Space-frequency robust beamforming method for unmanned aerial vehicle dual antenna GNSS

Abstract

The application relates to a space-frequency robust beamforming method for a UAV dual-antenna GNSS. The method comprises the following steps: performing space-frequency joint modeling on dual-frequency receiving signals of a long-baseline dual-antenna array, generating space-frequency joint receiving signals and constructing a corresponding space-frequency joint receiving covariance matrix; obtaining a real incident angle and a set of redundant aliasing angles corresponding to a first frequency point and a second frequency point; taking minimizing the total power of array output as a target, integrating scale constraints, real interference null constraints and lower limit constraints of independent gain of the frequency points, and constructing a space-frequency robust beamforming optimization model; solving the space-frequency robust beamforming optimization model to obtain an optimal space-frequency weight vector; and performing weighting processing on the space-frequency joint receiving signals by using the optimal space-frequency weight vector to obtain receiving signals corresponding to the first frequency point and the second frequency point after beamforming processing. The method can improve the receiving continuity and reliability of dual-frequency navigation signals of a UAV in a complex electromagnetic environment.

Description

Technical Field

[0001] This application relates to the field of navigation technology, and in particular to a space-frequency robust beamforming method for dual-antenna GNSS for unmanned aerial vehicles. Background Technology

[0002] With the rapid development of industrial-grade rotary-wing UAV technology, high-precision and high-reliability navigation and positioning capabilities have become the core support for completing various tasks such as aerial surveying, power line inspection, and emergency rescue. Dual-antenna GNSS direction finding technology, with its advantages of low cost, small size, and no cumulative error, directly calculates the heading and pitch angles of the UAV by measuring the phase difference between the signals received by the two antennas, and has become the mainstream solution for UAV attitude measurement.

[0003] To achieve high-precision direction finding at the 0.1° level in dual-antenna GNSS systems, the baseline length needs to be set to 0.5~0.7m, corresponding to 2~3.5 times the wavelength of the GPS L1 frequency. However, while long baseline configurations improve direction finding accuracy, they also introduce severe undersampling of the signal's spatial wavenumber, leading to unavoidable spatial frequency aliasing and grating lobe effects. Traditional adaptive nulling anti-interference algorithms simultaneously form deep nulls in both the actual interference direction and all aliasing directions. Because these algorithms rely on subspace orthogonality for interference suppression, they synchronously form deep nulls in all directions equivalent to the interference steering vector, causing navigation satellite signals falling near the interference aliasing location to be falsely suppressed, severely reducing the availability and continuity of the navigation system. Especially during the dynamic flight of UAVs, the satellite incident angle changes continuously, and redundant nulls can cause frequent signal reception interruptions, severely disrupting positioning continuity and potentially leading to UAV loss of control accidents. Therefore, solving the problem of false suppression of spatial aliasing in long-baseline dual-antenna GNSS systems has significant theoretical and engineering application value.

[0004] Extensive research has been conducted by scholars both domestically and internationally on the anti-jamming problem of GNSS arrays under long baselines. Traditional single-frequency adaptive nulling algorithms, such as the Power Inversion (PI) algorithm and the Linear Constrained Minimum Variance (LCMV) algorithm, are designed for small baseline arrays with half-wavelength spacing. Under long baselines, they cannot avoid the steering vector equivalence problem caused by grating lobes, inevitably resulting in redundant nulls. Grating lobe suppression methods based on array configuration optimization (such as using non-uniform linear arrays or sparse arrays) significantly increase hardware complexity and cost, and are incompatible with the standard dual-antenna systems already deployed on a large scale by UAVs. Existing DOA deambiguation methods for multi-frequency signals focus on radar direction finding and beam pointing optimization. Although they can estimate the true signal direction using the phase difference difference at different frequencies, they do not solve the fundamental contradiction that the weights will automatically form nulls in all aliasing directions during adaptive nulling. In addition, single-frequency dual-antenna arrays only have two degrees of freedom, and after applying interference null constraints, there are no extra degrees of freedom left to constrain the gain of redundant nulls.

[0005] In summary, how to simultaneously achieve unambiguous estimation of interference direction and reduce the false suppression of navigation signals by redundant nulls, thus forming a complete GNSS anti-interference solution for UAVs with long baseline dual antennas, has become an urgent problem to be solved. Summary of the Invention

[0006] Therefore, it is necessary to provide a space-frequency robust beamforming method for UAV dual-antenna GNSS to address the aforementioned technical problems.

[0007] A space-frequency robust beamforming method for dual-antenna GNSS of unmanned aerial vehicles, the method comprising: The received signals of the long baseline dual antenna array at the first and second frequency points are acquired and spatial-frequency joint modeling is performed to obtain the spatial-frequency joint received signal. The spatial-frequency joint received covariance matrix of the spatial-frequency joint received signal is then constructed. Obtain the true incident angle and the set of redundant aliasing angles corresponding to the first frequency point and the second frequency point; Based on the spatial frequency weight vector to be solved and the spatial frequency joint reception covariance matrix, the total output power of the array is determined. With minimizing the total output power of the array as the objective, a spatial frequency robust beamforming optimization model is constructed using constraints such as scale constraints, null constraints at the true interference incident angle, independent gain lower bound constraints at the first frequency point, and independent gain lower bound constraints at the second frequency point. The null constraints are used to form interference suppression nulls at the true interference incident angle. The independent gain lower bound constraint at the first frequency point applies to the redundancy aliasing angle at the first frequency point; the independent gain lower bound constraint at the second frequency point applies to the redundancy aliasing angle at the second frequency point. Solve the aforementioned space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector; The space-frequency joint received signal is weighted using the optimal space-frequency weight vector to obtain the received signals corresponding to the first and second frequency points after beamforming processing.

[0008] The aforementioned space-frequency robust beamforming method for dual-antenna GNSS for UAVs expands the system's signal processing degrees of freedom by performing joint space-frequency modeling of the dual-frequency received signals from a long-baseline dual-antenna array and constructing the corresponding covariance matrix. This overcomes the limitations of insufficient degrees of freedom in single-frequency arrays. By obtaining the true interference incident angle and the set of redundant aliasing angles at each frequency point, it can accurately distinguish between interference azimuth and false angles caused by grating lobes. By building an optimization model with the goal of minimizing the total array output power, and combining it with null constraints and independent gain lower bound constraints at frequency division points, it can specifically suppress real interference. Simultaneously, gain protection is set for the aliasing azimuth at different frequency points to prevent navigation signals from being falsely suppressed. By solving the model to obtain the optimal space-frequency weight vector and completing signal weighting processing, adaptive beam control can be achieved. This invention effectively improves the redundancy nulling problem caused by grating lobes in long-baseline arrays, enhancing the continuity and reliability of UAV dual-frequency navigation signal reception in complex electromagnetic environments. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a space-frequency robust beamforming method for dual-antenna GNSS for UAVs in one embodiment. Figure 2 This is a flowchart illustrating a dual-frequency unambiguity direction finding method in one embodiment; Figure 3 This is a flowchart illustrating the dual-frequency deblurring and real interference angle estimation algorithm in one embodiment; Figure 4 This is a flowchart illustrating a frequency division point independent constraint robust space-frequency beamforming algorithm in one embodiment; Figure 5 This is a schematic diagram showing the variation of the average space utilization rate of navigation signals with the normalized antenna spacing under different schemes in one embodiment. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0011] The gain distribution of an array antenna is determined by the ratio of antenna spacing to signal wavelength. When the antenna spacing exceeds half the signal wavelength, the array's sampling of the spatial signal does not satisfy the sampling theorem, leading to spatial undersampling and subsequently grating lobes. The aliasing spatial frequency then satisfies... Signals from multiple incident directions at the same frequency will generate a consistent spatial steering vector. When the antenna spacing is fixed, the wavelengths of signals at different frequencies are different, and the corresponding spatial aliasing periods and aliasing angle distributions also differ.

[0012] Typical single-frequency adaptive nulling algorithms are represented by the power inversion algorithm, which is based on the principle of subspace orthogonality. It achieves interference suppression by making the weight vector orthogonal to the interference steering vector and forming deep nulls in the interference direction. Under the grating lobe effect, the steering vectors of the real interference and all aliasing angles are completely equivalent in the single-frequency spatial domain. Therefore, while generating nulls in the real interference direction, traditional algorithms will inevitably generate unnecessary redundant nulls simultaneously in all aliasing azimuths, and the navigation satellite signals falling into these azimuths will be abnormally attenuated.

[0013] The grating lobe effect is an inherent physical characteristic caused by spatial undersampling of long baseline arrays, and this contradiction cannot be fundamentally solved by any single-frequency spatial processing method. It brings two core problems: first, single-frequency spatial processing cannot distinguish between real interference and grating lobes, leading to inherent angular ambiguity in interference direction estimation; second, navigation satellite signals experience undesirable attenuation when falling into grating lobe locations, significantly reducing the output signal-to-interference-plus-noise ratio (SNR). Especially in dynamic UAV flight scenarios, where the satellite incident angle changes continuously, redundant nulls can cause frequent signal reception interruptions, disrupting the continuity and reliability of navigation.

[0014] To solve this problem, it is necessary to first accurately estimate the actual incident direction of interference, and then decouple the correlation between the actual interference and the aliasing direction to avoid redundant nulls formed by adaptive nulling at the aliasing frequency. However, existing technologies all have obvious limitations: traditional single-frequency adaptive nulling algorithms, such as power inversion and linear constraint minimum variance algorithms, are designed for half-wavelength small baseline arrays. They cannot avoid the steering vector equivalence problem under long baselines, and will inevitably generate redundant nulls; grating lobe suppression methods based on array configuration optimization such as non-uniform linear arrays and sparse arrays will significantly increase hardware complexity and cost, and cannot be compatible with standard dual-antenna systems that have been deployed on a large scale; existing multi-frequency DOA deambiguation methods only focus on beam pointing and direction finding scenarios. Although they can estimate the actual signal direction, they do not solve the essential contradiction that the weights automatically generate nulls in the aliasing direction during adaptive nulling; at the same time, single-frequency dual-antenna arrays only have 2 degrees of freedom. After applying interference null constraints, there are no extra degrees of freedom to constrain the gain of redundant nulls. Therefore, it is necessary to introduce additional signal dimensions to construct a joint processing model and increase the system's degrees of freedom in order to simultaneously achieve accurate estimation of the true interference direction and effective suppression of redundant nulls.

[0015] In one embodiment, such as Figure 1 As shown, a space-frequency robust beamforming method for dual-antenna GNSS of UAVs is provided, including the following steps: Step 102: Obtain the received signals of the long baseline dual antenna array at the first and second frequency points and perform space-frequency joint modeling to obtain the space-frequency joint received signal, and construct the space-frequency joint received covariance matrix of the space-frequency joint received signal.

[0016] A long-baseline dual-antenna array refers to a dual-antenna receiving array with an antenna spacing greater than half the wavelength of the navigation signal. The first and second frequencies are two different carrier frequencies received by the UAV GNSS receiver. Space-frequency joint modeling integrates the multiple received signals from two frequencies and two antennas into a unified four-dimensional signal form. The space-frequency joint received signal is a composite received signal containing both spatial and frequency domain information after integration. The space-frequency joint reception covariance matrix is ​​used to characterize the correlation characteristics and energy distribution between the channels of the space-frequency joint received signal.

[0017] It is understandable that this step can integrate multi-channel signal information from dual-frequency dual-antenna systems, fully utilize the frequency dimension to expand the system's degrees of freedom, and provide a complete data foundation for subsequent beam optimization calculations.

[0018] Step 104: Obtain the actual incident angle and the set of redundant aliasing angles corresponding to the first frequency point and the second frequency point.

[0019] The true incident angle refers to the actual angle at which the airborne interference signal arrives at the dual-antenna array, distinct from the spurious angle caused by the grating lobe effect. Redundancy aliasing angles are spurious incident angles generated by long-baseline arrays due to spatial undersampling and the grating lobe effect; these angles are often misidentified as interference directions by traditional algorithms.

[0020] Step 106: Based on the spatial frequency weight vector and the spatial frequency joint receiver covariance matrix to be solved, determine the total array output power. With minimizing the total array output power as the objective, and using scale constraints, null constraints at the actual interference incident angle, independent gain lower bound constraints at the first frequency point, and independent gain lower bound constraints at the second frequency point as constraints, construct a spatial frequency robust beamforming optimization model. Null constraints are used to form interference suppression nulls at the actual interference incident angle. The independent gain lower bound constraint at the first frequency point applies to the redundancy aliasing angle at the first frequency point. The independent gain lower bound constraint at the second frequency point applies to the redundancy aliasing angle at the second frequency point.

[0021] The space-frequency weight vector is the combination of weighting coefficients for each channel of the jointly received space-frequency signal, and the total array output power is the overall output energy of the signal after weighting. Scale constraints are used to fix the reference channel weights, ensuring the stability of the output signal amplitude and phase. Null constraints are used to suppress signal energy in the target direction. Independent gain lower limit constraints are minimum gain limits set separately for different frequency points.

[0022] It is understandable that this step can build an optimized model that adapts to the space-frequency joint architecture, and control the signal gain of different directions and frequencies through multiple types of constraints and partitions. This is beneficial for suppressing energy only for real interference, while ensuring the normal transmission of signals in aliased directions.

[0023] Step 108: Solve the space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector.

[0024] Solving this problem involves using numerical algorithms to calculate the space-frequency robust beamforming optimization model, thereby obtaining the weighting coefficients that satisfy all constraints. This invention employs the active set algorithm to solve this optimization model. This algorithm simplifies the iterative process for low-dimensional convex optimization problems, resulting in low computational cost and strong real-time performance. Alternatively, algorithms suitable for linearly constrained convex optimization problems, such as the Lagrange multiplier method and the interior-point method, can also be used to complete the solution calculation. The optimal space-frequency weight vector is the optimal set of channel weighting coefficients that achieves the desired beamforming effect under all constraints.

[0025] Step 110: Use the optimal space-frequency weight vector to weight the space-frequency joint received signal to obtain the received signals corresponding to the first and second frequency points after beamforming processing.

[0026] Weighted processing is a computational process that multiplies and superimposes the optimal space-frequency weight vector with the space-frequency joint received signal channel by channel. The dual-frequency navigation signal is an effective GNSS signal that has been processed by beamforming and can be used by the UAV navigation module.

[0027] Understandably, this step can beamform the received signal according to the design rules, effectively reducing the strength of interference signals while improving the reception quality and continuity of navigation signals.

[0028] In the aforementioned space-frequency robust beamforming method for dual-antenna GNSS for UAVs, by performing space-frequency joint modeling of the dual-frequency received signals of a long-baseline dual-antenna array and constructing the corresponding covariance matrix, the system's signal processing degrees of freedom can be expanded, overcoming the limitations of insufficient degrees of freedom in single-frequency arrays. By obtaining the true interference incident angle and the set of redundant aliasing angles at each frequency point, the interference azimuth and false angles caused by grating lobes can be accurately distinguished. By building an optimization model with the goal of minimizing the total array output power, and combining it with null constraints and independent gain lower limit constraints at frequency division points, real interference can be specifically suppressed. At the same time, gain protection is set for the aliasing azimuth at different frequency points to avoid the navigation signal being falsely suppressed. By solving the model to obtain the optimal space-frequency weight vector and completing signal weighting processing, adaptive beam control can be achieved. This embodiment of the invention can effectively improve the redundancy null problem caused by grating lobes of long-baseline arrays and improve the reception continuity and reliability of dual-frequency navigation signals for UAVs in complex electromagnetic environments.

[0029] In one embodiment, such as Figure 2As shown, a flowchart of a dual-frequency unambiguity direction finding method is provided, which obtains the true incident angle and the redundant aliasing angle sets corresponding to the first and second frequency points, including: Step 202: Obtain the covariance matrix of the received signals of the long baseline dual-antenna array at the first and second frequency points; Step 204: Perform eigenvalue decomposition on the covariance matrix of the received signals at the first and second frequency points respectively, extract the interference-dominant eigenvector corresponding to the maximum eigenvalue of each frequency point, and calculate the spatial phase difference between the two antennas at the corresponding frequency point based on the interference-dominant eigenvector of each frequency point. Step 206: Calculate the fuzzy spatial frequency estimate for each frequency point based on the spatial phase difference, array baseline length, and signal wavelength of the corresponding frequency point. Step 208: Based on the fuzzy spatial frequency estimates of the first and second frequency points and their respective spatial aliasing periods, search for integer correction values ​​that satisfy the consistency of the dual-frequency spatial frequencies, and obtain the true incident spatial frequency based on the integer correction values ​​and the fuzzy spatial frequency estimates of the corresponding frequency points. Step 210: Calculate the true incident angle based on the true incident spatial frequency; Step 212: Based on the actual incident spatial frequency, offset by integer multiples according to the spatial aliasing period of the first frequency point and the second frequency point respectively, to generate a set of all corresponding redundant aliasing angles at each frequency point.

[0030] In this embodiment, it is important to note that to achieve high-precision direction finding at the 0.1° level, the baseline length of the dual-antenna GNSS system needs to be set to 0.5~0.7m, corresponding to 2~3.5 times the wavelength of the GPSL1 frequency. This long baseline configuration leads to undersampling of the signal spatial wavenumber, causing spatial frequency aliasing and grating lobe effects. This results in signals with multiple incident angles exhibiting identical steering vectors at the array receiver, making them indistinguishable using single-frequency spatial domain characteristics. This invention achieves dual-frequency deambiguity based on the spatial aliasing characteristics of long-baseline arrays. For an array with a given baseline length, each frequency has a fixed spatial aliasing period, the value of which is equal to the ratio of the signal wavelength at that frequency to the baseline length. When the spatial frequencies of two angles differ by an integer multiple of the spatial aliasing period, their steering vectors at that frequency are completely equivalent. Since the signal wavelengths at different frequencies are different, their spatial aliasing periods are also different. Therefore, aliasing angles that are completely equivalent in the original single-frequency spatial domain have a unique distinguishable feature in the dual-frequency joint domain.

[0031] To address the inherent indistinguishability between real interference and grating lobes in single-frequency airspace, this invention utilizes the multi-frequency reception capability commonly found in dual-antenna GNSS receivers for UAVs. It introduces a frequency dimension to construct a joint air-frequency processing model, jointly modeling the received data from two independent frequency points.

[0032] Consider a receiver array consisting of two dual-band antennas with a baseline length of d, receiving navigation signals at two arbitrary frequencies, with carrier frequencies f1 and f2, corresponding to wavelengths of . and Where c is the speed of light. Assuming the received data contains one broadband suppression jamming source, K navigation satellite signals, and additive white Gaussian noise, then the 4-channel space-frequency joint received data vector is: ; in, For space-frequency joint steering vector, To accurately represent the incident angle of the interference, This is a broadband interference signal. For the signal of the k-th navigation satellite, The vector is a 4-dimensional complex Gaussian white noise, and its covariance matrix is... , Let be the incident angle of the signal from the k-th navigation satellite.

[0033] For any incident angle of The far-field signal, whose space-frequency joint steering vector is defined as the cascade of the space-domain steering vectors of the two frequency points of the dual antennas: ; The spatial phase differences between the two frequency points are as follows: ; Based on the formula for the 4-channel space-frequency joint reception data vector, the space-frequency steering vector of the actual interference and single-frequency aliasing angles. and No longer equivalent The angle of single-frequency aliasing caused by the grating lobe effect is taken as an example, using the most widely used GPS L1 / L2 frequency combination. = 0.1903m, = 0.2442m, wavelength ratio It is not an integer, and fully satisfies the above distinguishability condition.

[0034] In the space-frequency steering vectors corresponding to the aliasing frequencies at each frequency point, since the interference is usually broadband and covers different frequency points, only the space-frequency steering vectors of the actual interference direction are the same at different frequency points. Therefore, after introducing a frequency dimension to establish a joint space-frequency steering vector, the difference in signal wavelength at different frequency points can be used to effectively decouple and separate the angle of the original spatial aliasing.

[0035] Based on the aforementioned distinguishability, the incident direction of the actual interference can be uniquely estimated. Simultaneously, the space-frequency joint model increases the system's degrees of freedom from 2D to 4D for a single frequency, providing ample design space for multi-constraint beamforming. Null constraints can be applied only in the direction of the actual interference, while gain lower bound constraints are applied in all aliasing angle directions. This achieves the goal of suppressing the satellite signal by generating deep nulls only in the direction of the actual interference, without suppressing the satellite signal at the original aliasing frequency.

[0036] Based on spatial frequency domain distinguishability, real interference is the only signal that has the same spatial frequency at two frequency points, while the spatial frequencies of all aliasing angles will inevitably differ at different frequency points due to differences in aliasing periods. Utilizing this characteristic, this invention proposes a deambiguation method based on dual-frequency phase difference consistency to achieve unambiguous estimation of the real interference direction. The flowchart of the dual-frequency deambiguation and real interference angle estimation algorithm is as follows: Figure 3 As shown.

[0037] Specifically, eigenvalue decomposition is performed on the single-frequency covariance matrices at frequencies f1 and f2, respectively, and the interference-dominant eigenvector corresponding to the largest eigenvalue is extracted. and Because in strong interference scenarios, the dominant interference feature vector is approximately proportional to the interference steering vector at the corresponding frequency point, the spatial phase difference between the two frequency points is... and It can be calculated using the ratio of the elements of the eigenvectors: ; in This represents the phase with a complex value, ranging from [-π, π].

[0038] This yields the fuzzy spatial frequency estimates for the two frequency points: ; Due to spatial aliasing, the above estimates are only the actual spatial frequencies. The result of taking the modulus of the aliasing period at the corresponding frequency point has ambiguity for integer multiples of the period.

[0039] Since the actual spatial frequencies of broadband interference are exactly the same at both frequency points, the Chinese Remainder Theorem (CRT) can be used to determine the aliasing period at the two frequency points. and They are coprime; search for integers that satisfy the following conditions. : ; This uniquely determines the true spatial frequency. Thus, the true angle of interference is obtained: ; The essence of this method is to find the unique common element of two ambiguous spatial frequency sets, which is the spatial frequency of the real interference.

[0040] Based on the estimated true interference angle, all redundant aliasing angles at the two frequency points can be calculated separately, forming a set of redundant grating lobe angles. and This is used for gain constraints in subsequent robust beamforming.

[0041] In one embodiment, the ratio of the signal wavelengths at the first frequency point and the second frequency point is not an integer.

[0042] Specifically, taking the commonly used GPS L1 and L2 frequencies as examples, The wavelength ratio between the two is approximately 0.779, which is a non-integer value. This parameter condition is a necessary prerequisite that the aliasing angle and the actual interference's steering vector in the spatial frequency domain are not equal. In this embodiment, by utilizing the inherent parameter characteristic that the dual-frequency wavelengths are non-integer multiples, it is ensured that the single-frequency aliasing angle cannot coincide with the actual interference at another frequency point. This achieves physical differentiation between the actual interference and the aliasing angle, which is the key constraint enabling the deambiguity of this invention.

[0043] In one embodiment, obtaining the true incident spatial frequency based on the integer correction value and the fuzzy spatial frequency estimate of the corresponding frequency point includes: multiplying the integer correction value of the first frequency point by the spatial aliasing period of the first frequency point, and adding it to the fuzzy spatial frequency estimate of the first frequency point to obtain a first calculated value; multiplying the integer correction value of the second frequency point by the spatial aliasing period of the second frequency point, and adding it to the fuzzy spatial frequency estimate of the second frequency point to obtain a second calculated value; and taking the consistent value between the first calculated value and the second calculated value as the true incident spatial frequency.

[0044] In this embodiment, due to spatial aliasing, the fuzzy spatial frequency estimates calculated for each frequency point are only the result of taking the modulus of the real spatial frequency with respect to the aliasing period of the corresponding frequency point, resulting in ambiguity with integer multiples of the period. Since the real spatial frequency of broadband interference is completely consistent at both frequency points, the Chinese Remainder Theorem is used to search for integer correction values ​​that satisfy the consistency of the two-frequency spatial frequencies. Essentially, this involves finding the unique common element of the fuzzy spatial frequency sets of the two frequency points, which is the spatial frequency of the real interference.

[0045] In one embodiment, the scale constraint includes: setting the first frequency channel of the first element of the long baseline dual antenna array as the reference channel, and fixing the space frequency weight vector component corresponding to the reference channel to 1.

[0046] In this embodiment, to avoid the false suppression of navigation signals by redundant grating lobes while ensuring effective suppression of broadband interference, this invention proposes a robust space-frequency beamforming algorithm with independent constraints at frequency division points. Based on the minimum output power criterion, this algorithm applies multiple sets of linear constraints to form deep nulls in the interference directions obtained after deambiguation, while simultaneously limiting the depth of redundant nulls at aliasing frequency locations.

[0047] The complete convex optimization problem model is as follows: ; Constraints: ; in γ is a 4-dimensional space-frequency joint covariance matrix, and γ is a preset gain threshold.

[0048] The physical meanings of each constraint are as follows: 1) Scale constraints Set the f1 frequency of the first antenna as the reference channel to ensure the scale and phase consistency of the output signal, where s is the scale constraint vector; 2) Disturbance Null Constraints A deep null is formed at the estimated true interference direction θ_hat_J to achieve complete suppression of broadband interference; 3) Independent redundancy null constraint at frequency division point , This ensures that the gain of frequencies f1 and f2 at their respective aliasing angles is not lower than the threshold γ. Unlike traditional joint constraint space-frequency beamforming, this constraint avoids the algorithm's defect of sacrificing the performance of one frequency to meet the joint constraint, ensuring that the navigation signal reception performance of both frequencies is guaranteed simultaneously.

[0049] In one embodiment, solving the space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector includes: iteratively solving the space-frequency robust beamforming optimization model using an active set algorithm to obtain the optimal space-frequency weight vector.

[0050] In this embodiment, since all constraints of the convex optimization problem of the present invention are linear constraints, its feasible region is a convex set, and the objective function is a quadratic convex function, a unique global optimal solution exists. For the Linear Constrained Minimum Variance (LCMV) problem, when the constraint is an equality constraint, a closed-form solution can be obtained through the Lagrange multiplier method. The present invention employs a customized active set algorithm for fast solution of this 4-dimensional low-dimensional problem, without relying on a general convex optimization toolkit.

[0051] In one embodiment, the active set algorithm iteratively solves the space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector, including: initializing the active set and incorporating scale constraints and null constraints of the actual interference incident angle into the active set; solving the linear constraint minimum variance problem based on the current active set to obtain the current space-frequency weight vector; calculating the actual gain corresponding to all redundant aliasing angles based on the current space-frequency weight vector, and determining whether there are any illegal aliasing angles with gains lower than a preset threshold; if there are illegal aliasing angles, distinguishing the frequency points to which the illegal aliasing angles belong, generating independent gain lower bound constraints for the corresponding frequency points and adding them to the active set, iteratively updating the space-frequency weight vector until the iteration stopping condition is met, stopping the iteration, and taking the currently output space-frequency weight vector as the optimal space-frequency weight vector.

[0052] In this embodiment, the flow of the frequency division point independent constraint robust space-frequency beamforming algorithm is as follows: Figure 4 As shown, Algorithm 2 starts with a basic LCMV solution containing only scale constraints and disturbance null constraints, which is the minimum constraint solution that satisfies the disturbance suppression requirement. A relaxation strategy of successively adding constraints is adopted, where each time only the most severely violated constraint is transformed into an equality constraint and added to the activity set, maximizing the preservation of system degrees of freedom while ensuring performance. Here, γ is the set gain threshold used to constrain the depth of redundant nulls. Since the 4-dimensional complex vector space can only hold a maximum of 4 linearly independent constraint vectors, and the initial activity set already contains 2 constraints, the algorithm converges in at most 2 iterations. The core operation of each iteration is the inversion of a 4×4 matrix, with a computational complexity of O(n log n). Therefore, the total time complexity of the entire algorithm is O(n). It involves only a small number of fixed-dimensional matrix operations, which fully meets the real-time processing requirements of UAV embedded platforms.

[0053] In one embodiment, calculating the actual gain corresponding to all redundant aliasing angles based on the current space-frequency weight vector includes: calculating the channel gain of each redundant aliasing angle at the first frequency point and the channel gain of each redundant aliasing angle at the second frequency point.

[0054] In one embodiment, distinguishing the frequency points to which the illegal aliasing angles belong and generating independent gain lower limit constraints for the corresponding frequency points includes: selecting the aliasing angle with the smallest actual gain value from the illegal aliasing angles as the target angle, and generating independent gain lower limit constraints for the corresponding frequency points based on the frequency points to which the target angles belong.

[0055] In one embodiment, the iteration stopping condition includes: the actual gain of all redundant aliasing angles is not lower than a preset gain threshold, or the total number of linear independent constraints in the active set reaches the maximum number.

[0056] The effectiveness of this invention was verified through experiments. Simulation results show that, under the long baseline grating lobe effect, the traditional single-frequency adaptive nulling algorithm synchronously forms deep nulls at the real interference direction and all aliasing angles, resulting in an attenuation of approximately -30dB for the navigation signal at the aliasing position. However, after adopting the dual-frequency defuzzification spatial frequency robust beamforming algorithm of this invention, deep nulls are formed only at the real interference direction, and the radiation pattern gain at each frequency aliasing angle position is constrained to above -10dB. The gain at the navigation signal direction is approximately 0dB. While ensuring interference suppression capability, this effectively solves the problem of navigation signal false suppression caused by the long baseline grating lobe effect.

[0057] Furthermore, by reducing the null depth at the aliasing frequency, the continuity of navigation signal reception is improved, resulting in a higher spatial utilization rate of the navigation signal after algorithm processing compared to ordinary long baselines. The curves showing the variation of the average spatial utilization rate of the navigation signal with the normalized antenna spacing under different schemes are as follows: Figure 5 As shown in the figure, the average spatial utilization of the navigation signal after processing by the DF-ARSF algorithm is 5% to 16% higher than that of ordinary long baselines. This effectively improves the robustness of navigation signal positioning solutions for UAVs in dynamic scenarios.

[0058] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this invention, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Furthermore, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0059] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.

[0060] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A space-frequency robust beamforming method for dual-antenna GNSS of unmanned aerial vehicles, characterized in that, The method includes: The received signals of the long baseline dual antenna array at the first and second frequency points are acquired and spatial-frequency joint modeling is performed to obtain the spatial-frequency joint received signal. The spatial-frequency joint received covariance matrix of the spatial-frequency joint received signal is then constructed. Obtain the true incident angle and the set of redundant aliasing angles corresponding to the first frequency point and the second frequency point; Based on the spatial frequency weight vector to be solved and the spatial frequency joint reception covariance matrix, the total output power of the array is determined. With minimizing the total output power of the array as the objective, a spatial frequency robust beamforming optimization model is constructed using constraints such as scale constraints, null constraints at the true interference incident angle, independent gain lower bound constraints at the first frequency point, and independent gain lower bound constraints at the second frequency point. The null constraints are used to form interference suppression nulls at the true interference incident angle. The independent gain lower bound constraint at the first frequency point applies to the redundancy aliasing angle at the first frequency point; the independent gain lower bound constraint at the second frequency point applies to the redundancy aliasing angle at the second frequency point. Solve the aforementioned space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector; The optimal space-frequency weight vector is used to weight the space-frequency joint received signal to obtain the received signals corresponding to the first and second frequency points after beamforming processing.

2. The method according to claim 1, characterized in that, The process of obtaining the true incident angle and the set of redundant aliasing angles corresponding to the first frequency point and the second frequency point includes: Obtain the covariance matrix of the received signals of the long baseline dual-antenna array at the first and second frequency points; The covariance matrices of the received signals at the first and second frequency points are decomposed into eigenvalues ​​respectively. The interference-dominant eigenvectors corresponding to the maximum eigenvalues ​​at each frequency point are extracted. Based on the interference-dominant eigenvectors at each frequency point, the spatial phase difference between the two antennas at the corresponding frequency point is calculated. Based on the spatial phase difference of each frequency point, the array baseline length, and the signal wavelength of the corresponding frequency point, the fuzzy spatial frequency estimate of each frequency point is calculated. Based on the fuzzy spatial frequency estimates of the first and second frequency points and their respective spatial aliasing periods, an integer correction value that satisfies the consistency of the dual-frequency spatial frequencies is searched. Based on the integer correction value and the fuzzy spatial frequency estimate of the corresponding frequency point, the true incident spatial frequency is obtained. The true incident angle is calculated based on the true incident spatial frequency. Based on the actual incident spatial frequency, the spatial aliasing period of the first frequency point and the second frequency point are offset by integer multiples to generate a set of all corresponding redundant aliasing angles at each frequency point.

3. The method according to claim 2, characterized in that, The ratio of the signal wavelengths at the first frequency point and the second frequency point is not an integer.

4. The method according to claim 2, characterized in that, Based on the integer correction value and the fuzzy spatial frequency estimate of the corresponding frequency point, the true incident spatial frequency is obtained as follows: Multiply the integer correction value of the first frequency point by the spatial aliasing period of the first frequency point, and add it to the fuzzy spatial frequency estimate of the first frequency point to obtain the first calculated value; Multiply the integer correction value of the second frequency point by the spatial aliasing period of the second frequency point, and add it to the fuzzy spatial frequency estimate of the second frequency point to obtain the second calculated value; The value that matches the first calculated value and the second calculated value is taken as the true incident space frequency.

5. The method according to claim 1, characterized in that, The scale constraints include: The first frequency channel of the first element of the long baseline dual antenna array is set as the reference channel, and the space frequency weight vector component corresponding to the reference channel is fixed to 1.

6. The method according to claim 1, characterized in that, The process of solving the space-frequency robust beamforming optimization model to obtain the optimal space-frequency weight vector includes: The optimal space-frequency weight vector is obtained by iteratively solving the space-frequency robust beamforming optimization model using the active set algorithm.

7. The method according to claim 6, characterized in that, The active set algorithm is used to iteratively solve the space-frequency robust beamforming optimization model, and the optimal space-frequency weight vector is obtained as follows: Initialize the activity set by incorporating the scale constraint and the null constraint of the actual disturbance incident angle into the activity set; Solve the linearly constrained minimum variance problem based on the current activity set to obtain the current space frequency weight vector; Based on the current space frequency weight vector, calculate the actual gain corresponding to all redundant aliasing angles, and determine whether there are any illegal aliasing angles with gains lower than a preset threshold. If there is an illegal aliasing angle, distinguish the frequency point to which the illegal aliasing angle belongs, generate an independent gain lower limit constraint for the corresponding frequency point and add it to the activity set, iteratively update the space frequency weight vector until the iteration stop condition is met, stop the iteration, and take the current output space frequency weight vector as the optimal space frequency weight vector.

8. The method according to claim 7, characterized in that, The step of calculating the actual gain corresponding to all redundant aliasing angles based on the current space-frequency weight vector includes: Calculate the channel gain at each redundant aliasing angle at the first frequency point and the channel gain at each redundant aliasing angle at the second frequency point.

9. The method according to claim 7, characterized in that, To distinguish the frequency points to which the illegal aliasing angles belong, and to generate independent gain lower bound constraints for the corresponding frequency points, the following are included: From the illegal aliasing angles, the aliasing angle with the smallest actual gain value is selected as the target angle. Based on the frequency point to which the target angle belongs, an independent gain lower limit constraint is generated for the corresponding frequency point.

10. The method according to claim 7, characterized in that, The iteration stopping conditions include: The actual gain of all redundant aliasing angles is not lower than the preset gain threshold, or the total number of linear independent constraints in the active set reaches the maximum number.

Images