Low-altitude target DOA tracking estimation method in impulse noise environment

Abstract

The invention discloses a low-altitude target DOA tracking estimation method in an impulse noise environment, and relates to the technical field of target tracking. Firstly, for the defects of a traditional correlation entropy method in the aspects of continuous similar amplitude noise suppression, fixed kernel width limitation, single kernel function adaptability and the like, a weighted mixed multiple correlation entropy function is provided, and the adaptive capacity of an algorithm to a complex noise environment is remarkably improved through a mixed Gaussian kernel and introduction of a dynamic weighting mechanism. And secondly, a cost function based on a WMMCC criterion is constructed, a weighted mixed maximum multiple correlation entropy criterion is combined with a PAST algorithm framework, and real-time joint estimation of the pitch angle and the azimuth angle is realized. The invention provides an effective technical solution for LSS target detection in the field of low-altitude security and protection, and has important theoretical value and engineering application prospect.

Description

Technical Field

[0001] This invention relates to the field of target tracking technology, and more specifically, to a method for estimating the DOA (Direct Oscillation of Atmosphere) of low-altitude targets under impulse noise conditions. Background Technology

[0002] With the increasing penetration of low-small-slow (LSS) targets, such as drone aerial surveying, balloon weather detection, and kite flying for recreational purposes, into civilian and commercial fields, the resulting security threats are becoming increasingly severe. Incidents of drone intrusions over airport runways causing flight delays and balloons carrying equipment illegally monitoring sensitive areas are commonplace, posing significant challenges to low-altitude airspace security systems. Due to their low flight altitude, small radar cross-section (RCS), and slow speed, LSS targets are easily obscured by strong ground clutter during detection. Furthermore, their weak echo signals result in low signal-to-noise ratio (SNR). In addition, when the target is in the near-field region of the array, the spherical wavefront effect breaks the traditional far-field plane wave assumption, causing the signal to exhibit non-stationary characteristics, further increasing the difficulty of target detection and parameter estimation, and seriously hindering the technological development of low-altitude security.

[0003] Detecting low-altitude, slow-moving, small targets in low-altitude environments is a significant challenge in radar signal processing. Direction of Arrival (DOA) estimation is a fundamental problem. Over the past few decades, high-resolution subspace-based methods, such as Multiple Signal Classification (MUSIC), rotation-invariant methods, and Weighted Subspace Fitting (WSF), have been developed for DOA estimation. A prerequisite for using these subspace-based methods is the reliable extraction of the signal or noise subspace from array observations. In stationary environments, the signal and noise subspaces can be estimated using eigenvalue decomposition (EVD) of the covariance matrix or singular value decomposition (SVD) of the data matrix. However, in non-stationary environments, continuous updates to the subspace are required. This leads to repetitive EVD / SVD operations, resulting in high computational costs. To address this issue, computationally inefficient subspace tracking algorithms have been proposed, such as Projection Approximation Subspace Tracking (PAST), Projection Approximation Subspace Tracking with Shrinkage, Orthogonal Projection Approximation Subspace Tracking, and Fast Approximation Power Iteration. These algorithms can achieve continuous estimation of the principal subspace even in Gaussian noise environments.

[0004] However, impulse noise is prevalent in natural environments. For example, radar clutter and electromagnetic noise in mobile radio channels exhibit short-duration impulse characteristics in the time domain. These noises are typically sudden and high-amplitude, posing a significant challenge to signal processing. In low-altitude environments, the impulse nature of noise is particularly pronounced, with larger pulse amplitudes and shorter durations, making low-altitude target detection even more challenging, especially under conditions of low signal-to-noise ratio and strong ground clutter interference. The Projection Approximate Subspace Tracking (PAST) algorithm is a classic subspace tracking algorithm based on Recursive Least Squares (RLS). RLS is highly sensitive to impulse noise, causing the performance of the PAST algorithm to degrade sharply in impulse noise environments.

[0005] In recent years, correlation entropy, as a novel measure of local similarity of random variables, has attracted widespread attention. Some scholars have proposed the Maximum Correlation Criterion (MCC), which, unlike the traditional MSE criterion, demonstrates adaptability to impulse noise environments. Researchers have applied the MCC criterion to channel blind equalization, time delay estimation, and DOA estimation under impulse noise environments, and simulation experiments have shown the adaptability of these algorithms to such environments. Although traditional single-kernel correlation entropy exhibits good robustness in non-Gaussian noise environments, its performance is highly dependent on the choice of kernel width—a narrow kernel width can suppress strong impulse noise but is sensitive to Gaussian noise; a wide kernel width adapts to Gaussian noise but weakens the ability to suppress outliers. Furthermore, a single kernel function struggles to simultaneously handle the complex noise mixture scenarios in low-altitude detection, making it difficult to balance heavy-tail noise suppression with signal detail preservation. Summary of the Invention

[0006] To address the shortcomings of traditional correlation entropy methods in suppressing continuous similar amplitude noise, fixed kernel width limitations, and the adaptability of single kernel functions, this invention provides a low-altitude target DOA tracking estimation method under impulse noise environments. A weighted hybrid complex correlation entropy function is proposed, and by mixing kernel functions and introducing a weighting mechanism, the algorithm's ability to suppress impulse noise is significantly improved. The objective function based on the weighted hybrid maximum complex correlation entropy criterion is constructed to modify the MSE criterion-based objective function in the PAST algorithm, deriving a resilient projection approximation subspace tracking algorithm suitable for impulse noise environments.

[0007] The technical means employed in this invention are as follows: A method for tracking and estimating the DOA of low-altitude targets under impulse noise conditions, applied to a uniform linear array, includes the following steps: Obtain the signal input vector and signal estimation vector, and initialize the signal subspace matrix; A cost function for iteratively estimating the signal subspace is constructed based on the weighted maximum mixed complex correlation entropy. The cost function is as follows:

[0008] in, , Represents the signal input vector. Represents the signal subspace matrix. Represents the signal estimation vector. i Indicates an index variable; , , Indicates the kernel width. Forgetting factor, Indicates the sampling point. Indicates the number of sampling points. Indicates conjugate transpose; The cost function is solved using a projection approximation subspace tracking algorithm based on the WMMCC criterion, and then the signal subspace matrix is ​​updated. ; From the updated signal subspace matrix Extracting the noise subspace matrix ; Construct a multi-signal classification spatial spectrum and search for peaks. The multi-signal classification spatial spectrum is as follows:

[0009] in, It is a direction vector; Obtain the spatial spectrum peaks corresponding to multi-signal classification This is the estimated direction of arrival.

[0010] Furthermore, a projection approximation subspace tracking algorithm based on the WMMCC criterion is employed to solve the cost function, including iteratively updating the signal subspace matrix according to the following algorithm. : Initialize random orthogonal matrix and , usually take , Denotes an r-order identity matrix, for each time... Perform the following iterative update calculations:

[0011] in, Represents the gain vector. Represents the inverse correlation matrix. Let t represent the residual, where t > 1.

[0012] Furthermore, from the updated signal subspace matrix Extracting the noise subspace matrix The calculation formula is:

[0013] in, Let represent the noise subspace matrix, and I represent the identity matrix.

[0014] Compared with the prior art, the present invention has the following advantages: This application proposes a low-altitude target tracking and estimation method based on an improved WMMCC-PAST algorithm. Firstly, it innovatively proposes a weighted hybrid complex correlation entropy function, significantly improving the algorithm's ability to suppress complex noise through a hybrid kernel function and the introduction of a weighting mechanism. Secondly, it constructs an objective function based on the weighted hybrid maximum complex correlation entropy criterion to modify the objective function based on the MSE criterion in the PAST algorithm, and derives a new resilient projection approximation subspace tracking algorithm suitable for impulse noise environments. This algorithm can be applied to target parameter tracking and estimation in low-altitude environments, and can simultaneously achieve joint estimation of the pitch and azimuth angles of near-field, low-altitude, slow-moving, and small targets.

[0015] This application proves the boundedness of the weighted mixed complex correlation entropy through theoretical derivation, further demonstrates the convergence of the algorithm iteration, analyzes the robustness of the algorithm in complex electromagnetic environments, and confirms its adaptability to low signal-to-noise ratio and near-field non-stationary signals, providing theoretical support for practical applications.

[0016] Simulation experiments show that the proposed method has better subspace tracking performance, especially better adaptability to complex noisy environments. Attached Figure Description

[0017] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a low-altitude target DOA tracking and estimation method under impulse noise environment according to an embodiment of the present invention.

[0019] Figure 2(a) is a schematic diagram of the subspace tracking estimation results using the PAST method in an embodiment of the present invention.

[0020] Figure 2(b) is a schematic diagram of the subspace tracking estimation results using the PFLOM-PAST method in an embodiment of the present invention.

[0021] Figure 2(c) is a schematic diagram of the subspace tracking estimation results using the MCC PAST method in an embodiment of the present invention.

[0022] Figure 2(d) is a schematic diagram of the subspace tracking estimation results using the WMMCC-PAST method in an embodiment of the present invention.

[0023] Figure 3(a) is a schematic diagram comparing the root mean square error of parameter estimation in the embodiments of the present invention.

[0024] Figure 3(b) is a schematic diagram comparing the estimation results of the principal direction angle in the embodiment of the present invention.

[0025] Figure 4 This is a schematic diagram illustrating the relationship between parameter estimation performance and noise characteristic index in an embodiment of the present invention.

[0026] Figure 5 This is a schematic diagram illustrating the relationship between parameter estimation performance and GSNR in an embodiment of the present invention.

[0027] Figure 6 This is a schematic diagram of the target tracking trajectory estimation result in an embodiment of the present invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0029] like Figure 1 As shown, the present invention provides a method for tracking and estimating the DOA of low-altitude targets under impulse noise conditions, which is applied to a uniform linear array and includes the following steps.

[0030] S1. Obtain the signal input vector and signal estimation vector, and initialize the signal subspace matrix. The signal subspace matrix is ​​a random orthogonal matrix.

[0031] S2. Construct a cost function for iterative estimation of the signal subspace based on the weighted maximum mixed complex correlation entropy.

[0032] Complex correlation entropy extends correlation entropy theory to the complex domain. This extension maintains its applicability to real signals while also enabling the processing of complex signals. Complex signals are frequently encountered in practical applications such as communications. Here, two complex variables... C 1 and C The complex correlation entropy of 2 is defined as (1) in and It is a complex random variable. It is a kernel function. σ This represents the kernel width. If the kernel function chosen is a complex Gaussian kernel, then the corresponding complex correlation entropy expression is: (2) It can be seen from formula (2) that when or When the noise is a large impulse, the difference between the two is significant and lies on the negative exponential term of the Gaussian function, resulting in a very small correlation entropy value. This is why correlation entropy can suppress impulse noise. However, when... and When both are impulse noise and their amplitudes are approximately the same, the difference between them is very small, resulting in a large correlation entropy value. An excessively large function value can affect the measurement of signal similarity. Therefore, traditional correlation entropy has the problem of failing to suppress continuous impulses with approximately the same amplitude.

[0033] In practical applications, due to the randomness and unmeasurability of impulse noise, a single correlation entropy kernel function is insufficient. Therefore, a more flexible hybrid correlation entropy function is constructed to handle data under different noise levels. The corresponding expression for the hybrid complex correlation entropy is as follows: (3) in and It is the complex Gaussian kernel function as shown in equation (2), with parameters , express The proportion. From the formula for the entropy of mixed complex correlation, it can be derived that when the parameter... or hour, It degenerates into the maximum complex correlation entropy of a single core.

[0034] As can be seen from formula (3), when large-amplitude impulse noise occurs, the value of the mixed correlation entropy function is very small, which can effectively suppress the impulse noise. However, the mixed correlation entropy function, like the traditional correlation entropy, has the problem of not being able to suppress continuous similar amplitude noise. To solve this problem, we improve the mixed entropy function and propose a weighted mixed complex correlation entropy function. (4) in Indicates the kernel width.

[0035] From formula (4), it can be seen that regardless of or Is it large-amplitude impulse noise or... and When both are large-amplitude impulse noises with similar amplitudes, a weighting term is always included. Therefore, the WMCC function can effectively suppress impulse noise and solve the problem that correlation entropy and mixed entropy cannot suppress continuous similar large-amplitude noise, making it a more robust noise suppression method.

[0036] In practical applications, the joint distribution function of two random variables is usually unknown and needs to be estimated using a finite number of samples. In this case, the discrete expression is: (5) in .

[0037] To improve the subspace tracking performance of the PAST algorithm in low-altitude complex noise environments, this paper proposes an improved cost function based on the weighted maximum mixed complex correlation entropy (WMMCC) criterion. The cost function based on WMMCC is: (6) in, , Represents the signal input vector. Represents the signal subspace matrix. Represents the signal estimation vector. i Indicates an index variable; , , Indicates the kernel width. Forgetting factor, Indicates the sampling point. Indicates the number of sampling points. This indicates the conjugate transpose.

[0038] S3. Using a projection approximation subspace tracking algorithm based on the WMMCC criterion, solve the cost function and then update the signal subspace matrix. .

[0039] Specifically, existing technologies include a Projection Approximate Subspace Tracking (PAST) algorithm based on least squares estimation (RLS). The PAST algorithm estimates the signal subspace by minimizing the following cost function. (7) Among them The basis matrix of the signal subspace. Forgetting factor; Let be the approximate projection vector. To obtain the vector that minimizes equation (7), Taking the derivative of this derivative and setting it to zero, we get ,in , .right By applying the matrix inversion theorem, a projection approximate subspace tracking algorithm based on least squares estimation (RLS) can be obtained.

[0040] RLS algorithm for It is highly sensitive to stable distributed impulse noise. This is because The formula is actually an approximation of the projected vector. and observation vector cross-correlation matrix The estimate, and It is actually an approximation of the projection vector. autocorrelation matrix The estimate, due to It is the observation vector A linear combination of the observed vectors exist Under a stable noise distribution environment, it obeys Stable distribution, therefore It is also obedience Stable distribution. As introduced above. Stable distribution ( Since the matrix does not possess the property of having finite second moments, the estimated matrix... and The elements in are affected by The impact of stable distributed impulse noise is much greater than the true value, thus affecting the PAST algorithm. Performance will degrade under stable noise conditions.

[0041] Based on the Wirtinger derivative, for about To find the gradient, applying the chain rule, we can obtain... (8) in, The gradient of the magnitude-weighted term is expressed as: (9) make , combined The expression, formula (8). It can be written as (10) Because of formula (9) It is nonlinear and complex, and usually uses a fixed-point approximation in a single-step iteration. Change Smaller, therefore, use calculate , Treat it as a constant, because This item serves to further constrain... growth, but through Amplitude weighting term in It has already been implicitly suppressed. Therefore, the magnitude weighting term... The gradient can be ignored; its effect is entirely through the weights. reflect.

[0042] Therefore, the approximate gradient is: (11) in: . Since the cost function based on WMMCC contains exponential terms, direct differentiation leads to complex nonlinear equations that cannot be solved analytically. This paper employs the concept of local linearization, adjusting the robustness of WMMCC through weights in each iteration. Injected into the least squares framework.

[0043] To solve analytically This paper constructs a "weighted least squares" function, whose gradient is consistent with the gradient formula (11) of WMMCC, and then defines: (12) right Its gradient can be obtained as follows: Setting the gradient to zero, we obtain the weighted normal equation: (13) At this point, a weighted correlation matrix can be defined. and They are respectively and Therefore, the optimal solution is .

[0044] For the weighted correlation matrix and The recursive update yields the following: (14) (15) For the inverse correlation matrix The update, firstly for The expression, applied using Woodbury's identity, yields: (16) After simplification, it becomes the inverse correlation matrix. The update formula is (17) Generalized gain The expression is (18) but . Therefore, based on the above formula, the projection approximation subspace tracking algorithm (WMMCC-PAST algorithm) based on the WMMCC criterion can be obtained as follows: Step 1. Initialize a random orthogonal matrix and ( (in decimals) Step 2. For each time period Iterative update calculation:

[0045] S4. From the updated signal subspace matrix Extracting the noise subspace matrix .

[0046] S5. Construct a multi-signal classification spatial spectrum and search for peak values, wherein the multi-signal classification spatial spectrum is...

[0047]

[0048] in, It is a direction vector. It obtains the spectral peaks corresponding to the spatial spectrum of multi-signal classification. This is the estimated direction of arrival.

[0049] The effects of the present invention will be further illustrated below through specific application examples.

[0050] This application example studies the target parameter tracking and estimation problem under non-stationary conditions. The performance of various PAST algorithms is evaluated using a time-varying direction-of-arrival (DOA) estimation problem. It is assumed that a uniform linear array of 9 elements is formed, with an element spacing of half a wavelength, and 3 independent narrowband plane wave incident sources with arrival direction angles of [missing information]. , and The incident signal s(t) is set as a QPSK (quad phase shift keying) signal. Simulation experiments have shown that, under impulse noise conditions, the subspace tracking performance based on the MCC-PAST algorithm is comprehensively superior to the traditional M-estimation-based RLM-PAST. Due to space limitations, this paper presents experimental simulations and comparisons of the PAST, PLOM-PAST, and MCC-PAST algorithms.

[0051] Experiment 1: Tracking results of a one-dimensional angle.

[0052] The additive noise in the array output signal vector is set to an Alpha stable distribution. Considering that fractional low-order stable random variables do not have finite second moments, the generalized signal-to-noise ratio (GSNR) is defined as... ,in Indicates signal power. yes The coefficient of dispersion of the distribution. In this experiment, the noise characteristic index is taken as... and The number of data points was set to 1000. The experiment simulated the time-varying incoming wave direction angles of three targets. Group 1: linearly changing from 20° to 40° with time t; Group 2: linearly changing from 40° to 20° with time t; Group 3: fixed at 10°. The simulation results of the four algorithms under the incoming wave direction angle conditions are given in Figures 2(a)-2(d). The three subgraphs distributed from top to bottom in the figures represent the estimated value of the algorithm's signal subspace tracking during the iteration process, the intensity of the iteration error vector, and the relationship between the true value of the signal subspace and the algorithm's estimated value. Figures 2(a)-2(d) show that both MCC-PAST and the algorithm presented in this paper can achieve good tracking estimation.

[0053] To further evaluate their real-time performance in target parameter estimation, this application quantitatively compares the four algorithms based on two key metrics, as shown in Figure 3(a) and Figure 3(b). Figure 3(a) shows the average root mean square error (RMSE) of the angle estimation for the three targets, and Figure 3(b) shows the accuracy of the principal direction estimation.

[0054] As shown in Figures 3(a) and 3(b), the estimation performance of the MCC-PAST and WMMCC-PAST methods is significantly better than other algorithms. MCC-PAST uses a single kernel function, which is not flexible enough when dealing with multi-source noise or complex signals. It employs a fixed complex maximum correlation entropy criterion, assigning the same weight to all data points, which may not fully utilize the dynamic characteristics of the data in some cases. WMMCC-PAST, by introducing a weighting mechanism and a hybrid kernel function, is better able to adapt to complex noise environments. This weighting mechanism can dynamically adjust the weights according to the characteristics of the signal, thereby more effectively suppressing noise and making the algorithm more flexible and efficient when dealing with non-stationary signals. Therefore, the performance of the WMMCC-PAST algorithm is superior to that of the MCC-PAST algorithm.

[0055] Experiment 2 shows the relationship between noise characteristic index and generalized signal-to-noise ratio.

[0056] This experiment discusses the relationship between the performance of the WMMCC-PAST and MCC-PAST algorithms and the characteristic exponent of impulse noise and the generalized signal-to-noise ratio. In this experiment, 200 Monte Carlo experiments were performed for each algorithm, and the root mean square error of the estimated direction angle of arrival for three targets corresponding to the two algorithms was calculated. Figure 4 When The characteristic index of stable distributed impulse noise is The average estimation error when using the two algorithms described above to track changes in the incident angle under different generalized signal-to-noise ratios is calculated. Figure 5 The following is given when the generalized signal-to-noise ratio is At different characteristic indices In a stable distributed noise environment, two algorithms were used to track the root mean square error when the wave angle changes. The results are as follows: Figure 4 and Figure 5 As shown. Observation Figure 4 and Figure 5 We can draw the same experimental conclusions as in Experiment 1.

[0057] Experiment 3: Tracking estimation results of two-dimensional angles.

[0058] When the target is in the near-field region of the array, its radiated wavefront exhibits significant spherical wave characteristics. This phenomenon breaks the traditional DOA estimation model under the far-field plane wave assumption, making it necessary to accurately describe the target's spatial positioning through a joint representation of elevation and azimuth angles. In this section's experiment, the subspace tracking results obtained by the algorithm are combined with the two-dimensional ESPRIT algorithm to obtain estimates of the target's elevation and azimuth angles, and the target's estimated tracking trajectory is displayed in a three-dimensional graph, such as... Figure 6 As shown. The experimental parameters for this section are set as follows: the motion trajectories are designed as follows: Target 1: azimuth 20°→40°, pitch 30°→50° (linear change); Target 2: azimuth 40°→20°, pitch 40°→60° (opposite phase change); Target 3: azimuth fixed at 10°, pitch 10°→30° (linear change). From Figure 6 It can be seen that the WMMCC-PAST algorithm proposed in this application has better tracking and estimation performance than the MCC algorithm.

[0059] To address the problem of tracking low-altitude, slow, and small targets in complex low-altitude noise environments, this application proposes a low-altitude target tracking estimation method based on an improved WMMCC-PAST algorithm. First, a weighted hybrid complex correlation entropy function is innovatively proposed. By mixing kernel functions and introducing a weighting mechanism, the algorithm's ability to suppress complex noise is significantly improved. The objective function based on the weighted hybrid maximum complex correlation entropy criterion is constructed to modify the objective function based on the MSE criterion in the PAST algorithm. A new resilient projection approximation subspace tracking algorithm suitable for impulse noise environments is derived, which can be applied to target parameter tracking estimation in low-altitude environments and can simultaneously estimate the pitch and azimuth angles of near-field low-altitude, slow, and small targets. Furthermore, to evaluate the algorithm's performance, this paper conducts a theoretical analysis: the boundedness of the weighted hybrid complex correlation entropy is proven through theoretical derivation; the convergence of the algorithm's iterations is further demonstrated; the robustness of the algorithm in complex electromagnetic environments is analyzed; and its adaptability to low signal-to-noise ratio and near-field non-stationary signals is confirmed, providing theoretical support for practical applications. Simulation results show that the proposed WMMCC-PAST algorithm has better subspace tracking performance, especially in complex noisy environments.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for tracking and estimating the DOA of low-altitude targets under impulse noise conditions, applied to a uniform linear array, characterized in that, Includes the following steps: Obtain the signal input vector and signal estimation vector, and initialize the signal subspace matrix; A cost function for iteratively estimating the signal subspace is constructed based on the weighted maximum mixed complex correlation entropy. The cost function is as follows: in, , Represents the signal input vector. Represents the signal subspace matrix. Represents the signal estimation vector. i Indicates an index variable; , , Indicates the kernel width. Forgetting factor, Indicates the sampling point. Indicates the number of sampling points. Indicates conjugate transpose; The cost function is solved using a projection approximation subspace tracking algorithm based on the WMMCC criterion, and then the signal subspace matrix is ​​updated. ; From the updated signal subspace matrix Extracting the noise subspace matrix ; Construct a multi-signal classification spatial spectrum and search for peaks. The multi-signal classification spatial spectrum is as follows: in, It is a direction vector; Obtain the spatial spectrum peaks corresponding to multi-signal classification This is the estimated direction of arrival.

2. The method for tracking and estimating the DOA of low-altitude targets under impulse noise environment according to claim 1, characterized in that, The cost function is solved using a projection approximation subspace tracking algorithm based on the WMMCC criterion, including iteratively updating the signal subspace matrix according to the following algorithm. : Initialize random orthogonal matrix and , usually take , Denotes an r-order identity matrix, for each time... Perform the following iterative update calculations: in, Represents the gain vector. Represents the inverse correlation matrix. Let t represent the residual, where t >

1.

3. The method for estimating the DOA of a low-altitude target under impulse noise environment according to claim 1, characterized in that, From the updated signal subspace matrix Extracting the noise subspace matrix The calculation formula is: in, Let represent the noise subspace matrix, and I represent the identity matrix.

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