A method and system for dynamic angle of arrival estimation of a drone array

Abstract

The application relates to a UAV array dynamic angle of arrival estimation method and system, which comprises the following steps: S1, acquiring array snapshot data after reference channel auxiliary synchronization and waveform compensation; S2, establishing a parameterized space-time coupling phase model in a short coherence processing interval; S3, based on the array snapshot data, obtaining a single-channel input sequence through beam forming, and estimating a radial parameter pair by using time domain atom matching filtering; S4, based on the radial parameter pair, performing common time phase compensation on the array snapshot data to obtain a compensated snapshot matrix; S5, performing two-dimensional correlation calculation by using a space-time steering atom to estimate an angle parameter pair; S6, constructing a complete space-time dictionary atom, and estimating a complex amplitude by using a least square criterion; and S7, performing successive interference cancellation to update a residual error. Compared with the prior art, the application has the advantages of keeping low signal-to-noise ratio coherence gain and significantly reducing calculation complexity.

Description

Technical Field

[0001] This invention relates to the field of passive sensing and array signal processing technology, and in particular to a method and system for dynamic angle of arrival estimation of UAV arrays based on Low Earth Orbit (LEO) satellite signal of opportunity (SoO). Background Technology

[0002] Passive detection using signals of opportunity (SoO) has garnered significant attention in areas such as military-civilian integration monitoring and key area inspection due to its advantages of not actively emitting electromagnetic waves, good concealment, and flexible system deployment. This system typically includes a reference channel and a surveillance channel. It receives direct signals from third-party illumination sources (such as broadcast or communication satellites) and target-scattered signals, and performs synchronization and matched filtering processes to achieve target detection and parameter estimation. Existing passive sensing technologies using SoO usually focus on the coherent accumulation and detection of echo signals in the range-Doppler domain. Methods such as Keystone transform and time-frequency analysis have been used to correct envelope migration caused by platform motion. However, most of these methods implicitly assume that the array manifold remains unchanged within a processing window, or only provide coarse compensation. When there is high-speed relative motion between the illumination source and the receiving platform (such as between a low-orbit satellite and an unmanned aerial vehicle platform), within a single coherent processing interval (CPI), not only will the echo envelope migrate, but its carrier phase will also undergo higher-order evolution due to the drastic changes in the bistatic distance. At the same time, the motion and attitude changes of the receiving platform will cause the signal incident angle to drift continuously over time, making the array steering vector a time-varying function, thereby destroying the two basic premises of "data stationarity" and "manifold invariance" on which traditional array signal processing methods rely.

[0003] Low Earth Orbit (LEO) satellites offer advantages such as global coverage, predictable orbits, and high signal availability, making them ideal sources of opportunistic signal illumination. Combining them with mobile and flexible UAV array receiving platforms can construct a wide-coverage, angle-adjustable aerial passive sensing system. However, this combination also introduces significant high-dynamic characteristics: the relative speed between the LEO satellite and the UAV can reach thousands of meters per second, causing rapid changes in bistatic geometry within milliseconds. This leads to rapid changes in signal propagation delay (range migration and higher-order phase terms) and continuous changes in the target angle of arrival (DOA) during the coherent accumulation time. This strong coupling between space (angle) and time (phase) results in significantly non-stationary characteristics in the snapshot data from the receiving array.

[0004] Conventional beamforming and Capon (MVDR) beamforming methods rely on accurate array steering vectors. Subspace methods such as Multiple Signal Classification (MUSIC) and Rotation Invariant Subspace (ESPRIT) depend on the sampling covariance matrix estimated from multiple stationary snapshots. In high-dynamic scenarios, time-varying steering vectors lead to decreased beamformer output gain and main lobe distortion; non-stationary snapshot data prevents the sampling covariance matrix from accurately reflecting the signal subspace structure, causing problems such as spectral peak broadening, shift, increased spurious peaks, and decreased resolution in algorithms like MUSIC. Although the stationarity condition can be approximated by shortening the processing window, this comes at the cost of coherent processing gain, severely limiting the detection and estimation performance of weak targets under low signal-to-noise ratio conditions.

[0005] To address the need for limited snapshots or super-resolution, DOA estimation methods based on sparse representation or compressed sensing have been developed. However, directly applying these methods to the high-dynamic-range multi-parameter estimation scenario described in this invention presents significant challenges: joint meshing and sparse reconstruction of the four parameters—initial angle of arrival, angle drift rate, equivalent bistatic radial velocity, and radial acceleration—results in an excessively high dictionary dimension, leading to an explosion in computational complexity and making it difficult to meet the requirements of airborne real-time processing. Furthermore, the "off-grid" error caused by discretization is amplified in the high-dimensional parameter space, affecting estimation accuracy. Although off-grid correction or meshless methods exist, their computation is typically more complex and difficult to implement in engineering.

[0006] In real-world monitoring scenarios, multiple targets exist, and their echo intensities can vary significantly (near-far effect). Existing methods have limited effectiveness in suppressing strong targets and extracting weak targets; the estimation residuals of strong targets can easily mask weak targets. Furthermore, in wide-field-of-view surveillance missions, if a fixed beam pointing is used for preprocessing, the signal gain of targets deviating from this pointing direction will drop sharply, potentially causing subsequent processing link failures. From an engineering implementation perspective, achieving high-precision, robust estimation of high dynamics, multiple parameters, and multiple targets under limited airborne computing resources remains a challenging problem that current technologies have not adequately solved.

[0007] Therefore, existing technologies for solving the problem of dynamic angle of arrival estimation in passive sensing of UAV arrays under low-Earth orbit satellite opportunistic signal illumination conditions mainly include: (1) The high-speed relative motion between the low-orbit satellite and the UAV platform causes the common carrier phase to evolve rapidly within a single coherent processing interval. At the same time, the platform motion causes the array to drift over time, resulting in non-stationary array snapshot data, which leads to the performance degradation of existing angle of arrival estimation methods. (2) In multi-target scenarios, the near-far effect causes the residuals of strong targets to mask weak targets, affecting the estimation of weak target parameters; (3) The computational complexity is too high when performing four-dimensional joint estimation of the initial arrival angle, turning drift rate, equivalent bistatic radial velocity and equivalent bistatic radial acceleration, which is difficult to meet the real-time processing requirements of the UAV platform. (4) There is a grid error under wide field of view and discrete grid conditions, which leads to insufficient estimation robustness.

[0008] A search of Chinese Patent Publication No. CN110515038A reveals an adaptive passive positioning device and implementation method based on UAV-array. Specifically, it discloses a system comprising M UAVs, an integrated array module, a signal processing module, a data storage module, and a communication module. The M UAVs are arbitrarily arranged in the air to form a distributed passive positioning system. Each UAV integrates a uniform linear array for receiving electromagnetic signals radiated from a target source. The implementation method involves the following steps: each UAV collects an initial received signal, and the signal angle of arrival is estimated using the structural characteristics of the antenna array; the UAV's attitude is adaptively adjusted using its maneuverability to reconstruct the received signal model; each UAV simultaneously collects a secondary received signal, and the time difference of arrival is estimated based on the reconstructed received signal model; the final radiation source location is performed based on the estimated time difference. This existing patent better combines angle information and time difference of arrival information, solving the problem of rapidly decreasing positioning performance under low signal-to-noise ratio conditions.

[0009] However, the existing patent assumes a fixed angle of arrival (DOA) and is mainly for single-target or multi-target scenarios of equal intensity. It cannot be applied to the scenario in which the DOA of this invention continuously drifts within millisecond-level CPI. At the same time, the existing patent improves the array gain through attitude adjustment, but cannot solve the signal decoherence problem within CPI caused by platform movement.

[0010] In summary, existing technologies struggle to effectively balance long-coherent accumulation gain, accurate compensation for spatial-temporal coupling non-stationarity, multi-target resolution, and real-time algorithm feasibility in passive sensing scenarios where UAV arrays are illuminated by low-Earth orbit satellite opportunistic signals. Therefore, a novel dynamic angle-of-arrival estimation method is urgently needed, capable of explicitly modeling dynamic phase histories, decoupling high-dimensional parameter estimation, and possessing good engineering applicability. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a method and system for dynamic angle of arrival estimation of UAV arrays based on low-orbit satellite opportunistic signals. While maintaining a low signal-to-noise ratio coherent gain, it significantly reduces computational complexity and is suitable for passive monitoring and inspection of critical infrastructure such as power corridors.

[0012] The objective of this invention can be achieved through the following technical solutions: According to one aspect of the present invention, a method for dynamic angle of arrival estimation of an unmanned aerial vehicle (UAV) array is provided, characterized in that the method is based on low-Earth orbit (LEO) satellite opportunistic signals, and the method includes the following steps: Step S1: Obtain array snapshot data after reference channel-assisted synchronization and waveform compensation; Step S2: Establish a parameterized space-time coupled phase model within the short coherence processing interval. The model includes a second-order Taylor approximation of the bistatic distance and a first-order approximation of the direction cosine. Step S3: Based on the array snapshot data, a single-channel input sequence is obtained through beamforming, and matched filtering is performed using time-domain atoms to estimate the radial parameter pair. ,in For equivalent bistatic radial velocity, This is the equivalent bistatic radial acceleration; Step S4: Based on the radial parameter pair, perform common time phase compensation on the array snapshot data to obtain the compensated snapshot matrix; Step S5: Based on the compensated snapshot matrix, perform two-dimensional correlation calculations using space-time turning atoms to estimate the angle parameter pair. ,in The initial angle of arrival. This refers to the array steering drift rate; Step S6: Based on the radial parameter pair and the angular parameter pair, construct a complete space-time dictionary atom and estimate the complex amplitude using the least squares criterion; Step S7: Perform successive disturbance cancellation to update the residuals, and repeat steps S3 to S6 to achieve dynamic angle of arrival estimation for multiple targets.

[0013] As a preferred technical solution, the parameterized space-time coupled phase model in step S2 is specifically as follows: The direction and angle satisfy the cosine condition: in, For the fast-time variable within the coherent processing interval, for Location at any given moment The initial position, , .

[0014] As a preferred technical solution, the time-domain atoms in step S3 The Each element satisfies: in, For carrier wavelength, For the first Each sampling time, The imaginary unit; The radial parameter in step S3 is estimated using a normalized matched filter metric, as shown in the following formula: in, For single-channel input sequences, For the radial parameter search set, This indicates the conjugate transpose. For time-domain atoms, For speed, It is acceleration.

[0015] As a preferred technical solution, the common time phase compensation in step S4 specifically includes: in, This is the original snapshot matrix. For the compensated snapshot matrix, Indicates conjugate. This represents constructing a diagonal matrix from vectors. For time-domain atoms.

[0016] As a preferred technical solution, the space-time orientation atom in step S5 The The elements satisfy the following formula: in, For array element index, For the spacing between array elements, For the first Each sampling time; The angle parameters in step S5 are estimated using a normalized Frobenius correlation metric, as follows: in, Search for a set of angle and steering drift parameters. Represents the Frobenius inner product. Denotes the Frobenius norm. For angle, ω is the angular velocity.

[0017] As a preferred technical solution, in step S3, multi-beam pre-screening is performed before the radial parameter pair estimation. Specifically, multiple beam pointing angles are preset and corresponding beam output sequences are formed; the radial matched filter peak value is calculated for each beam output sequence; and the beam with the largest peak value is selected as the input for subsequent radial parameter estimation. After obtaining the estimated values ​​of the radial parameter pair and the angular parameter pair, local refinement is performed in the neighborhood of each estimated value. The local refinement includes fine-resolution research or coordinate descent optimization.

[0018] As a preferred technical solution, the least squares magnitude estimation in step S6 satisfies: in, , , This represents a vectorization operator.

[0019] As a preferred technical solution, in step S7, the successive interference elimination iteratively processes multiple targets in order from strong to weak.

[0020] As a preferred technical solution, under broadband or large radial velocity conditions, distance migration correction is performed before parameter estimation; the narrow-band condition of the short coherence processing interval at least includes the array aperture narrow-band condition. Distance migration conditions caused by motion ,in For effective baseband bandwidth, The maximum differential delay within the array aperture, This refers to the change in propagation delay within the coherent processing interval; By using low-Earth orbit satellite ephemeris information and UAV navigation or attitude information, the search boundary is set to limit the parameter search set. and The range of values ​​is determined to ensure the physical feasibility and computational efficiency of parameter estimation.

[0021] According to another aspect of the present invention, a dynamic angle of arrival estimation system for an unmanned aerial vehicle (UAV) array is provided, comprising: The unmanned aerial vehicle platform is equipped with a uniform linear array consisting of M array elements, which is used to collect the array received signals within the coherent processing interval; The reference channel receiving and synchronization module is used to acquire the direct wave and perform synchronization, waveform estimation and matched filtering, and output array snapshot data after waveform compensation. A processor and a memory, wherein the memory stores instructions, and the processor is configured to perform the method according to any one of claims 1-9; The element positions of the uniform linear array satisfy the following: in, For the fastest time Time of the first The position vectors of each array element , For the spacing between array elements, is the unit vector along the array axis.

[0022] Compared with the prior art, the present invention has the following advantages: 1) This invention establishes a parameterized space-time coupled phase model within the short coherence processing interval (CPI) and divides the carrier phase into a common time phase term and a differential space-time steering term. By combining common time phase compensation and two-dimensional correlation estimation, it can significantly improve the impact of array snapshot nonstationarity on angle of arrival estimation in high dynamic scenarios and maintain long coherence accumulation gain. 2) This invention transforms the originally coupled four-dimensional parameter estimation into two two-dimensional searches through a two-stage low-dimensional search process of "radial parameter estimation + common phase compensation + angle and steering drift estimation", which significantly reduces computational complexity and facilitates real-time implementation on UAV platforms. 3) This invention uses least squares amplitude estimation and successive interference cancellation (SIC) iterative processing to handle multiple targets, which can effectively reduce the masking of weak targets by strong targets under near-far effects and improve the multi-target resolution capability. 4) This invention can significantly improve robustness and engineering applicability under wide field of view, off-grid, and broadband or large radial velocity conditions by means of multi-beam pre-screening, local refinement, range migration correction, and setting search boundaries using ephemeris and navigation / attitude information. 5) The present invention can maintain high estimation accuracy under low signal-to-noise ratio conditions, and is suitable for passive monitoring and inspection scenarios of critical infrastructure such as power corridors. Attached Figure Description

[0023] Figure 1 A schematic diagram of the geometric relationship and linear motion model within the CPI for bistatic passive sensing of LEO-SoO-UAV-Ground targets; Figure 2 This is a flowchart illustrating the specific process of the method of the present invention; Figure 3 This is a schematic diagram of spatial spectrum comparison in a highly dynamic multi-object scenario (e.g., a comparison between MUSIC and the method of this invention). Figure 4 This is a schematic diagram showing the comparison of the root mean square error (RMSE) of DOA with the change of SNR. Figure 5 This is a comparative curve showing how computation time varies with grid resolution (used to illustrate the complexity advantage of decompositional two-stage search). Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] This invention provides a method and system for estimating the dynamic direction of arrival (DOA) of unmanned aerial vehicle (UAV) arrays based on Low Earth Orbit (LEO) satellite signal of opportunity (SoO), belonging to the field of passive sensing and array signal processing technology. To address the array snapshot nonstationarity problem caused by the rapid evolution of the common carrier phase and array steering drift within a single coherent processing interval (CPI) due to the relatively high-speed motion between low-Earth orbit satellites and UAV platforms, this invention proposes a Decomposed Sparse Reconstruction with Successive Interference Cancellation (D-SR-SIC) framework. This framework achieves dynamic angle-of-arrival estimation through the following steps: A parameterized space-time coupled phase model is established within a short CPI, using a second-order Taylor approximation of bistatic distance and a first-order cosine approximation of direction, decomposing the carrier phase into a common time phase term and a differential space-time steering term; a two-stage low-dimensional search is employed: first, the equivalent bistatic radial velocity and acceleration are estimated on a single-channel time series; then, the initial angle of arrival and array steering drift rate are estimated on the matrix data after common phase compensation; multi-target stripping is achieved by combining least-squares amplitude estimation and successive interference cancellation (SIC); and local refinement and multi-beam pre-screening are introduced to enhance off-grid error and wide field-of-view robustness. This invention significantly reduces computational complexity while maintaining low signal-to-noise ratio coherent gain, making it suitable for passive monitoring and inspection of critical infrastructure such as power corridors.

[0026] In one implementation, such as Figure 1The diagram illustrates a bistatic passive sensing scenario constructed using LEO (Left Opportunity Occurrence) signal illumination (SoO) and reception by a UAV (Unmanned Aerial Vehicle) Uniform Linear Array (ULA). The system includes a UAV platform, a reference channel receiving and synchronization module, and a processor and memory. The UAV platform carries a Uniform Linear Array (ULA) consisting of M array elements, used to acquire the array-received signal within the Coherent Processing Interval (CPI). The array element positions can be represented as follows: in, For the fastest time Time of the first The position vectors of each array element , For the spacing between array elements, is the unit vector along the array axis.

[0027] The reference channel receiving and synchronization module acquires direct waves from low-Earth orbit satellites and performs synchronization and waveform compensation, outputting waveform-compensated array snapshot data. In the presence of direct wave leakage or strong interference, direct wave suppression can be optionally performed; under broadband or large radial velocity conditions, range migration correction can be optionally performed before parameter estimation to align the target echo envelope within the range cell. The processor executes the dynamic angle-of-arrival estimation process, and the memory stores instructions and intermediate results. The processing flow is as follows: Figure 2 As shown.

[0028] Within each coherent processing interval (CPI), array snapshot data can be organized into a snapshot matrix according to array elements and snapshot time. , of which k Listed as number k The array observation vector corresponding to each fast time sample Fast sampling time The processor performs the following processing sequentially according to steps 1 to 7 of the Decomposition-Sparse Reconstruction and Successive Interference Cancellation (D-SR-SIC) framework: Step 1: Acquire array snapshot data after reference channel assisted synchronization and waveform compensation .

[0029] Step 2: Establish a parameterized space-time coupled phase model within the Coherent Processing Interval (CPI). A second-order Taylor approximation is used for the bistatic propagation distance, and a first-order approximation is used for the direction cosines, to characterize the common time phase term and the differential space-time steering term. This can be written as: in, The initial angle of arrival. For array steering drift rate, For equivalent bistatic radial velocity, It is the equivalent bistatic radial acceleration.

[0030] Step 3: Based on the array snapshot data, obtain a single-channel input sequence through beamforming. In radial parameters Search Collection Construct time-domain atoms and perform matched filtering to estimate radial parameter pairs. .For example: in, Where is the carrier wavelength. The radial parameter pair can be estimated using the following normalized matched filter metric: Step 4: Based on the radial parameter pair, perform common time phase compensation on the array snapshot data to obtain the compensated snapshot matrix. ,For example: Step 5: Based on the compensated snapshot matrix, perform two-dimensional correlation calculations using space-time turning atoms to estimate the angle parameter pairs. For example, space-time orientation atoms The Each element can be represented as: Correspondingly, this can be estimated using a normalized Frobenius correlation metric: in, Represents the Frobenius inner product. This represents the Frobenius norm.

[0031] Step 6: Construct a complete space-time dictionary of atoms based on the radial and angular parameter pairs, and estimate the complex amplitude using the least squares criterion. Let... , If we denote the vectorization operator, then the complex magnitude estimate can be expressed as: in, .

[0032] Step 7: Perform Successive Interference Cancellation (SIC) to update the residuals, and repeat steps 3 through 6 to achieve dynamic angle of arrival estimation for multiple targets. Successive Interference Cancellation (SIC) can iteratively process multiple targets in descending order of strength. The iteration termination condition can be determined based on residual energy, relevant peak threshold, or a preset number of targets.

[0033] Alternatively, to enhance the applicability and robustness of the project, the following treatments can be introduced: (1) Perform multi-beam pre-screening before step 3: preset multiple beam pointing angles and form corresponding beam output sequences, calculate the radial matched filter peak for each beam output sequence, and select the beam with the largest peak as the subsequent radial parameter estimation input; (2) After obtaining the estimated values ​​of the radial parameter pair and the angular parameter pair, local refinement is performed in the neighborhood of each estimated value. Local refinement includes fine-resolution re-search or coordinate descent optimization to reduce off-grid error. (3) Use low-orbit satellite ephemeris information and UAV navigation / attitude information to set search boundaries to limit the parameter search set. and The range of values ​​is determined to ensure the physical feasibility and computational efficiency of parameter estimation; (4) Under broadband or large radial velocity conditions, perform range migration correction before parameter estimation; the narrow band condition for short coherence processing intervals should at least include the array aperture narrow band condition. Distance migration conditions caused by motion Where $B$ is the effective baseband bandwidth, The maximum differential delay within the array aperture, This represents the change in propagation delay within the coherent processing interval.

[0034] To facilitate understanding and reproduction, a set of simulation / verification parameter settings are provided as shown in Table 1. In multi-target verification scenarios, the target parameter configurations shown in Table 2 can be used. The above parameters are only examples and can be adjusted according to the platform, signal system, and computing power conditions.

[0035] Table 1. Examples of Simulation / Verification Parameter Settings (Adjustable) Table 2 Examples of parameter settings for multi-target scenarios To illustrate the effectiveness of this invention, simulation or semi-physical verification can be performed under the above parameter settings, and the results are as follows: Figures 3 to 5 As shown: Figure 3 As shown, under conditions of rapid evolution of the common phase and array steering drift, this invention can form more concentrated spectral peaks and suppress false peaks, thereby improving multi-target resolution; Figure 4As shown, the present invention can still achieve relatively stable angle of arrival estimation performance under low signal-to-noise ratio conditions; for example... Figure 5 As shown, by replacing the four-dimensional joint search with a two-stage low-dimensional search, the computation time of this invention increases less, making it easier for UAV platforms to implement in real time.

[0036] Compared to existing technologies (such as the existing patents in the background section), the technical solution of this application brings about technical effects that existing patents do not possess: 1) Adaptability to high dynamic scenarios: By establishing a space-time coupled phase model and explicitly estimating the angle drift rate, this invention is able to achieve accurate angle of arrival estimation in a high dynamic environment for the first time on a UAV array platform illuminated by low-orbit satellite opportunistic signals; this is something that existing patented technical solutions cannot achieve at all, because their basic assumptions no longer hold.

[0037] 2) Significantly reduced computational complexity: Through the innovative two-stage low-dimensional search strategy of "radial parameter estimation + common phase compensation + angle and steering drift estimation" (D-SR-SIC framework), the originally coupled four-dimensional parameter estimation problem is transformed into two two-dimensional search problems, which greatly reduces the computational burden and enables the algorithm to have the potential for real-time processing under the condition of limited onboard computing resources of UAVs. Although existing patents do not address this issue, if they adopt direct four-dimensional joint estimation, the computational load will be explosive.

[0038] 3) Enhanced multi-target resolution and anti-interference capability: Combining the sparse reconstruction concept and the successive interference cancellation (SIC) mechanism, it can effectively suppress the masking effect of strong target echoes on weak target echoes (i.e., solve the "near-far effect"), so that even when there are multiple targets with huge intensity differences, the dynamic parameters of all targets can still be accurately estimated; the existing patent process is mainly aimed at single target or equal intensity multi-target scenarios.

[0039] 4) Preserving long coherence processing gain: The method of this invention does not rely on shortening the processing window to approximate the stationary condition. Instead, it accurately compensates for the dynamic phase within the full CPI, enabling the system to make full use of the long coherence accumulation time to improve the signal-to-noise ratio. This is crucial for detecting low-observable targets. Existing patents improve array gain through attitude adjustment, but cannot solve the signal decoherence problem within the CPI caused by platform motion.

[0040] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array, characterized in that, This method is based on low-Earth orbit satellite opportunity signals and includes the following steps: Step S1: Obtain array snapshot data after reference channel-assisted synchronization and waveform compensation; Step S2: Establish a parameterized space-time coupled phase model within the short coherence processing interval. The model includes a second-order Taylor approximation of the bistatic distance and a first-order approximation of the direction cosine. Step S3: Based on the array snapshot data, a single-channel input sequence is obtained through beamforming, and matched filtering is performed using time-domain atoms to estimate the radial parameter pair. ,in For equivalent bistatic radial velocity, This is the equivalent bistatic radial acceleration; Step S4: Based on the radial parameter pair, perform common time phase compensation on the array snapshot data to obtain the compensated snapshot matrix; Step S5: Based on the compensated snapshot matrix, perform two-dimensional correlation calculations using space-time turning atoms to estimate the angle parameter pair. ,in The initial angle of arrival. This refers to the array steering drift rate; Step S6: Based on the radial parameter pair and the angular parameter pair, construct a complete space-time dictionary atom and estimate the complex amplitude using the least squares criterion; Step S7: Perform successive disturbance cancellation to update the residuals, and repeat steps S3 to S6 to achieve dynamic angle of arrival estimation for multiple targets.

2. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, The parameterized space-time coupled phase model in step S2 is specifically as follows: The direction and angle satisfy the cosine condition: in, For the fast-time variable within the coherent processing interval, for Location at any given moment The initial position, , .

3. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, The time-domain atoms in step S3 The Each element satisfies: in, For carrier wavelength, For the first Each sampling time, The imaginary unit; The radial parameter in step S3 is estimated using a normalized matched filter metric, as shown in the following formula: in, For single-channel input sequences, For the radial parameter search set, This indicates the conjugate transpose. For time-domain atoms, For speed, It is acceleration.

4. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, The common time phase compensation in step S4 specifically involves: in, This is the original snapshot matrix. For the compensated snapshot matrix, Indicates conjugate. This represents constructing a diagonal matrix from vectors. For time-domain atoms.

5. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, The space-time orientation atom in step S5 The The elements satisfy the following formula: in, For array element index, For the spacing between array elements, For the first Each sampling time; The angle parameters in step S5 are estimated using a normalized Frobenius correlation metric, as follows: in, Search for a set of angle and steering drift parameters. Represents the Frobenius inner product. Denotes the Frobenius norm. For angle, ω is the angular velocity.

6. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, In step S3, multi-beam pre-screening is performed before the radial parameter pair estimation. Specifically, multiple beam pointing angles are preset and corresponding beam output sequences are formed; the radial matched filter peak value is calculated for each beam output sequence; and the beam with the largest peak value is selected as the input for subsequent radial parameter estimation. After obtaining the estimated values ​​of the radial parameter pair and the angular parameter pair, local refinement is performed in the neighborhood of each estimated value. The local refinement includes fine-resolution research or coordinate descent optimization.

7. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, The least squares magnitude estimation in step S6 satisfies: in, , , This represents a vectorization operator.

8. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, In step S7, successive interference elimination iteratively processes multiple targets in order from strong to weak.

9. The method for estimating the dynamic angle of arrival of an unmanned aerial vehicle (UAV) array according to claim 1, characterized in that, Under broadband or large radial velocity conditions, range migration correction is performed before parameter estimation; the narrow-band condition of the short coherence processing interval includes at least the array aperture narrow-band condition. Distance migration conditions caused by motion ,in For effective baseband bandwidth, The maximum differential delay within the array aperture, This refers to the change in propagation delay within the coherent processing interval; By using low-Earth orbit satellite ephemeris information and UAV navigation or attitude information, the search boundary is set to limit the parameter search set. and The range of values ​​is determined to ensure the physical feasibility and computational efficiency of parameter estimation.

10. A dynamic angle-of-arrival estimation system for an unmanned aerial vehicle (UAV) array, characterized in that, include: The unmanned aerial vehicle platform is equipped with a uniform linear array consisting of M array elements, which is used to collect the array received signals within the coherent processing interval; The reference channel receiving and synchronization module is used to acquire the direct wave and perform synchronization, waveform estimation and matched filtering, and output array snapshot data after waveform compensation. A processor and a memory, wherein the memory stores instructions, and the processor is configured to perform the method according to any one of claims 1-9; The element positions of the uniform linear array satisfy the following: in, For the fastest time Time of the first The position vectors of each array element , For the spacing between array elements, is the unit vector along the array axis.

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