Off-grid target direction finding method and system based on array amplitude linear approximation and medium

Abstract

The invention discloses an off-grid target direction finding method and system based on array amplitude linear approximation and a medium. According to the method, a high-power reference signal with a known angle is introduced to the edge of an observation area, and a nonlinear array amplitude signal model is approximately linearized into a linear signal model about sine difference frequency of a target and a reference signal; then, under a sparse representation framework, first-order Taylor expansion about sine difference frequency is carried out on column vectors in the frequency steering matrix, and an off-grid sparse model containing a grid deviation item is constructed; and finally, through a two-step iteration strategy, an initial target orientation is determined by using a coarse grid, and then signal difference frequency and off-grid deviation are alternately corrected through a closed-form solution. According to the method, phase information is not needed, the influence of array phase errors on the estimation precision can be effectively eliminated, the problem that the precision is limited due to grid mismatch is solved through off-grid correction, and the estimation precision of an amplitude-only direction finding system is remarkably improved under the condition that the calculation complexity is not increased.

Description

Technical Field

[0001] This invention relates to the fields of signal processing and array direction finding technology, specifically to a method and system for off-grid target direction finding based on linear approximation of array amplitude. This invention is particularly applicable to low-cost radar, passive sonar, or UAV detection systems, enabling high-precision estimation of the direction of arrival (DOA) of an incident target using only the amplitude information of the received signal from the array (without phase information). Background Technology

[0002] Direction of arrival (DOA) estimation is a core problem in array signal processing and is widely used in radar detection, wireless communication, and sound source localization. Traditional DOA estimation methods, such as the MUSIC (Multiple Signal Classification) algorithm, the ESPRIT (Rotation Invariant Subspace) algorithm, and sparse reconstruction algorithms based on compressed sensing, typically rely on the complex information of the array received data, i.e., they require accurate amplitude and phase information simultaneously.

[0003] However, in practical engineering applications, especially in low-cost, large-scale deployments or edge computing scenarios (such as low-altitude UAV detection radar arrays), maintaining strict phase synchronization between array element channels is extremely difficult. Factors such as cable length errors, temperature drift, and device aging in the RF link can introduce unknown phase errors. When phase errors exist, the performance of the aforementioned high-resolution algorithms that rely on phase consistency will drop sharply, or even fail completely.

[0004] Currently, in order to overcome the impact of phase error on direction finding systems, the academic community has proposed some DOA estimation methods that only utilize the array amplitude response. Among them, one representative method is to use a high-power reference signal to transform the nonlinear amplitude model into a linear model (see: Y.Tian, ​​J.Shi, Y.Wang, and Q.Lian, "Non-coherent direction of arrival estimation utilizing linear model approximation," Signal Process., vol.157, pp.261-265, 2019).

[0005] However, the aforementioned existing technologies still have significant limitations in practical applications: ① Accuracy limitations due to grid effect: This method is based on an "on-grid" sparse model, assuming that the direction of arrival of the target signal strictly falls on a preset discrete angle grid. However, in actual detection scenarios, the target angle is often continuous and it is difficult for it to be exactly located on the grid point. When the target is in an "off-grid" state, this method will produce a significant grid mismatch error, and this error cannot be eliminated by improving the signal-to-noise ratio.

[0006] ② The contradiction between computational load and resolution: In order to mitigate the decrease in accuracy caused by grid mismatch, existing technologies usually need to improve resolution by dividing the grid into extremely fine grids. However, this will lead to a dramatic increase in the dimension of the sensing matrix, which greatly increases the computational overhead in the sparse recovery process and makes it difficult to meet the real-time processing requirements of embedded direction finding devices.

[0007] ③ Lack of deviation compensation mechanism: This method can only provide the estimated value of the closest grid point, and lacks a mechanism for online compensation and iterative correction of grid deviation, resulting in poor robustness in complex electromagnetic environments.

[0008] Therefore, how to achieve low computational cost and high accuracy in off-grid target direction finding using only array amplitude and with grid mismatch is a technical problem that urgently needs to be solved in the field of low-altitude detection. Summary of the Invention

[0009] This invention aims to solve the aforementioned technical problems by providing a method and system for off-grid target direction finding based on a linear approximation of array amplitude. This invention linearizes the nonlinear amplitude model by introducing a high-power reference signal and combines this with a two-step iterative optimization strategy to correct off-grid deviations, thereby achieving high-precision DOA estimation using only amplitude information.

[0010] The technical solution adopted in this invention is as follows: 1. Construct an amplitude direction finding system architecture based on an active reference signal. This invention introduces a high-power active reference signal transmitter based on a uniform linear array (ULA). This reference signal transmitter is deployed at the edge of the array's observation area (e.g., -90° or 90°). The array receiving model considers element phase errors, but only extracts the amplitude response of the received signal during processing, thus fundamentally avoiding the influence of phase errors.

[0011] 2. Linearized approximation modeling based on high-power reference signal To address the nonlinear characteristics of the received signal amplitude, this invention leverages the fact that the power of the reference signal is significantly greater than the power of the target signal (e.g., the reference signal power is more than 10 times that of the target signal) to process the square of the covariance matrix amplitude. By ignoring weak self-crossing terms of the target signal and retaining only the cross-crossing terms between the target signal and the reference signal, the originally complex nonlinear amplitude response model is approximated as a linear observation model with respect to the target signal power. This model links the amplitude measurement value with the spatial spectrum of the target through a frequency steering matrix.

[0012] 3. Construct a sparse signal model incorporating off-grid bias. To address the issue that the target angle is not on the preset grid, this invention performs a first-order Taylor expansion on the frequency form corresponding to the array guide vector within a sparse representation framework.

[0013] A first-order Taylor expansion with respect to frequency is performed on the column vectors in the frequency steering matrix to construct an overcomplete dictionary containing grid point basis vectors and grid deviation basis vectors. The off-grid deviation is introduced into the model as a parameter to be estimated, thereby transforming the off-grid DOA estimation problem into a sparse reconstruction problem.

[0014] 4. A two-step estimation method of "coarse estimation + fine correction" is proposed. This invention solves the above model in two stages, balancing computational efficiency and estimation accuracy: Step 1 (coarse estimation): Ignoring grid deviations, based on a preset discrete grid, a coarse sparse recovery is performed using a convex optimization algorithm (such as FISTA or CVX to solve the L1 norm minimization problem) to determine the initial position of the target signal.

[0015] The second step (iterative correction of deviation): Based on the support set determined in the first step, a correction matrix containing the first derivative is constructed. Through an iterative optimization algorithm, the signal power and deviation are updated alternately to gradually approximate the true angle of the target until convergence.

[0016] 5. System-level elimination strategy for multiple ambiguities This invention comprehensively solves the three major angular ambiguity problems of amplitude-only direction finding through system parameter design: Mirror blur and translation blur: These are eliminated by placing a reference signal at the edge of the observation area (e.g., -90°) and knowing its angle.

[0017] Spatial ordering fuzziness: explicitly defining the element spacing of a uniform linear array satisfy ( (for signal wavelength), rather than the traditional This fundamentally avoids frequency aliasing caused by the periodicity of the cosine function.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. Resistant to phase error interference, reducing hardware costs: This invention utilizes only the amplitude response of the array for direction finding, requiring no phase information whatsoever. This makes the system extremely robust to phase inconsistencies in the RF channel, cable length errors, and phase jitter caused by the environment. In engineering implementation, it reduces the requirements for high-precision clock synchronization and calibration hardware, making it particularly suitable for low-cost, distributed detection systems or those operating in various harsh environments.

[0019] 2. Overcoming grid limitations and significantly improving estimation accuracy: Compared to traditional "in-grid" sparse optimization methods, the off-grid model and two-step iterative correction algorithm introduced in this invention can effectively compensate for the off-grid deviation between the target's true angle and the preset grid. Simulation results show that, under the same grid density, the method of this invention can achieve a lower root mean square error (RMSE) than traditional methods, especially under high signal-to-noise ratio conditions, where the accuracy improvement is particularly significant.

[0020] 3. The algorithm exhibits good convergence and avoids local optima: The linearization approximation achieved through a high-power reference signal transforms the originally complex non-convex phase recovery problem into a convex optimization problem (sparse reconstruction). This avoids the local optimum traps common in nonlinear optimization and ensures that a globally optimal solution can be obtained when the power condition is met.

[0021] 4. The system architecture is simple and efficient, making it easy to implement in engineering projects: This invention only requires adding a single-frequency reference source (or utilizing the system's built-in transmitter) to the traditional array, without the need for a complex non-uniform array structure. Furthermore, the two-step strategy avoids the enormous computational burden caused by extremely fine meshes while maintaining accuracy, thus possessing high real-time processing potential.

[0022] 5. Completely eliminate direction-finding ambiguity: Through specific array element spacing design ( The system employs a layout strategy for reference signals to systematically eliminate the mirroring, translation, and sorting ambiguities commonly found in amplitude-only direction finding, ensuring the uniqueness and accuracy of direction finding results across the entire observation field.

[0023] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the array and reference signal layout used to eliminate direction-finding ambiguity in an embodiment of the invention. It clearly shows that the reference signal is located at the observation edge (…). ) and ULA element spacing d=λ / 4 The key geometric relationships.

[0026] Figure 2: Comparison of normalized spectra in frequency estimation between the embodiments of the present invention and existing technologies; where (a) is the estimation result of the existing on-grid method, and (b) is the estimation result of the off-grid method of the present invention. It intuitively demonstrates that the present invention, through off-grid correction, enables the estimated spectral peaks to accurately align with the true frequency position of the target, effectively eliminating errors caused by grid mismatch.

[0027] Figure 3: Comparison of root mean square error (RMSE) between the embodiments of the present invention and existing technologies at different signal-to-noise ratios (SNR); where (a) is the RMSE statistics for frequency estimation and (b) is the RMSE statistics for angle estimation. The data demonstrates the accuracy advantage of the present invention.

[0028] Figure 4 The RMSE statistics for angle estimation in this embodiment of the invention under different numbers of array elements (M) demonstrate the scalability of the algorithm.

[0029] Figure 5 The graph shows the effect of reference signal power variation on angle estimation accuracy in this embodiment of the invention. As can be seen from the graph, the error only stabilizes and converges when the power ratio is >20.

[0030] Figure 6 Flowchart of the off-grid amplitude target direction finding method provided in this embodiment of the invention.

[0031] Figure 7 : A schematic diagram of the hardware architecture of the direction finding system provided in this embodiment of the invention. Detailed Implementation

[0032] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] I. Example 1: Direction Finding Method for Off-Grid Targets Based on Linear Approximation of Array Amplitude Please see Figures 1 to 7 This embodiment provides a direction finding method for off-grid targets based on a linear approximation of array amplitude. The core of this method lies in transforming the nonlinear amplitude model into a linear model by introducing a high-power reference signal, establishing a sparse representation that includes off-grid deviations, and achieving high-precision direction finding through a two-step iterative solution.

[0034] like Figure 6 As shown, the method specifically includes the following steps: 1. Step S1: Establish the array received signal model and obtain the amplitude response. Assume the direction finding system contains a... M A uniform linear array (ULA) consisting of n elements, with an element spacing of 1. d Assume there is K A narrowband far-field signal is incident on the array at an incident angle of . Furthermore, to address the phase loss problem in amplitude-only direction finding, this invention introduces a known direction of arrival. And a high-power reference signal.

[0035] Considering the phase error of the array elements and additive noise, the first p The array receiving signal model for a single snapshot is represented as follows: in, This is the received signal vector; The phase error matrix of the array elements. The unknown phase error of the m-th array element; This is a steering matrix containing the target and reference signals, and its column vectors are steering vectors. It is a signal waveform vector; This is the noise vector for the array elements.

[0036] To eliminate the influence of phase error E, this method does not process the directly received data, but instead is based on the signal covariance matrix. Perform the operation. Squaring each element of the covariance matrix, we obtain... As can be seen, the phase error matrix E is eliminated during the modulo operation. For a uniform linear array, the first column of R is extracted as the amplitude observation vector y: in Let be the power vector of each signal. For the first The power of the incident signal.

[0037] 2. Step S2: Construct a linearized approximation model based on the reference signal. Solving the amplitude equation directly using the above method is a nonlinear problem and is difficult to solve. This step utilizes the characteristic that the reference signal power is much greater than the target signal power to perform linearization.

[0038] Let the reference signal power be The target signal power is .when When the observation vector y is expanded, ignoring the weak target signal self-crossing terms and retaining only the dominant crossing terms containing the reference signal, the following approximate linear relationship can be obtained: Where z represents the processed observation data; Δ represents the residual term (including noise and omitted self-crossing terms); and σ represents the target signal power vector to be determined.

[0039] The frequency steering matrix has column vectors. It contains information on wavelength and element spacing, and is composed of cosine functions: In the formula, variables Defined as the sinusoidal difference between the target signal and the reference signal.

[0040] 3. Step S3: Construct a sparse signal model that includes off-grid bias. In practical applications, the true angle of the target often does not fall on the preset discrete grid. If the range of the sine difference (e.g., (-2, 0)) is discretized into... G grid points Directly using a grid-based overcomplete dictionary This will introduce mesh mismatch error.

[0041] This invention performs a variable-wise analysis on the guiding vector b(f). f First-order Taylor expansion, constructing a delattice model: in, Based on grid points Constructing an overcomplete dictionary matrix; for For variables f The first-order differential matrix, whose elements correspond to b( f )right fThe result of differentiation; It is a diagonal matrix, and its diagonal elements represent the off-grid deviation between the true value and the grid point. δ ; This is the sparsely extended signal power vector.

[0042] 4. Step S4: Execute the two-step iterative estimation algorithm To reduce computational complexity and ensure global convergence for efficient solution of the above model, this invention employs a two-step strategy: ① Step 1: Rough sparse recovery (ignoring bias).

[0043] Temporarily ignore the deviation from the standard (i.e., assume) 0), Solve the following convex optimization problem to obtain the initial frequency estimate: Using FISTA (Fast Iterative Shrinking Thresholding Algorithm) or the CVX toolbox, a coarse sparse solution is obtained. The initial grid point where the target is located is determined based on the position of the non-zero elements. .

[0044] ② Second step: Iterative correction of deviation.

[0045] Based on the support set determined in the first step, the signal power and deviation are updated iteratively and alternately.

[0046] In the i In this iteration, the signal power is first updated as follows: .

[0047] Subsequently, the off-grid deviation matrix is ​​solved by minimizing the residuals. diagonal elements : Its closed-form solution is: in: Seeking Then, update the variables. The estimated value: And update the matrix accordingly. and .

[0048] Repeat the above process until convergence or the maximum number of iterations is reached (e.g.) I =10).

[0049] 5. Step S5: Output DOA estimation results Finally, based on the final estimate after convergence Combined with the known reference signal direction of arrival The direction of arrival of the target under test is calculated using the following formula. : The direction of arrival of the target is calculated using the following formula. : This formula is universal and can accurately solve for the target angle regardless of whether the reference signal is deployed at -90° or 90°.

[0050] II. Example 2: Hardware Configuration and Defuzzing Strategy of Direction Finding System This embodiment focuses on describing the hardware system architecture for implementing the above method, especially how to solve the three types of ambiguity inherent in amplitude-only direction finding (mirror ambiguity, translation ambiguity, and spatial ordering ambiguity) through hardware configuration.

[0051] 1. System Hardware Components The system includes: Uniform Linear Array (ULA): Contains M One omnidirectional receiving antenna (e.g.) M =19), used to receive space signals.

[0052] Receiver module: Used to acquire amplitude data and connected to the array, it includes an RF front-end, a downconverter, and an analog-to-digital converter (ADC). A key feature of this system is that the receiver only needs to provide the amplitude (envelope) detection output or the modulus of the digital signal; strict phase synchronization between channels is not required.

[0053] An active reference transmitter is a standalone signal source configured to transmit a single-frequency continuous wave (CW) or a signal of known waveform at a frequency that matches the center frequency of the signal under test.

[0054] Signal processing unit: A DSP or FPGA that runs the algorithm described in Example 1.

[0055] like Figure 7 As shown, the receiver module preprocesses the acquired raw data (such as calculating the covariance matrix and taking the square modulus) and outputs the amplitude observation vector y to the signal processing unit (DSP). The vector y contains the amplitude cross term information of the target signal and the reference signal, which is the basis for subsequent linearization modeling.

[0056] 2. Key Parameter Design and Defuzzing Strategy Strategy 1: Eliminate mirror blur and translation blur (refer to signal deployment) Because the amplitude response includes a cosine term There is mirror blurring of positive and negative frequencies; at the same time, the sinusoidal difference has translational uncertainty.

[0057] Implementation: The active reference transmitter is physically deployed at the edge of the array observation area, specifically at -90° or 90°. For example... Figure 1 As shown, this layout strategy utilizes the known angle of the reference signal to simultaneously eliminate mirror and translation blur. In this embodiment, the reference signal is fixed at a -90° azimuth. Since the angle of the reference signal is known and it is located at the boundary, the difference frequency sign of the target signal relative to the reference signal can be uniquely determined, thereby completely eliminating mirror and translation blur.

[0058] Strategy 2: Eliminate spatial order ambiguity (element spacing constraints) Amplitude direction finding involves taking the square of the modulus of the signal covariance, which in the frequency domain is equivalent to self-convolution of the signal spectrum, resulting in a doubling of the bandwidth of the frequency components. If the half-wavelength spacing of traditional phase direction finding is used... This will result in spatial frequency aliasing (i.e., sorting ambiguity).

[0059] Implementation method: Strictly limit the spacing between array elements. d .set up ,in λ λ is the wavelength of the incident signal.

[0060] For example, for those working at 3GH Z ( λ For a radar with an array element spacing of 0.1m, the spacing between the array elements is... d Set to 0.025m.

[0061] If the observation range is limited to [0, 90°], then d It can be appropriately relaxed to However, for observations covering the entire area [-90°, 90°], the following conditions must be met: .

[0062] Strategy 3: Ensure linearization is approximately effective (power control) Implementation method: Adjust the transmission power of the active reference transmitter so that the signal power reaching the receiving array is significantly higher than the signal power of the target under test.

[0063] Specific quantitative standard: Set the reference signal power to be at least 10 times (i.e., 10 dB difference) of the minimum target signal power expected to be received, preferably 20 to 100 times.

[0064] At this power ratio, the formula above ignores... (Objective autocorrelation terms) and retained Compared to cross-correlation terms, it is a second-order small quantity. The model error caused by linear approximation can be controlled within the algorithm's tolerance range and will not lead to direction finding failure.

[0065] Example 3: Simulation Verification and Performance Analysis To verify the effectiveness of this invention, multiple simulation experiments were conducted. The simulation parameters were set as follows: number of ULA array elements. M =19, element spacing The reference signal is located at -90° and has a power 100 times (20dB) that of the target signal. Target under test. K =2, located at -20° and 40° respectively.

[0066] 1. Frequency estimation accuracy comparison: As shown in Figure 2, the "off-grid method" of this invention is compared with the traditional "in-grid method" (Tian method).

[0067] The results show that, due to the grid resolution limitation (step size 0.05Hz), the peak value of the spectrum in the grid method deviates significantly from the true value (dashed line); while the off-grid method of the present invention, through iterative correction, accurately aligns the peak value of the spectrum with the true frequency.

[0068] 2. RMSE Performance Analysis: As shown in Figure 3, during the change of signal-to-noise ratio (SNR) from 5dB to 25dB, the RMSE of the lattice method is limited by the grid effect, exhibiting an "error plateau" that is difficult to reduce with increasing SNR. In contrast, the RMSE of the off-grid method of this invention shows a linear decreasing trend with increasing SNR, and its accuracy is significantly better than the former.

[0069] 3. Array size and robustness: such as Figure 4 As shown, with the number of array elements M As the value increased from 11 to 35, the RMSE of this method continued to decrease, indicating that the algorithm can effectively utilize the advantages of large apertures.

[0070] 4. The influence of reference signal power: such as Figure 5 As shown, the preconditions for linearization approximation are verified. When the reference signal power is low (e.g., comparable to the target power, Reference Power=1), the error is extremely large; when the power reaches more than 20 times that of the target signal, the RMSE tends to be stable and extremely low, verifying the necessity of a "high-power reference signal".

[0071] IV. Example 4: Electronic Devices and Storage Media The present invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in Embodiment 1. The electronic device may be a radar signal processing board, an embedded system, or a general-purpose computer.

[0072] In addition, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in Embodiment 1.

[0073] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

Claims

1. A method for determining the direction of an off-grid target based on a linear approximation of array amplitude, characterized in that, Includes the following steps: A direction-finding system is constructed, comprising a uniform linear array and a reference signal transmitter, wherein the reference signal transmitter is used to transmit a reference signal with a known direction of arrival, and the power of the reference signal is higher than the power of the target signal to be measured. Obtain the amplitude response data of the received signal from the uniform linear array; Based on the high-power reference signal, the nonlinear amplitude signal model of the uniform linear array is approximated as a linear observation model, which characterizes the linear relationship between the received signal amplitude and the sine difference of the incident angle of the target signal. Based on the linear observation model, an off-grid sparse signal model incorporating off-grid bias is constructed. The off-grid sparse signal model is solved using a two-step estimation method: First, sparse optimization is performed on a preset discrete coarse grid to obtain the initial position of the target; Second, based on the obtained initial position, the off-grid deviation of the target signal relative to the preset grid is calculated using an iterative optimization algorithm. Finally, the direction of arrival of the target signal is determined based on the initial grid position and the calculated grid deviation.

2. The method according to claim 1, characterized in that, The reference signal source is arranged at the edge of the observation area of ​​the uniform linear array; The approximation of the nonlinear amplitude signal model of the uniform linear array as a linear observation model based on the high-power reference signal specifically includes: Calculate the amplitude square of the received signal covariance matrix and extract its first column as the observation vector; Taking advantage of the fact that the power of the reference signal is much greater than that of the target signal, and ignoring the cross terms between the target signals, the following approximate linear relationship is constructed: Where z is the processed observation vector, Let B be the reference signal power, B be the frequency steering matrix, σ be the target signal power vector to be determined, and Δ be the residual term.

3. The method according to claim 2, characterized in that, The construction of the off-grid sparse signal model including off-grid deviation specifically includes: Perform a first-order Taylor expansion of the column vectors in the frequency steering matrix with respect to the sinusoidal difference frequency: in, For an overcomplete dictionary matrix, The matrix is ​​a differential matrix with respect to frequency. It is a diagonal matrix that includes off-grid deviations. This is the sparse signal power vector.

4. The method according to claim 3, characterized in that, The first step is coarse sparse recovery: Ignoring off-grid deviations, the initial sparse signal power vector is obtained by solving the following convex optimization problem. : in, This is the regularization parameter.

5. The method according to claim 4, characterized in that, The second step calculates the deviation from the standard using an iterative optimization algorithm, specifically including: In the In this iteration, a matrix is ​​constructed based on the current frequency estimate. and And based on the signal power estimated in the previous round The diagonal elements of the deviation matrix are solved by minimizing the residuals. ; Based on the obtained Update frequency estimate: ; Repeat the above steps until the convergence condition is met or the preset maximum number of iterations is reached; The convergence condition includes the root mean square error of the frequency estimation being lower than a preset threshold.

6. The method according to claim 1, characterized in that, The element spacing of the uniform linear array satisfy ,in The wavelength of the reference signal is used to eliminate spatial order ambiguity; the direction of arrival of the reference signal is known and located at the edge of the observation area.

7. The method according to claim 1, characterized in that, The power of the reference signal is at least 10 times that of the target signal to be measured, to ensure that the unknown target signal self-crossing term in the nonlinear amplitude signal model can be ignored.

8. A direction-finding system for off-grid amplitude targets based on a linear sparse frame, characterized in that, include: Uniform linear array, used to receive spatial signals; A reference signal transmitting module transmits a high-power single-frequency reference signal, and the reference signal transmitting module is deployed at a preset angle position of the uniform linear array; The receiver module is used to acquire the amplitude information output by the uniform linear array; A signal processing module is configured to perform the steps of the method as described in any one of claims 1 to 7, and to calculate and output the direction of arrival of the target signal.

9. The system according to claim 8, characterized in that, The reference signal transmission module is an active transmitter built into the system, and the transmission frequency of the reference signal is consistent with the center frequency of the target signal.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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