to the set conditions;

[0070] The decision optimization module is used to perform sparse modeling on the echo signals using an over-complete dictionary matrix to obtain a sparsity matrix, obtain a convex optimization target by relaxing the non-convex norm to an equivalent convex norm form; introduce a Lagrange operator to transform the convex optimization target to obtain an unconstrained optimization target; introduce auxiliary variables to transform and marginally constrain the unconstrained optimization target to obtain a second-order cone programming optimization target;

[0071] The task execution module is used to process the sparsity matrix by using the Grey Wolf Optimization algorithm, and at the same time update the strategy of the Grey Wolf Optimization algorithm by using the perturbation mechanism based on the heavy-tailed distribution to obtain a dynamic complete matrix; solve the dynamic complete matrix by using a solver according to the second-order cone programming optimization objective to obtain a parameter estimation result; perform iterative solution on the dynamic complete matrix, and when the set number of times or the set conditions are reached, obtain the final UAV multi-dimensional parameter estimation value.

[0072] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0073] (1) The present invention proposes a multi-dimensional parameter joint estimation mechanism based on angle-time delay-Doppler frequency shift. Different from the traditional independent parameter estimation methods such as time delay estimation based on cross-correlation or sliding window, and angle estimation based on beam scanning or subspace projection, the new mechanism fully considers the multi-dimensional parameter coupling characteristics in the UAV millimeter-wave channel, supports joint modeling of multiple parameters under a unified framework, can avoid error accumulation caused by separate estimation of multiple parameters, and thus helps to improve the perception accuracy and estimation stability of UAV targets.

[0074] (2) In view of the low signal-to-noise ratio characteristic of the echo signal, the present invention proposes a parameter estimation method based on sparse recovery and convex optimization. Different from the existing subspace-based estimation methods such as Multiple Signal Classification (MUSIC) or Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT), the new method takes into account the characteristics that the echo signal of the UAV target is vulnerable to multipath interference and noise in a complex environment, uses the sparse characteristics of the millimeter-wave signal to construct a joint sparse representation of angle-time delay-Doppler, and then performs global solution based on the Second-order Conic Programming (SOCP) algorithm, which can effectively improve the robustness and anti-noise ability of parameter estimation. Simulation results show that this method has better estimation accuracy than traditional methods under low signal-to-noise ratio conditions, providing technical support for UAV parameter detection in complex environments. [[ID=,11]]

[0075] (3) By combining the sparse recovery theory with SOCP technology, the present invention uses sparse representation to reconstruct the high-dimensional observation matrix and transforms the target problem into a standard SOCP form, so that a mature and efficient convex optimization solver can be used to obtain the estimation value of multi-dimensional parameters, improving the solution accuracy and efficiency.

[0076] (4) To solve the problem that the calculation of the high-dimensional observation matrix is too complex, the present invention further designs a dictionary matrix dimensionality reduction method based on an intelligent optimization algorithm. Different from existing sparse recovery schemes, this method further combines the intelligent optimization process with SRCO-SPE, and also adds a perturbation mechanism based on heavy-tailed distribution, enabling the optimization algorithm to have stronger global exploration ability, greatly reducing the dimensionality of the dictionary matrix, thus significantly reducing the algorithm complexity and further improving the solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] To more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0078] Figure 1 It is a flowchart of the multi-dimensional parameter joint estimation method for UAV target detection in the embodiments of the present invention;

[0079] Figure 2 It is a flowchart of the complete matrix dimensionality reduction process based on the grey wolf optimization algorithm in the embodiments of the present invention;

[0080] Figure 3 It is a comparison chart of the AoA performance of the SRCO-SPE method and the traditional MUSIC method in the embodiments of the present invention;

[0081] Figure 4 It is a comparison chart of the DFS performance of the SRCO-SPE method and the traditional MUSIC method in the embodiments of the present invention;

[0082] Figure 5 It is a comparison chart of the ToF performance of the SRCO-SPE method and the traditional MUSIC method in the embodiments of the present invention

[0083] Figure 6 It is a schematic structural diagram of the multi-dimensional parameter joint estimation system for UAV target detection in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0084] To enable those skilled in the art to better understand the solutions of the present application, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative efforts fall within the scope of protection of the present application.

[0085] References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0086] Technical terms:

[0087] Based on millimeter-wave orthogonal frequency division multiplexing (OFDM) signals;

[0088] Unmanned Aerial Vehicle (UAV);

[0089] Gray Wolf Optimization (GWO);

[0090] Mechanism of multi-parameter joint estimation (MJE);

[0091] Sparse Recovery and Convex Optimization Aided SOCP Parameter Estimation (SRCO-SPE) method.

[0092] Embodiment 1.

[0093] Please refer to Figure 1 , this embodiment provides a multi-parameter joint estimation method for UAV target detection, including the following steps:

[0094] S1. The receiver receives the echo signals reflected by the multi-path UAV through the antenna array, processes the echo signals to extract the signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift.

[0095] At this time, this embodiment obtains the representation of the relevant parameters. In order to obtain the optimal signal parameters or signal parameter combinations, this embodiment performs optimization estimation through the multi-parameter joint estimation mechanism of angle-time delay-Doppler frequency shift.

[0096] First, in the low-altitude scenario, there are multiple UAV targets in the airspace. The movement of each UAV in three-dimensional space can be determined by its position, velocity, and heading angle. The millimeter-wave OFDM transceiver system for implementing the present invention mainly includes three parts: a signal transmitter, a UAV target, and a signal receiver, where the transmitter and receiver are located at the same or different base stations.

[0097] The transmitter sends millimeter-wave OFDM signals to the airspace and performs multi-carrier modulation using N sub-carriers. The transmitted signal can be expressed as:

[0098]

[0099] where: X n is the modulation symbol of the nth sub-carrier, f n = f1+(n - 1)Δf is the frequency of the nth sub-carrier, f1 is the minimum sub-carrier frequency, and Δf is the sub-carrier spacing. Considering the angle, delay, and Doppler effect during signal propagation, the echo signal reflected by the UAV to the receiver can be expressed as:

[0100]

[0101] where: f C is the carrier frequency, L is the number of propagation paths, α l is the channel attenuation coefficient of the lth path, f D,l is the Doppler frequency shift of the lth path, τ l is the propagation delay of the lth path, and n(t) is additive white Gaussian noise.

[0102] Next, the receiver processes the echo signal through the UPA antenna array and extracts the angle, delay, and Doppler frequency shift parameters to achieve the detection of the UAV. The modeling of signal parameters such as angle, delay, and Doppler frequency shift is described in detail in step S2.

[0103] S2. According to the attributes of the antenna array and the signal parameters, construct a received signal model, use the received signal model to estimate the state of the UAV, and obtain a non-convex optimization objective according to the set conditions.

[0104] Assume that the array elements of the receiving antenna array are arranged on a two-dimensional plane, and the number of array elements is M = M x ×M y . The antenna spacing is set to where is the wavelength and c is the speed of light. The position of each antenna element is represented by a two-dimensional grid index as (m x , m y ), where: m x = 1, 2,..., M x , m y= 1, 2, …, M y According to the arrangement of the UPA, the two-dimensional coordinates of the (m x , m y )-th antenna element are defined as:

[0105] x m = d(m x - 1), y m = d(m y - 1) (3)

[0106] where: x m is the position of the antenna on the x-axis, y m is the position of the antenna on the y-axis, and the origin of the first antenna, i.e., the UPA, is set at (0, 0). Assume that the far-field signal on the l-th path is incident from the direction (φ l , θ l ), where: φ l is the elevation angle, representing the angle between the signal and the z-axis; θ l is the azimuth angle, representing the projection direction of the signal on the xy plane. When the wavefront is incident, the relative phase shift of different antennas depends on their projections in the wavefront direction. According to the plane wave model, the phase shift x , m y )-th antenna is jointly determined by the projections of the incident wave in the x and y directions: is jointly determined by the projections of the incident wave in the x and y directions:

[0107]

[0108] where: the x-direction component of the wave number vector is l x = cosφ l sinθ l , and the y-direction component is l y = sinφ l sinθ l . Substituting l x , l y and Equation (3) into Equation (4) gives:

[0109]

[0110] Therefore, for the components of angle estimation, there are:

[0111]

[0112] Assume that the transmitted signal is an OFDM signal with equal subcarrier spacing. Since each path in multipath propagation has a different propagation delay τ l , this will introduce different phase offsets at different frequencies. For the l-th path, the phase shift caused by the delay on the n-th subcarrier is:

[0113]

[0114] In addition, the Doppler frequency shift f D,l is determined by the moving speed v l of the target, the wavelength λ of the signal, and the Doppler angle γ l , that is: Assume that the sensed OFDM symbol with a known transmission sequence, and the time interval between the same sampling points in two sensed OFDM symbols is T p , then the phase difference of the corresponding sampling points of the two sensed OFDM symbols is:

[0115] ρ p (f D ) = arg(x(t)[p]) - arg(x(t)[p - 1]) (8)

[0116] where: [p] represents the p-th sensed OFDM symbol, f D = [f D,1 , …, f D,L .

[0117] The mechanism of multi-parameter joint estimation (MJE) for UAV targets in the low-altitude scenario of this embodiment effectively solves the problem of error propagation and accumulation caused by independent estimation of each parameter in the traditional method by embedding the parameters of the angle of arrival (AoA), time of flight (ToF), and Doppler frequency shift (DFS) of the UAV into a joint estimation model of multi-dimensional parameters. At the same time, in this embodiment, by means of this MJE mechanism, the structural characteristics of the millimeter-wave channel in the spatial, temporal, and frequency dimensions are fully utilized, and combined with the two-dimensional spatial resolution ability of the uniform planar array (UPA) antenna structure, a basis is provided for realizing higher-precision UAV parameter estimation.

[0118] Considering L paths comprehensively, each path has its own pitch angle φ l , azimuth angle θ l , propagation delay τ l , and Doppler frequency shift f D,l , then the total received signal measured at the receiver can be converted into the following vector form:

[0119] X = A(φ, θ, f D , τ)s + n (9)

[0120] A(φ, θ, fD ,τ)=[Ω(φ1,θ1)ρ p (f D,1 )Γ(τ1),…,Ω(φ L ,θ L )ρ p (f D,L )Γ(τ L )] (10)

[0121] Where s is the vector of the L×1 transmitted signal and the UAV echo signal superimposed, n is the additive Gaussian noise, φ=[φ1,…,φ L ],θ=[θ1,…,θ L ],τ=[τ1,…,τ L ],A(φ,θ,f D ,τ) is the transposed matrix containing multidimensional parameters, with dimension (MN)×L, where ρ p (f D,l ),l=1,…,L represents the phase difference caused by Doppler frequency shift on the lth path.

[0122] The equation (9) containing φ,θ,f D ,τ, the received signal model can be used to estimate the direction, distance and speed of the UAV. Specifically, based on formula (9), the above parameter estimation problem can be further modeled as an optimization problem:

[0123]

[0124] Where: ε is the given constraint tolerance or error upper bound. Considering that the multipath channel propagation path in low-altitude scenarios is generally sparse, an overcomplete dictionary matrix can be constructed To support sparse modeling of signals:

[0125]

[0126] Among them: a k =a(φ k ,α k ,f D k ,τ k )=[Ω(φ k ,α k )ρ p (f D k )Γ(τ k )],k=1,…,K,matrix The element φ constructed in k ,α k ,f D k ,τk , where \(k = 1,\ldots,K\) respectively represent the elevation angle, azimuth angle, Doppler shift, and time delay traversed according to a certain step size within the given search range of each parameter. has a dimension of \((MN)\times K\), and \(K\gg L\). The value of \(K\) is determined by the search range and step size set by the four parameters of the elevation angle, azimuth angle, Doppler shift, and time delay. For example, let the value ranges of the elevation angle, azimuth angle, Doppler shift, and time delay be \(0 - 90^{\circ}\), \(0 - 360^{\circ}\), \(0 - 1000\mathrm{Hz}\), \(0 - 1000\mathrm{ns}\) respectively. Among them, the search step size of the elevation angle and azimuth angle is \(1^{\circ}\), the search step size of the Doppler shift is \(1\mathrm{Hz}\), and the search step size of the time delay is \(1\mathrm{ns}\). Then the calculation method of \(K\) is: where represents the ceiling operator. Substitute all the values of \(\varphi\) k , \(\theta\) k , \(f\) D k , \(\tau\) k , \(k = 1,\ldots,K\) selected according to their respective search step sizes into equations (6), (7), and (8) to calculate the corresponding parameter values, and then substitute all combinations of these parameter values into (12) for calculation, and the complete As can be seen from the above, \(A\) in equation (10) is a sub - matrix composed of some column vector combinations in can be regarded as the extended search space of \(A\).

[0127] S3. Use the over - complete dictionary matrix to perform sparsity modeling on the echo signal to obtain the sparsity matrix. By relaxing the non - convex norm to an equivalent convex norm form, obtain the convex optimization objective; introduce the Lagrange operator to transform the convex optimization objective to obtain the unconstrained optimization objective; introduce auxiliary variables to transform and marginally constrain the unconstrained optimization objective to obtain the second - order cone programming optimization objective

[0128] Based on the above MJE mechanism, this embodiment further utilizes the characteristic that the low - altitude millimeter - wave channel parameters show a sparse distribution, designs a SOCP parameter estimation method based on sparse recovery and convex optimization, and proposes a complete matrix dimension reduction method based on the gray wolf optimization algorithm GWO and heavy - tailed distribution. It can effectively show stronger anti - noise ability and robustness than traditional schemes in low - signal - to - noise ratio environments, significantly improve the estimation accuracy, enhance the adaptability of the system to complex multipath environments, and provide reliable parameter support for the effective perception of UAV targets.

[0129] Specifically, step S3 includes the following steps:

[0130] Based on the non - convex optimization objective obtained by decision - making, in this embodiment, by relaxing the non - convex norm optimization problem to an equivalent convex The canonical form is such that the problem can be transformed into a convex optimization problem, which is expressed as follows:

[0131]

[0132] where is the signal source symbol corresponding to , which includes the transmitted signal and the echo signal, and the dimension is K×1. However, the solution complexity of Equation (13) is relatively high. Therefore, the Lagrange operator can be introduced to convert P2 into an unconstrained form to achieve more efficient solution:

[0133]

[0134] where μ is the regularization parameter used to enhance sparsity.

[0135] However, although Equation (14) itself is convex, it does not conform to the standard optimization modeling format. Therefore, in the present invention, by equivalently transforming it into an SOCP problem and using a mature and efficient solver, numerical stability and scalability can be improved while ensuring the global optimal solution, so that the model is more suitable for large-scale or complex constraint problems in engineering practical scenarios. Specifically, by introducing auxiliary variables w and q, the problem P3 can be transformed into a linear form:

[0136]

[0137] To further represent it in the SOCP form, the residual term and the sparse term in Equation (15) can also be transformed into the standard form of SOCP. Therefore, a set of auxiliary variables are introduced for upper bound constraint, where r k satisfies where represents the k-th element. Further, define z l =X l -As l , where X l , s l respectively represent the received signal, the transmitted signal and the vector signal of the superposition of the UAV echo signal in the l-th path. Therefore, in this embodiment, the optimization objective is transformed into:

[0138]

[0139] where, (·) T represents the transpose operator, 1 represents the column vector with all elements being 1, r=(r1,…,r K ) T. It can be observed that equation (16) is in the standard SOCP form and can be solved using the conventional CVX toolkit. The parameters of the column vectors corresponding to the L largest values in are the parameter estimation values of each path signal.

[0140] However, as can be seen from the above calculation method of K, the dimension of matrix is very large, resulting in extremely high system computational complexity. To further reduce the search dimension of sparse recovery and improve the computational efficiency, should be dimensionally reduced. For this purpose, this embodiment further proposes a complete matrix dimensional reduction method based on the gray wolf optimization algorithm, as detailed in step S4.

[0141] S4. Use the gray wolf optimization algorithm to process the sparsity matrix, and at the same time use the perturbation mechanism based on the heavy-tailed distribution to update the strategy of the gray wolf optimization algorithm to obtain a dynamic complete matrix; use a solver to solve the dynamic complete matrix according to the second-order cone programming optimization objective to obtain the parameter estimation result; perform iterative solution on the dynamic complete matrix, and when the set number of times or set conditions are reached, obtain the final UAV multi-dimensional parameter estimation value.

[0142] First, the individuals of the gray wolf optimization algorithm (Gray Wolf Optimization, GWO) are directly used as the construction units of the dictionary atoms, and a dynamic adaptive dictionary is constructed through population evolution, thereby compressing the search space and enhancing the representation ability. The complete matrix dimensional reduction processing flow based on the GWO algorithm is as Figure 2 shown.

[0143] Let the number of gray wolf individuals be G, where the individual represents a vector extracted from . To make the distribution of the search space more uniform, the method of uniformly extracting individuals should be adopted to construct a new complete matrix, that is, the extraction interval is where represents the floor operator. Therefore, the new complete matrix can be expressed as:

[0144]

[0145] Therefore, equation (14) can be correspondingly rewritten as:

[0146]

[0147] where is the vector corresponding to the superposition of the transmitted signal and the UAV echo signal, and is used as the fitness value in the GWO algorithm. Calculate a according to equation (16) respectively g ​​, the vector signal strength corresponding to the transmitted signals at g = 1, …, G and the UAV echo signals is superimposed, arranged from large to small, and then the first ψ h largest values are selected, and the corresponding a g are respectively denoted as the elements corresponding to them in are used as the leaders in the GWO algorithm, and are respectively expressed as:

[0148]

[0149] Therefore, according to the GWO algorithm, taking the pitch angle as an example, its update method can be expressed as:

[0150]

[0151] where: ξ = 1, …, ξ max represents the iteration index, ξ max represents the maximum number of iterations, represents the g-th pitch angle element in at the ξ-th iteration , g = 1, …, G, is an adjustment factor used to control the exploration balance of particles during the search process.

[0152] However, the above standard GWO algorithm has the problem of being easily trapped in local optimal solutions, resulting in the loss of the global optimal solution. Therefore, it is necessary to further improve the ability to jump out of local optimal solutions, enhance the global exploration ability, and obtain better performance in high-dimensional search spaces. Therefore, the present invention proposes a perturbation mechanism based on the heavy-tailed distribution (HTD) to optimize the update strategy of the GWO algorithm. The heavy-tailed distribution allows the algorithm to generate certain random perturbations, so that when the GWO algorithm updates individuals, in addition to being pulled by the leaders, additional perturbations will be added to increase the chance of jumping out of local optima.

[0153] Specifically, Equation (20) can be rewritten as:

[0154]

[0155] where: is the jump amplitude control based on exponential decay, η0 is the initial perturbation intensity, Λ is used to control the decay rate, Levy(ι) represents the heavy-tailed distribution, and usually the Mantegna algorithm can be used for approximation:

[0156]

[0157] where: Γ represents the gamma distribution, and ι represents the standard deviation used for control. Similarly, the update methods of the remaining parameters can be obtained:

[0158]

[0159]

[0160] The definitions of the variables are similar to those in Equation (20). After the above processing, new Therefore, continue to solve using Equation (18) corresponding to and determine whether either of the two conditions of reaching the maximum number of iterations or the calculated result being less than the given upper bound of the constraint is satisfied. If the end condition is met, select the parameters of the column vectors corresponding to the largest L values in as the parameter estimation values of each path signal. If the end condition is not met, continue to update the leader of the GWO algorithm, update the parameter values according to the above process, and generate new until the end condition is met, and then output the final parameter estimation result.

[0161] Embodiment 2.

[0162] In this embodiment, a millimeter-wave signal simulation system based on OFDM is constructed on the MATLAB R2022a platform, and the parameter estimation algorithm optimized by SOCP-SPE is adopted to realize the joint estimation of angle, delay, and Doppler frequency shift. The simulation respectively shows the comparison of the AoA, DFS, and TOF performance results obtained by the proposed SRCO-SPE method and the traditional MUSIC method of the present invention with the true values under different signal-to-noise ratios (SNRs). In the simulation, the signal carrier frequency is set to f C = 28 GHz, the system adopts a UPA antenna structure, the bandwidth is 200 MHz, the number of subcarriers is N = 256, the AoA is 150°, the DFS is 550 Hz, and the ToF is 900 ns.

[0163] Figure 3 The shown AoA performance comparison demonstrates the angle estimation effects of the SOCP-SPE method and the traditional MUSIC method under different SNR conditions. It can be observed from the figure that the MUSIC method has relatively serious main peak shift and multiple false peaks, especially with poor resolution ability in a strong noise environment. While the SOCP-SPE method can still accurately estimate the AoA at low SNR, the main peak is sharp and clear, and the side lobes are significantly suppressed. Moreover, with the increase of SNR, the stability and accuracy of the estimation results can be further enhanced, verifying the high robustness and anti-noise ability of this method in angle estimation.

[0164] Figure 4It is a comparison graph of DFS performance, used to evaluate the performance of different algorithms in Doppler frequency shift estimation. Under the condition that the SNR is 0 dB, there are many interference peaks in the spectrogram of the MUSIC method and the main peak position deviates from the true value, making it difficult to accurately judge the Doppler frequency shift of the target. In contrast, the SOCP-SPE method can maintain a clear and accurate main peak response in the noise background, with a positioning accuracy significantly better than that of the MUSIC method, and it achieves better performance under medium and high SNR conditions. This result shows that the SOCP-SPE method has higher resolution and anti-noise ability for Doppler frequency shift estimation, and is suitable for precise detection of high-speed moving targets.

[0165] Figure 5 It provides the performance comparison results of ToF estimation, reflecting the capabilities of each algorithm in target ranging and time delay perception. It can be seen from the figure that the MUSIC method can hardly determine the true ToF value when the SNR is 0 dB, and its output results have serious false peaks and blurred main peaks, showing the defect of low resolution. While the SOCP-SPE method can accurately lock the true ToF value under the same conditions, with its main peak sharp and concentrated and small errors. As the SNR increases, the performance of the MUSIC method improves to some extent, but it is always less stable than the SOCP-SPE method. This result verifies the robustness and high precision of the SOCP-SPE method for flight time parameter estimation, and reflects its potential for being more suitable for high-precision ranging requirements in millimeter-wave radars.

[0166] In summary, the estimation performance of the SOCP-SPE method in the three key parameter dimensions of AoA, DFS and ToF is significantly better than that of the traditional MUSIC method, especially in a low SNR environment, it still has good resolution ability and anti-noise ability. This method can not only improve the parameter estimation accuracy by more than 30%, but also shows high stability and practicality. It is expected to be applied to various low-altitude scenarios such as UAV target detection, vehicle-mounted millimeter-wave radar, and intelligent communication perception fusion, and has great application prospects.

[0167] It should be noted that for the foregoing method embodiments, for the sake of simplicity of description, they are all expressed as a series of action combinations. However, those skilled in the art should know that the present invention is not limited by the described action sequence, because according to the present invention, certain steps can be performed in other sequences or simultaneously.

[0168] Based on the same idea as the multi-dimensional parameter joint estimation method for UAV target detection in the above embodiments, the present invention also provides a multi-dimensional parameter joint estimation system for UAV target detection, which can be used to execute the multi-dimensional parameter joint estimation method for UAV target detection. For the sake of convenience of description, in the structural schematic diagram of the embodiment of the multi-dimensional parameter joint estimation system for UAV target detection, only the parts related to the embodiments of the present invention are shown. Those skilled in the art can understand that the illustrated structure does not constitute a limitation on the device, and it may include more or fewer components than those illustrated, or combine certain components, or arrange different components.

[0169] Please refer to Figure 6 , in another embodiment of the present application, a multi-dimensional parameter joint estimation system 10 for UAV target detection is provided. The system includes a millimeter-wave transmitter 11, a millimeter-wave receiver 12, a UAV target 13, a channel 14, and a parameter estimation module 15; both the millimeter-wave transmitter 11 and the millimeter-wave receiver 12 include antenna arrays (111, 121) and power units (112, 122);

[0170] The parameter estimation module 15 includes a signal processing module 151, a target decision module 152, a decision optimization module 153, and a task execution module 154;

[0171] The signal processing module 151 is used for the receiver to receive the echo signals reflected by the multi-path or multi-channel UAV through the antenna array, process the echo signals to extract signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift;

[0172] The target decision module 152 is used to construct a received signal model according to the attributes of the antenna array and the signal parameters, estimate the state of the UAV using the received signal model, and obtain a non-convex optimization target according to the set conditions;

[0173] The decision optimization module 153 is used to perform sparsity modeling on the echo signals using an over-complete dictionary matrix to obtain a sparsity matrix, obtain a convex optimization target by relaxing the non-convex norm to an equivalent convex norm form; introduce a Lagrange operator to transform the convex optimization target to obtain an unconstrained optimization target; introduce auxiliary variables to transform and marginally constrain the unconstrained optimization target to obtain a second-order cone programming optimization target;

[0174] The task execution module 154 is configured to process the sparsity matrix by using the grey wolf optimization algorithm, and update the strategy of the grey wolf optimization algorithm by using a perturbation mechanism based on a heavy-tailed distribution to obtain a dynamic complete matrix; solve the dynamic complete matrix by using a solver according to the second-order cone programming optimization objective to obtain a parameter estimation result; perform iterative solution on the dynamic complete matrix, and when the set number of times or set conditions are reached, obtain the final UAV multi-dimensional parameter estimation value.

[0175] It should be noted that the multi-dimensional parameter joint estimation system for UAV target detection of the present invention corresponds one-to-one with the multi-dimensional parameter joint estimation method for UAV target detection of the present invention. The technical features and their beneficial effects described in the embodiments of the above-mentioned multi-dimensional parameter joint estimation method for UAV target detection are applicable to the embodiments of the multi-dimensional parameter joint estimation method for UAV target detection. For specific content, reference can be made to the description in the method embodiments of the present invention, which will not be elaborated here. This is hereby declared.

[0176] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered that the scope described in this specification is covered.

[0177] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A multi-dimensional parameter joint estimation method for UAV target detection, characterized in that It includes the following steps: The receiver receives the echo signals reflected by the multi-path UAVs through the antenna array, processes the echo signals to extract signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift; According to the attributes of the antenna array and the signal parameters, a received signal model is constructed, the state of the UAV is estimated using the received signal model, and a non-convex optimization objective is obtained according to the set conditions; The echo signals are sparsity modeled using an over-complete dictionary matrix to obtain a sparsity matrix. By relaxing the non-convex norm to an equivalent convex norm form, a convex optimization objective is obtained; a Lagrange operator is introduced to transform the convex optimization objective to obtain an unconstrained optimization objective; Auxiliary variables are introduced to transform and marginally constrain the unconstrained optimization objective to obtain a second-order cone programming optimization objective; The gray wolf optimization algorithm is used to process the sparsity matrix, and at the same time, a perturbation mechanism based on the heavy-tailed distribution is used to update the strategy of the gray wolf optimization algorithm to obtain a dynamic complete matrix; According to the second-order cone programming optimization objective, a solver is used to solve the dynamic complete matrix to obtain the parameter estimation result; The dynamic complete matrix is iteratively solved. When the set number of times or the set conditions are reached, the final multi-dimensional parameter estimation value of the UAV is obtained.

2. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, wherein The constructing of the received signal model according to the attributes of the antenna array and the signal parameters includes: The angle of arrival is obtained by calculating the relative phase shift when the wavefront of the echo signal of a single antenna element is incident on the l-th path, as shown in the following formula: Among them, d(m x -1) represents the abscissa of the antenna element, and d(m y -1) represents the ordinate of the antenna element. φ l is the elevation angle, θ l is the azimuth angle, and λ is the wavelength of the echo signal; For the l-th path, the phase shift caused by the time delay τ on the n-th subcarrier is given by the following equation: l ​ Transmit a sensing OFDM symbol with a known sequence, and the time interval between the same sampling points in two sensing OFDM symbols is T p , then the phase difference between the corresponding sampling points of the two sensing OFDM symbols is as follows: ρ p (f D ) = arg(x(t)[p]) - arg(x(t)[p - 1]); where [p] represents the p-th sensed OFDM symbol, and f D represents the set of Doppler frequency shifts of all paths; Considering all paths comprehensively, a received signal model is constructed.

3. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 2, characterized in that The received signal model is as follows: X = a(φ, θ, f D , τ) s + n; A(φ,θ,f D ,τ) = [Ω(φ1,θ1)ρ p (F D,1 )Γ(τ1),…,Ω(φ L ,θ L )ρ p (f D,L )Γ(τ L )]; φ = [φ1, …, φ L , θ = [θ1, …, θ L , τ = [τ1, …, τ L , f D = [f D,1 , …, f D,L ; where \(s\) is an \(L\times1\) vector of the superposition of the transmitted signal and the UAV echo signal, \(n\) is the additive Gaussian noise, and \(A(\varphi,\theta,f D ,\tau)\) represents the transposed matrix of multi-dimensional parameters with dimensions \((MN)\times L\).

4. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, wherein The estimating of the state of the UAV using the received signal model and obtaining the non-convex optimization objective according to the set conditions includes: The state of the UAV is estimated using the received signal model, and a non-convex optimization objective is obtained according to the given constraint tolerance or error upper bound, as shown in the following formula: where s is a vector of the superposition of the transmitted signal and the UAV echo signal of L×1, X represents the received signal model, A represents the transposed matrix of multi-dimensional parameters, ε is the given constraint tolerance or error upper bound, and the state of the UAV includes azimuth, distance, and speed.

5. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, characterized in that The echo signal is sparsity modeled using an over-complete dictionary matrix to obtain a sparsity matrix By relaxing the non-convex norm to an equivalent convex norm form, a convex optimization objective is obtained, including: Traverse the signal parameters within a given search range according to a certain step size, set the value of dimension K according to the traversed signal parameters, input the traversed signal parameters and the K value into the overcomplete dictionary matrix, and obtain the sparsity matrix As follows: a k = a(φ k , θ k , f D k , τ k ) = [Ω(φ k , θ k )ρ p (f D k )Γ(τ k )], k = 1, …, K; where, Ω(φ k , θ k ) represents the angle of arrival for determining the pitch angle φ k and the azimuth angle θ l , ρ p (f D k ) represents the phase difference of the sampling points of the Doppler frequency shift f D k , Γ(τ k ) represents the phase shift caused by the time delay τ k ; By relaxing the non-convex l0 norm optimization problem of the non-convex optimization objective to an equivalent convex e1 norm form, as shown in the following formula: Among them, is the signal source symbol corresponding to , including the transmitted signal and the echo signal, with a dimension of K×1, and X represents the received signal model.

6. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, characterized in that The introducing of the Lagrange operator to transform the convex optimization objective is as follows: where X represents the received signal model, is the sparsity matrix, is the signal source symbol corresponding to and μ is the regularization parameter used to enhance sparsity.

7. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, characterized in that The introducing of auxiliary variables to transform and marginally constrain the unconstrained optimization objective to obtain a second-order cone programming optimization objective includes: Auxiliary variables w and q are introduced to transform the unconstrained optimization objective into a linear form, as shown in the following formula: P4: min w + μq; where X represents the received signal model, is the signal source symbol corresponding to the sparsity matrix ; Introduce a set of auxiliary variables Impose an upper bound constraint on the optimization objective, where r k Satisfy: Define z l = X l - As l , obtain the second-order cone programming optimization objective as follows: P5: min w + μq, Among them, X l represents the received signal in the l-th path, s l is the vector signal obtained by superimposing the transmitted signal and the UAV echo signal, denotes the k-th element, (·) T represents the transpose operator, 1 represents a column vector with all elements being 1, r = (r1, …, r K ) T .

8. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 1, wherein The processing of the sparsity matrix using the gray wolf optimization algorithm and the updating of the strategy of the gray wolf optimization algorithm using a perturbation mechanism based on the heavy-tailed distribution includes: Initialize the wolf pack uniformly. Let the number of gray wolf individuals be G, and randomly select individuals from the sparsity matrix at a uniform interval of Obtain a new complete matrix Calculate the vector signal strength of the superposition of the transmitted signal corresponding to each individual and the UAV echo signal respectively according to the second-order cone programming optimization objective, arrange the vector signal strengths from large to small, and select the first ψ j individuals corresponding to the largest values; use the selected individuals as the leaders of the grey wolf optimization algorithm to update the individuals; When updating an individual, additional perturbations are added through a perturbation mechanism based on the heavy-tailed distribution to explore the individual globally.

9. The multi-dimensional parameter joint estimation method for UAV target detection according to claim 8, wherein The updating of the individual is specifically: The pitch angle is updated as follows where ξ represents the iteration index, ξ max represents the maximum number of iterations, represents the g-th pitch angle element in the ξ-th iteration in, is the jump amplitude control based on exponential decay, and Levy(l) represents the heavy-tailed distribution; The azimuth angle is updated as follows: The time delay is updated as follows: The Doppler frequency shift is updated as follows:

10. A multi-dimensional parameter joint estimation system for UAV target detection, characterized in that, Applied to the multi-dimensional parameter joint estimation method for UAV target detection described in any one of claims 1-9, which includes a millimeter-wave transmitter, a millimeter-wave receiver, a UAV target, a channel, and a parameter estimation module; both the millimeter-wave transmitter and the millimeter-wave receiver include an antenna array and a power unit; The parameter estimation module includes a signal processing module, a target decision module, a decision optimization module, and a task execution module; The signal processing module is used for the receiver to receive the echo signals reflected by the multi-path or multi-channel UAV through the antenna array, process the echo signals to extract signal parameters, and the signal parameters include the angle of arrival, time delay, and Doppler frequency shift; The target decision module is used to construct a received signal model according to the attributes of the antenna array and the signal parameters, estimate the state of the UAV using the received signal model, and obtain a non-convex optimization target according to the set conditions; The decision optimization module is used to perform sparse modeling on the echo signals using an over-complete dictionary matrix to obtain a sparse matrix, obtain a convex optimization target by relaxing the non-convex norm to an equivalent convex norm form; introduce a Lagrange operator to transform the convex optimization target to obtain an unconstrained optimization target; introduce auxiliary variables to transform and marginally constrain the unconstrained optimization target to obtain a second-order cone programming optimization target; The task execution module is used to process the sparse matrix using the grey wolf optimization algorithm, and at the same time update the strategy of the grey wolf optimization algorithm using a perturbation mechanism based on a heavy-tailed distribution to obtain a dynamic complete matrix; Solve the dynamic complete matrix using a solver according to the second-order cone programming optimization target to obtain a parameter estimation result; Iteratively solve the dynamic complete matrix. When the set number of times or set conditions are reached, obtain the final multi-dimensional parameter estimation value of the UAV.

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