Two-dimensional super-resolution direction finding method based on AR-MVDR algorithm

Abstract

The application discloses a two-dimensional super-resolution angle measurement method based on an AR-MVDR algorithm, which comprises the following steps: receiving a first signal through a digital phased array antenna; wherein the first signal is formed by target signals emitted by signal sources from multiple different directions; performing amplitude and phase estimation on sampling points of the first signal based on an AR algorithm; and accurately estimating the amplitude estimated by the AR algorithm through an MVDR algorithm to obtain the angle of arrival of the target signal. The application can simultaneously detect multiple target response signals at any position within the range of the array antenna, and can obtain accurate time, position and amplitude estimation. Compared with the process of time domain correlation peak pulse detection, pulse deinterleaving and monopulse angle measurement, the application simplifies the angle measurement process under the condition of multiple target signal interleaving, has better anti-interference capability, and has a relatively simple algorithm, low FPGA resource consumption and easy engineering transformation.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a two-dimensional super-resolution angle measurement method based on the AR-MVDR algorithm. Background Technology

[0002] For the problem of aerial multi-target identification, the resolution capability of the identification system directly affects the accuracy of the identification result. Some identification system platforms improve the overall azimuth pointing accuracy and azimuth resolution by adding a single-pulse processing function with azimuth angle measurement capability. However, single-pulse angle measurement can only effectively handle the problem of identifying multiple targets in the same distance loop in a single dimension. Two-dimensional super-resolution signal detection and estimation technology can make full use of the multi-dimensional information of the raw data, exceed the conventional resolution limitations, and overcome the difficulties in multi-target identification and resolution.

[0003] Therefore, researching super-resolution angle measurement technology to improve the accuracy of multi-target recognition is of great theoretical and practical significance for reducing the impact of the airframe environment on angle measurement errors and for recognizing clustered targets.

[0004] Digital phased array antennas employing traditional digital beamforming technology typically require processing steps such as time-domain correlation peak pulse detection, pulse deinterleaving, and single-pulse angle measurement when dealing with interleaved multi-target signals. This algorithm is complex, and its performance in terms of signal detection probability, angle measurement accuracy, and azimuth resolution is generally poor. DOA estimation algorithms such as FFT (Fast Fourier Transform), MUSIC (Multiple Signal Classification), and AR (Autoregressive Model) can quickly calculate the spatial spectrum of a signal to obtain its direction of arrival (DOA). However, the FFT algorithm has weak target azimuth resolution and is only suitable for simple applications with sparse targets. While the MUSIC algorithm offers high resolution, its implementation in engineering suffers from difficulties in porting singular value decomposition and source number estimation, and may also face challenges due to insufficient FPGA resources. The AR algorithm approaches the resolution performance of the MUSIC algorithm, but with lower computational complexity, easier portability, and lower resource consumption. Subsequently, by combining MVDR (Minimum variance Distortionless Response) adaptive beamforming technology, the accuracy of signal amplitude estimation is improved and false detection results are reduced. Summary of the Invention

[0005] In view of this, the present invention provides a two-dimensional super-resolution angle measurement method based on the AR-MVDR algorithm, which solves the above-mentioned technical problems.

[0006] A two-dimensional super-resolution angle measurement method based on the AR-MVDR algorithm includes:

[0007] A first signal is received via a digital phased array antenna; wherein the first signal is composed of target signals superimposed from multiple signal sources in different directions;

[0008] Based on the AR algorithm, amplitude and phase estimation are performed on the sampling points of the first signal;

[0009] The angle of arrival of the target signal is obtained by accurately estimating the amplitude estimated by the AR algorithm using the MVDR algorithm.

[0010] Furthermore, the digital phased array antenna includes N receiving elements for receiving the first signal; wherein N is greater than or equal to 2; there are a total of M target signals, where M is a positive integer greater than 1 and less than or equal to N / 2-1.

[0011] Furthermore, the amplitude and phase estimation of the sampling points of the first signal based on the AR algorithm includes:

[0012] Obtain the input for the AR algorithm;

[0013] Based on the input of the AR algorithm, estimate the covariance matrix;

[0014] Calculate the AR coefficients based on the covariance matrix;

[0015] Based on the AR coefficients, the phase and amplitude of the possible signals are estimated.

[0016] Furthermore, obtaining the input to the AR algorithm includes:

[0017] The first signal received by the N-element digital phased array antenna is sampled once using a fast-sampling method.

[0018] The preprocessed amplitude and phase are used as the complex vector input of the AR algorithm; the preprocessing includes digital down-conversion and filtering.

[0019] Furthermore, the estimation of the covariance matrix based on the AR algorithm input includes:

[0020] Calculate the (N / 2)×(N / 2) dimensional forward matrix corresponding to the complex vector using a sliding window method:

[0021]

[0022] Among them, A f Let x be the forward matrix. i Let i be the i-th element of the complex vector input. For x i The conjugate of , where N is the number of sampling points; the complex vector is X = [x1, x2, ..., x...]. N ] T x iThis represents the amplitude and phase sampling point of the i-th element antenna;

[0023] Calculate the backward matrix of a complex vector:

[0024] Rearrange the elements of the forward matrix to obtain the backward matrix A. b :

[0025]

[0026] Among them, A b Let a be a backward matrix. f (i,j) represents the element in the i-th row and j-th column of the forward matrix; i = 1, 2, ..., N / 2; j = 1, 2, ..., N / 2;

[0027] Calculate the covariance matrix based on the calculated forward and backward matrices:

[0028] A=(A f +A b )

[0029] Where A is the covariance matrix of a complex vector.

[0030] Further, the calculation of AR coefficients based on the covariance matrix includes:

[0031] Solving for AR coefficients using the Yule-Walker equation:

[0032]

[0033] Among them, a1, a2, ..., a N / 2-1 These are the AR coefficients we are looking for. It is the variance of the observed values ​​of the independent variable.

[0034] Furthermore, estimating the phase and amplitude of the possible signal based on the AR coefficient includes:

[0035] Establish the following equation:

[0036] 1+a1x+a2x 2 +...+a N / 2-1 x N / 2-1 =0

[0037] The phases corresponding to the N / 2-1 roots obtained by solving are the normalized frequencies of the possible signals, and the corresponding magnitudes are the corresponding amplitudes.

[0038]

[0039] Where, φ k Let m be the phase of the k-th root. kLet be the amplitude of the k-th root, where k = 1, 2, ..., N / 2-1.

[0040] Further, the step of accurately estimating the amplitude estimated by the AR algorithm using the MVDR algorithm to obtain the angle of arrival of the target signal includes:

[0041] Based on the calculated phase, the calculated amplitude is estimated using the MVDR algorithm;

[0042] From the estimated amplitudes, the M signals with the largest amplitudes are selected as the target signals to be detected;

[0043] The phase corresponding to each target signal to be detected is determined as the angle at which it reaches the digital phased array antenna.

[0044] Further, the step of estimating the calculated amplitude using the MVDR algorithm based on the calculated phase includes:

[0045] The MVDR algorithm reduces the amplitude estimation error based on the frequency estimate obtained from the AR algorithm.

[0046]

[0047]

[0048] Where, p k For the magnitude estimation of the MVDR algorithm, φ k For phase, a(φ) k ) is φ k The corresponding AR coefficient, a H (φ k ) is a(φ k The conjugate transpose of ).

[0049] Further, determining the phase corresponding to each target signal to be detected as its angle of arrival at the digital phased array antenna includes:

[0050] The phases of each target signal to be detected are sequentially converted into their angles of arrival using the following formula:

[0051]

[0052] Where θ is the angle at which the target signal arrives at the digital phased array antenna. d is the antenna array element spacing, and λ is the source wavelength.

[0053] Because of the adoption of the above technical solution, the present invention has the following advantages:

[0054] (1) The super-resolution angle measurement technology based on AR-MVDR algorithm proposed in this invention can simultaneously detect the first signals of multiple targets (including targets in the same distance loop) in any direction within the range of the array antenna, and can obtain accurate time, azimuth and amplitude estimates.

[0055] (2) The super-resolution angle measurement technology based on AR-MVDR algorithm proposed in this invention can achieve the identification of small signals and has high accuracy in detecting orientation compared with the single pulse angle measurement technology.

[0056] (3) The super-resolution angle measurement technology based on AR-MVDR algorithm proposed in this invention simplifies the angle measurement process under multi-target signal interleaving conditions compared with the process of time-domain correlation peak pulse detection, pulse deinterleaving and single pulse angle measurement.

[0057] (4) The super-resolution angle measurement technology based on AR-MVDR algorithm proposed in this invention has better anti-interference ability, and the algorithm is relatively simple, consumes less FPGA resources, and is easy to transform into engineering. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0059] Figure 1 This is a flowchart illustrating a two-dimensional super-resolution angle measurement method based on the AR-MVDR algorithm according to an embodiment of the present invention.

[0060] Figure 2(a) is a schematic diagram of AR time-spatial spectrum estimation according to an embodiment of the present invention;

[0061] Figure 2(b) is a schematic diagram of a time-orientation relationship between two targets according to an embodiment of the present invention;

[0062] Figure 2(c) is a schematic diagram of a two-target time-amplitude relationship according to an embodiment of the present invention. Detailed Implementation

[0063] The present invention will be further described in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0064] To achieve accurate identification of multiple targets in the air and improve the detection and recognition accuracy of the system, this invention first uses an AR-based super-resolution algorithm to estimate the amplitude and azimuth of the interleaved response signals. Subsequently, the MVDR algorithm is used to accurately estimate the amplitude of the azimuth signal detected by the AR algorithm, compensating for the inaccuracy of pulse amplitude estimation in the AR algorithm. This invention employs multi-dimensional signal processing technology combining spatial and temporal domains, fully leveraging the advantages of digital array hardware to replace the original pulse detection, signal deinterleaving, and angle measurement processing. This simplifies the multi-target recognition function, improves signal resolution performance, and thus enhances the accuracy of multi-target recognition while reducing the false alarm probability.

[0065] See Figure 1 This invention provides an embodiment of a two-dimensional super-resolution angle measurement method based on the AR-MVDR algorithm, which includes:

[0066] S1. Receive the first signal through a digital phased array antenna; wherein the first signal is composed of target signals superimposed from multiple signal sources in different directions.

[0067] In this embodiment, the digital phased array antenna includes N (N is greater than or equal to 2) receiving array elements for receiving the first signal; there are M target signals in total, where M is a positive integer greater than 1 and less than or equal to (N / 2-1).

[0068] S2. Based on the AR algorithm, the amplitude and phase of the sampling points of the first signal are estimated.

[0069] In this embodiment, based on the AR algorithm, amplitude and phase estimation is performed on the sampling points of the first signal, including:

[0070] Obtain the input for the AR algorithm;

[0071] Based on the input of the AR algorithm, estimate the covariance matrix;

[0072] Calculate the AR coefficients based on the covariance matrix;

[0073] The AR coefficients can be solved using the Yule-Walker equation, the Levinson-Durbin recursive algorithm, or the least squares method.

[0074] Based on the AR coefficients, the phase and amplitude of the possible signals are estimated.

[0075] In this embodiment, obtaining the input to the AR algorithm includes:

[0076] The first signal received by the eight-element digital phased array antenna is sampled once using a fast-sampling method.

[0077] The preprocessed amplitude and phase sampling points are used as the complex vector input of the AR algorithm; the preprocessing includes digital down-conversion and filtering.

[0078] In this embodiment, the covariance matrix is ​​estimated based on the input of the AR algorithm, including:

[0079] Calculate the (N / 2)×(N / 2) dimensional forward matrix corresponding to the complex vector using a sliding window method:

[0080]

[0081] Among them, A f Let x be the forward matrix. i Let i be the i-th element of the complex vector input. For x i The conjugate of , where N is the number of sampling points; the complex vector is X = [x1, x2, ..., x...]. N ] T x i This represents the amplitude and phase sampling point of the i-th element antenna;

[0082] Calculate the backward matrix of a complex vector:

[0083] Rearrange the elements of the forward matrix to obtain the backward matrix A. b :

[0084]

[0085] Among them, A b Let a be a backward matrix. f (i,j) represents the element in the i-th row and j-th column of the forward matrix; i = 1, 2, ..., N / 2; j = 1, 2, ..., N / 2;

[0086] Calculate the covariance matrix based on the calculated forward and backward matrices:

[0087] A=(A f +A b )

[0088] Where A is the covariance matrix of a complex vector.

[0089] In this embodiment, the AR coefficients are calculated based on the covariance matrix, including:

[0090] Solving for AR coefficients using the Yule-Walker equation:

[0091]

[0092] Among them, a1, a2, ..., a N / 2-1 These are the AR coefficients we are looking for. It is the variance of the observed values ​​of the independent variable.

[0093] In this embodiment, the phase and amplitude of the possible signal are estimated based on the AR coefficient, including:

[0094] Establish the following equation:

[0095] 1+a1x+a2x 2 +...+a N / 2-1 x N / 2-1 =0

[0096] The phases corresponding to the N / 2-1 roots obtained by solving are the normalized frequencies of the possible signals, and the corresponding magnitudes are the corresponding amplitudes.

[0097]

[0098] Where, φ k Let m be the phase of the k-th root. k Let be the amplitude of the k-th root, where k = 1, 2, ..., N / 2-1.

[0099] S3. The amplitude of the target signal estimated by the AR algorithm is accurately estimated using the MVDR algorithm, and the angle of arrival of the detected target signal is obtained.

[0100] In this embodiment, the angle of arrival of the target signal is obtained by accurately estimating the amplitude estimated by the AR algorithm using the MVDR algorithm, including:

[0101] Based on the calculated phase, the calculated amplitude is estimated using the MVDR algorithm;

[0102] From the estimated amplitudes, the M signals with the largest amplitudes are selected as the target signals to be detected;

[0103] The phase corresponding to each target signal to be detected is determined as the angle at which it reaches the digital phased array antenna.

[0104] In this embodiment, based on the calculated phase, the calculated amplitude is estimated using the MVDR algorithm, including:

[0105] The MVDR algorithm reduces the amplitude estimation error based on the frequency estimate obtained from the AR algorithm.

[0106]

[0107]

[0108] Where, p k For amplitude estimation, φ k For phase, a(φ) k ) is φ k The corresponding AR coefficient, a H (φ k) is a(φ k The conjugate transpose of ).

[0109] In this embodiment, the phase corresponding to each target signal to be detected is determined as its angle of arrival at the digital phased array antenna, including:

[0110] The phases of each target signal to be detected are sequentially converted into their angles of arrival using the following formula:

[0111]

[0112] Where θ is the angle at which the target signal arrives at the digital phased array antenna. d is the antenna array element spacing, and λ is the source wavelength.

[0113] This method uses the forward and backward matrices of a multi-element input complex vector to estimate its covariance matrix, and calculates the forward and backward matrices using a sliding window method to reduce resource consumption and ensure the real-time performance of the algorithm.

[0114] This method achieves accurate angle measurement of multiple targets in a ring at the same distance using the AR algorithm. The MVDR algorithm accurately estimates the amplitude of multiple signals based on the results of the AR algorithm, making up for the inaccuracy of amplitude estimation in the AR algorithm and reducing false detection results.

[0115] For ease of understanding, the present invention provides a more specific embodiment:

[0116] The AR-MVDR algorithm proposed in this invention was tested and verified on two interleaved signals of equal magnitude and azimuth interval of 10 degrees, and two interleaved signals of equal magnitude and azimuth interval of 5 degrees. The experimental results are shown in Figure 2, where yellow and red dots correspond to different test targets. Figures 2(a), 2(b), and 2(c) demonstrate that the AR-MVDR algorithm has strong signal deinterleaving capability, and high azimuth resolution and angle measurement accuracy. Furthermore, multiple experiments were conducted on the AR-MVDR algorithm, achieving a 90% recognition probability and an angle measurement accuracy of less than 2° when two targets at the same distance are 10° apart.

[0117] 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 it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A two-dimensional super-resolution direction finding method based on AR-MVDR algorithm, characterized in that, The method comprises the steps of: receiving a first signal through a digital phased array antenna; wherein the first signal is superimposed by target signals emitted by signal sources from multiple different directions; performing amplitude and phase estimation on sampling points of the first signal based on an AR algorithm; precisely estimating the amplitudes estimated by the AR algorithm through an MVDR algorithm to obtain the angles of arrival of the target signals; the step of performing amplitude and phase estimation on sampling points of the first signal based on the AR algorithm comprises the steps of: obtaining an input of the AR algorithm; estimating a covariance matrix based on the input of the AR algorithm; calculating AR coefficients according to the covariance matrix; estimating the phases and amplitudes of possible signals according to the AR coefficients; the step of estimating the covariance matrix based on the input of the AR algorithm comprises the steps of: calculating a (N / 2)×(N / 2) dimension forward matrix corresponding to a complex vector in a sliding window manner: where A f is a forward matrix, x i is the i-th element of a complex vector input, is the conjugate of x i , and N is the number of sampling points; the complex vector is X = [x1, x2,..., x N ] T , x i denotes the amplitude-phase sampling point of the i-th element antenna. calculating a backward matrix of the complex vector: rearranging elements of the forward matrix to obtain the backward matrix A b : where A b is a backward matrix, a f (i,j) denotes an element in the ith row and jth column of the forward matrix; i = 1, 2,..., N / 2; j = 1, 2,..., N / 2; calculating the covariance matrix according to the calculated forward matrix and backward matrix: A = (A f + A b ) wherein A is the covariance matrix of the complex vector; the step of calculating the AR coefficients according to the covariance matrix comprises the step of: solving the AR coefficients by using a Yule-Walker equation: wherein a1, a2,..., a N / 2-1 are the AR coefficients to be found, is the variance of the argument observations; the step of estimating the phases and amplitudes of possible signals according to the AR coefficients comprises the steps of: establishing the following equation: 1 + a1x + a2x 2 +...+a N / 2-1 x N / 2-1 = 0 the phases corresponding to N / 2-1 roots obtained by solving the equation are normalized frequencies of possible signals, and the modulus values corresponding to the phases are corresponding amplitudes: where φk= arctan (Im (ak) / Re (ak) ), m k is the phase of the kth root, m k is the magnitude of the kth root, k = 1, 2,..., N / 2 - 1.

2. The method of claim 1, wherein, the digital phased array antenna comprises N receiving elements for receiving the first signal; wherein N is greater than or equal to 2; the target signals are M in total, and M is a positive integer greater than 1 and less than or equal to N / 2-1.

3. The method of claim 1, wherein, the step of obtaining the input of the AR algorithm comprises the steps of: performing one-shot sampling on the first signal received by the N-element digital phased array antenna; inputting the preprocessed amplitudes and phases as a complex vector of the AR algorithm; the preprocessing comprises digital down-conversion and filtering.

4. The method of claim 1, wherein, the step of precisely estimating the amplitudes estimated by the AR algorithm through the MVDR algorithm to obtain the angles of arrival of the target signals comprises the steps of: estimating the amplitudes calculated through the MVDR algorithm according to the calculated phases; selecting M signals with the largest amplitudes from the estimated amplitudes as target signals to be detected; determining the phases of the target signals to be detected as the angles of arrival of the target signals to the digital phased array antenna.

5. The method of claim 4, wherein, the step of estimating the amplitudes calculated through the MVDR algorithm according to the calculated phases comprises the step of: reducing the amplitude estimation error on the basis of the frequency estimation calculated by the AR algorithm through the MVDR algorithm, that is, where p k is the MVDR algorithm magnitude estimate, φ k is the phase, a(φ k ) is the AR coefficient corresponding to φ k , and a H (φ k ) is the conjugate transpose of a(φ k ).

6. The method of claim 5, wherein, the step of determining the phases of the target signals to be detected as the angles of arrival of the target signals to the digital phased array antenna comprises the step of: converting the phases of the target signals to be detected into the angles of arrival of the target signals according to the following formula in sequence: Wherein, θ is the angle of the target signal to be detected reaching the digital phased array antenna, d is the antenna element spacing, and λ is the wavelength of the signal source.

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