A method and system for coherent signal direction of arrival estimation

Abstract

The application discloses a coherent signal direction of arrival estimation method and system, which is used for solving the technical problem that the existing coherent signal direction of arrival estimation method leads to high estimation cost. The method comprises the following steps: acquiring a plurality of far-field coherent spatial narrowband source signals at multiple time points; constructing an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at the multiple time points; determining a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix; constructing a minimum mean square error optimization model by using the reference auxiliary output signal and the signal subspace estimation value; solving the minimum mean square error optimization model by using a gradient descent method to determine a target to-be-estimated parameter; and determining a target coherent signal direction of arrival based on the target to-be-estimated parameter.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a method and system for estimating the direction of arrival of a coherent signal. Background Art

[0002] Traditional array signal processing, as an important signal processing technology, has rapidly developed in fields such as communications, radar, sonar, and seismic exploration. Array signal processing involves using sensor arrays of varying spatial geometries to detect and process incoming signals, enabling estimation of the number of signal sources, direction of arrival, and accurate frequency.

[0003] Direction-of-Arrival (DOA) estimation is an important branch of array signal processing. It refers to using array antennas to receive spatial signals and processing the received signals through statistical signal processing techniques and various optimization methods to recover the direction information of the incident signal. It has a wide range of applications in radar, sonar, voice, and wireless communications.

[0004] Most existing coherent signal direction-of-arrival (DOA) estimation methods use the spatially smoothed (SS) MUSIC algorithm (SS-MUSIC) to restore the rank of the signal covariance matrix to complete DOA estimation. However, in practical applications, MUSIC-based algorithms require prior information on the number of signal sources. Moreover, for large-scale signal covariance matrices, a large amount of computing resources is required to perform eigendecomposition, resulting in excessively high estimation costs. Summary of the Invention

[0005] The present invention provides a coherent signal direction of arrival estimation method and system, which are used to solve the technical problem that the existing coherent signal direction of arrival estimation method causes the estimation cost to be too high.

[0006] A first aspect of the present invention provides a method for estimating the direction of arrival of a coherent signal, comprising:

[0007] Acquire multiple far-field coherent spatial narrowband source signals at multiple times;

[0008] constructing an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at each moment;

[0009] determining a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix;

[0010] Constructing a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value;

[0011] The minimum mean square error optimization model is solved by using a gradient descent method to determine the target parameters to be estimated;

[0012] Based on the target parameters to be estimated, the direction of arrival of the target coherent signal is determined.

[0013] Optionally, constructing an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at various moments includes:

[0014] Determining a plurality of array element output signals at each moment based on the plurality of far-field coherent spatial narrowband source signals at each moment;

[0015] Arranging the plurality of array element output signals at each moment to generate an output signal column vector at each moment;

[0016] An output signal matrix is ​​constructed according to the output signal column vectors at each moment.

[0017] Optionally, the reference auxiliary output signal includes a reference output signal and an auxiliary output signal; and determining the reference auxiliary output signal and the signal subspace estimation value based on the output signal matrix includes:

[0018] determining a sample covariance matrix based on the output signal matrix;

[0019] Determining a reference output signal and an auxiliary output signal according to matrix elements in the sample covariance matrix;

[0020] determining a noise subspace estimate based on the sample covariance matrix;

[0021] A signal subspace estimation value is determined based on the noise subspace estimation value.

[0022] Optionally, the adopting of a gradient descent method to solve the minimum mean square error optimization model to determine the target parameter to be estimated includes:

[0023] Derivative the minimum mean square error optimization model to determine the gradient direction of the model;

[0024] Based on the gradient direction of the model, the minimum mean square error optimization model is solved using the gradient descent method, and the target parameters are to be estimated.

[0025] Optionally, determining the target coherent signal direction of arrival based on the target parameter to be estimated includes:

[0026] constructing a signal spatial spectrum according to the target parameter to be estimated;

[0027] The peak position of the signal spatial spectrum is identified to determine the direction of arrival of the target coherent signal.

[0028] Optionally, the minimum mean square error optimization model is specifically:

[0029] ;

[0030] in, Optimize the model for minimum mean square error; is the reference output signal; It is the auxiliary output signal; is the signal subspace estimate; is a weight vector of (M-1)×1 dimensions; is the square of the L2 norm; is the transpose operation; is the conjugate transpose operation.

[0031] A second aspect of the present invention provides a coherent signal direction of arrival estimation system, comprising:

[0032] An acquisition module, used for acquiring multiple far-field coherent spatial narrowband source signals at multiple moments;

[0033] A first construction module is configured to construct an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at various moments;

[0034] Based on a module, for determining a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix;

[0035] A second construction module is configured to construct a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value;

[0036] A solution module, configured to solve the minimum mean square error optimization model using a gradient descent method to determine target parameters to be estimated;

[0037] The determination module is used to determine the direction of arrival of the target coherent signal based on the target parameters to be estimated.

[0038] A third aspect of the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the coherent signal direction of arrival estimation method as described in any one of the above items.

[0039] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed, implements the steps of the coherent signal direction of arrival estimation method as described in any one of the above items.

[0040] A fifth aspect of the present invention provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium, and the computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer is caused to perform the steps of the coherent signal arrival direction estimation method as described in any one of the above items.

[0041] It can be seen from the above technical solutions that the present invention has the following advantages:

[0042] The above technical solution of the present invention provides a method for estimating the direction of arrival of a coherent signal. First, multiple far-field coherent spatial narrowband source signals at multiple moments are obtained; then, an output signal matrix is ​​constructed based on the multiple far-field coherent spatial narrowband source signals at each moment; based on the output signal matrix, a reference auxiliary output signal and a signal subspace estimation value are determined; a minimum mean square error optimization model is constructed using the reference auxiliary output signal and the signal subspace estimation value; the minimum mean square error optimization model is solved using the gradient descent method to determine the target parameters to be estimated; finally, based on the target parameters to be estimated, the target coherent signal direction of arrival is determined; based on the above solution, the multiple far-field coherent spatial narrowband source signals at multiple moments are processed to obtain the reference auxiliary output signal and the signal subspace estimation value and construct the minimum mean square error optimization model, which is solved using the gradient descent method to obtain the process of obtaining the direction of arrival of the target coherent signal. This process does not require the prior determination of the information on the number of prior signal sources, nor does it require the consumption of a large amount of computing resources to perform eigendecomposition on the covariance matrix, thereby reducing the estimation cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 A flowchart of a method for estimating the direction of arrival of a coherent signal provided in the first embodiment of the present invention;

[0045] Figure 2 A schematic diagram of a process for solving a minimum mean square error optimization model using a gradient descent method according to the first embodiment of the present invention;

[0046] Figure 3 A schematic diagram of a simulation of the signal spatial spectrum of the present invention provided in the first embodiment of the present invention when the number of snapshots is 200 and the signal-to-noise ratio is -5dB;

[0047] Figure 4A schematic diagram of a simulation of the signal spatial spectrum of the present invention provided in the first embodiment of the present invention when the number of snapshots is 200 and the signal-to-noise ratio is 5 dB;

[0048] Figure 5 A schematic flow chart of a method for estimating the direction of arrival of a coherent signal provided in the second embodiment of the present invention;

[0049] Figure 6 This is a structural block diagram of a coherent signal direction-of-arrival estimation system provided in Embodiment 3 of the present invention. DETAILED DESCRIPTION

[0050] The embodiments of the present invention provide a method and system for estimating the direction of arrival of a coherent signal, which are used to solve the technical problem that the existing method for estimating the direction of arrival of a coherent signal causes excessively high estimation costs.

[0051] In order to make the purpose, features, and advantages of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described below are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0052] See also Figure 1 , Figure 1 This is a flowchart of the steps of a coherent signal direction of arrival estimation method provided in Example 1 of the present invention.

[0053] The present invention provides a method for estimating the direction of arrival of a coherent signal, comprising:

[0054] Step 101: Acquire multiple far-field coherent spatial narrowband source signals at multiple moments.

[0055] The far-field coherent spatial narrowband source signal is a far-field and coherent spatial narrowband source signal (spatial narrowband source signal).

[0056] It should be noted that a number of far-field and coherent spatial narrowband source signals emitted from different directions are received by the antenna array unit on the uniform linear array receiver; wherein the uniform linear array receiver is composed of a number of antenna units, and the spacing between the antenna units is less than or equal to half the wavelength of the incident signal.

[0057] Step 102: construct an output signal matrix according to multiple far-field coherent spatial narrowband source signals at each moment.

[0058] It should be noted that when several far-field and coherent spatial narrowband source signals are incident on a uniform linear array receiver from different directions, the antenna array unit receives the spatial narrowband source signals, the output signal of the antenna array unit is expressed in vector form, and the received signals at different times (different time sampling points) are expressed in matrix form to obtain an output signal matrix.

[0059] Specifically, the process of constructing the output signal matrix according to the multiple far-field coherent spatial narrowband source signals at each moment can be achieved by executing the following steps S21 to S23:

[0060] Step S21: determining a plurality of array element output signals at each moment based on a plurality of far-field coherent spatial narrowband source signals at each moment;

[0061] It should be noted that if there are K spatial narrowband source signals in the far field, When incident on a uniform linear array receiver composed of M antenna array units (array elements) with arbitrary directivity and an array element spacing of d, the wavelength of the far-field coherent spatial narrowband source signal is , K spatial narrowband source signals are mutually coherent; taking the leftmost array element as the reference element of the array, the DOA of the source signal can be expressed as the angle between the signal propagation direction and the array normal direction. The array elements are arranged according to the array element spacing. In order to avoid phase ambiguity, the antenna unit spacing d must be less than or equal to the wavelength of the incident signal. half of which is the set of directions of arrival of spatial narrowband source signals, is the first direction of arrival of the spatial narrowband source signal, is the second direction of arrival of the spatial narrowband source signal, is the Kth direction of arrival of the spatial narrowband source signal, and T is the transpose.

[0062] It is worth mentioning that for uniform linear arrays, the DOA is limited to between -90° and 90°, i.e. , is the kth direction of arrival of the spatial narrowband source signal.

[0063] Based on the above foundation, the mth element of the antenna array outputs the signal at the nth snapshot (time). It can be expressed as:

[0064] ;

[0065] in, is the array element output signal of the mth array element at the nth snapshot (time); is the far-field coherent spatial narrowband source signal; is the amplitude fading coefficient of the kth coherent signal component; d is the spacing between adjacent array elements of the uniform linear array receiver; is the kth direction of arrival of the spatial narrowband source signal; is the additive noise of the mth array element; K is the number of spatial narrowband sources; M is the number of uniform linear array receivers; j is the imaginary unit, ;e is a natural constant; is the wavelength of the far-field coherent spatial narrowband source signal;

[0066] Step S22: Arrange the output signals of multiple array elements at each moment to generate an output signal column vector at each moment;

[0067] It should be noted that the output signals of the M array elements at each snapshot (time n) are arranged into a column vector (output signal column vector), wherein the processing process of the output signal column vector can be expressed as:

[0068] ;

[0069] in, is the M×1-dimensional output signal column vector of the array at the nth moment, , is the output signal of the first array element at the nth snapshot (time), is the output signal of the second array element at the nth snapshot (time), is the output signal of the M-1th element at the nth snapshot (time), and T is the transpose; is a 1×1 dimensional spatial source signal vector; is an M×K dimensional array manifold matrix, is the M×1-dimensional steering vector of the first array element output signal, is the M×1-dimensional steering vector of the second array element output signal, is the M×1-dimensional steering vector of the K-th array element output signal; is the amplitude fading coefficient vector of the coherent signal component, , is the amplitude fading coefficient of the first coherent signal component, is the amplitude fading coefficient of the second coherent signal component, is the amplitude fading coefficient of the Kth coherent signal component; is an M×1-dimensional additive noise vector array, , is the additive noise of the first array element, is the additive noise of the second array element, is the additive noise of the M-1th array element.

[0070] It is worth mentioning that for additive noise, express All zero vectors with mean M×1 , the covariance is The complex circular Gaussian distribution of represents the variance of the noise, Represents the M×M-dimensional identity matrix and is independent of the source signal.

[0071] Step S23: construct an output signal matrix according to the output signal column vectors at each moment.

[0072] It should be noted that when the uniform linear array (uniform linear array receiver) outputs N snapshot signals, that is, when the output signals of multiple array elements at each moment are obtained and the output signal column vectors at each moment are generated, they will be represented in matrix form, that is, the output signal matrix can be expressed as:

[0073] ;

[0074] Where X is the M×N dimensional output signal matrix of the uniform linear array, , is the output signal column vector at the first moment, is the output signal column vector at the second moment, is the output signal column vector at the Nth moment; A is the M×K dimensional array manifold matrix; a is the amplitude fading coefficient vector of the coherent signal component; s is the 1×N dimensional spatial source signal vector, , is the far-field coherent spatial narrowband source signal at the first moment, is the far-field coherent spatial narrowband source signal at the second moment, is the far-field coherent spatial narrowband source signal at the Nth moment; W is the M×N dimensional additive noise matrix, , is the additive noise vector at the first moment, is the additive noise vector at the second moment, is the additive noise vector at the Nth moment.

[0075] Step 103: Determine a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix.

[0076] The reference auxiliary output signal includes a reference output signal and an auxiliary output signal.

[0077] Specifically, the process of determining the reference auxiliary output signal and the signal subspace estimation value based on the output signal matrix can be achieved by executing the following steps S31 to S34:

[0078] Step S31: determining a sample covariance matrix based on the output signal matrix;

[0079] It should be noted that the calculation process of the sample covariance matrix can be expressed as:

[0080] ;

[0081] in, is the sample covariance matrix of M×M dimensions; N is the total number of moments; is the output signal matrix; is the conjugate transpose operation.

[0082] Step S32: determining a reference output signal and an auxiliary output signal according to the matrix elements in the sample covariance matrix;

[0083] It should be noted that based on the sample covariance matrix, the leftmost antenna unit is selected as the reference antenna unit, the autocorrelation function of the reference antenna unit is selected as the reference output signal, and the cross-correlation function between the reference antenna unit and the remaining antenna units is selected as the auxiliary output signal. Specifically, the matrix element in the first column and first row of the sample covariance matrix is ​​used as the reference output signal, denoted as y r , then:

[0084] ;

[0085] in, is the reference output signal; is the matrix element in the first column and first row of the sample covariance matrix; N is the total number of moments; The output signal of the first array element at the nth snapshot (time); is the conjugate operation; is the power of the array element output signal; is the amplitude fading coefficient of the kth coherent signal component; is the noise power.

[0086] Furthermore, the elements from the second row of the first column to the Mth row of the first column of the sample covariance matrix are used as auxiliary output signals, denoted as , then:

[0087] ;

[0088] in, It is the auxiliary output signal; The second row element of the first column to the Mth row element of the first column of the sample covariance matrix; N is the total number of moments; The output signal of the second array element at the nth snapshot (time); The output signal of the third array element at the nth snapshot (time); The output signal of the M-1th element at the nth snapshot (time); is the power of the array element output signal; is the amplitude fading coefficient of the kth coherent signal component; d is the array element spacing of the antenna array unit (element); is the kth direction of arrival of the spatial narrowband source signal; is the wavelength of the far-field coherent spatial narrowband source signal; M is the number of antenna array elements; is the conjugate operation; is the first direction of arrival of the spatial narrowband source signal; is the second direction of arrival of the spatial narrowband source signal; is the Kth direction of arrival of the spatial narrowband source signal; is the amplitude fading coefficient of the first coherent signal component, is the amplitude fading coefficient of the second coherent signal component, is the amplitude fading coefficient of the Kth coherent signal component; Guide vector The column vector consisting of the remaining elements after removing the first element, ; Guide vector The column vector consisting of the remaining elements after removing the first element, ; Guide vector The column vector consisting of the remaining elements after removing the first element, ; is the amplitude fading coefficient vector of the coherent signal component; K is the number of spatial narrowband sources.

[0089] Step S33: determining a noise subspace estimate based on the sample covariance matrix;

[0090] It should be noted that the noise subspace estimation value is estimated based on the sample covariance matrix. The estimation process of the noise subspace estimation value is specifically as follows:

[0091] ;

[0092] in, is the noise subspace of M×M dimensions The noise subspace estimate of ; is the identity matrix of M×M dimensions; is the sample covariance matrix; is a hyperparameter; is the conjugate transpose operation; To take the inverse operation.

[0093] Step S34: Determine the signal subspace estimation value according to the noise subspace estimation value.

[0094] It should be noted that the signal subspace estimation value is estimated based on the noise subspace estimation value, and the estimation process of the signal subspace estimation value is specifically as follows:

[0095] ;

[0096] in, is the signal subspace of M×M dimensions The signal subspace estimate of ; is the identity matrix of M×M dimensions; is the noise subspace of M×M dimensions The noise subspace estimate of ; is the conjugate transpose operation; To take the inverse operation.

[0097] Step 104: construct a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value.

[0098] It should be noted that based on the reference output signal, the auxiliary output signal and the signal subspace estimation value, the weight vector is used as the parameter to be optimized, and an optimization model based on the minimum mean square error is constructed; wherein, the minimum mean square error optimization model is specifically:

[0099] ;

[0100] in, Optimize the model for minimum mean square error; is the reference output signal; It is the auxiliary output signal; is the signal subspace estimate; is a weight vector of (M-1)×1 dimensions; is the square of the L2 norm; is the transpose operation; is the conjugate transpose operation.

[0101] Step 105: Use the gradient descent method to solve the minimum mean square error optimization model to determine the target parameters to be estimated.

[0102] Specifically, step 105 may include the following sub-steps S51-S52:

[0103] Step S51: derive the minimum mean square error optimization model to determine the model gradient direction;

[0104] Step S52: Based on the model gradient direction, the minimum mean square error optimization model is solved using the gradient descent method, and the target parameters are to be estimated.

[0105] It should be noted that based on the minimum mean square error optimization model, the model gradient direction of the optimization model is obtained. Specifically, the gradient of the minimum mean square error optimization model is It can be expressed as:

[0106] ;

[0107] in, Optimize the gradient of the model for minimum mean square error; It is the auxiliary output signal; is the reference output signal; is a weight vector of (M-1)×1 dimensions; To obtain The elements from the 2nd to the Mth column of ; To obtain The element of the first column of ; is the conjugate transpose operation; is the conjugate operation.

[0108] Furthermore, the model gradient direction for:

[0109] ;

[0110] in, is the model gradient direction; It is the auxiliary output signal; is the reference output signal; is a weight vector of (M-1)×1 dimensions; To obtain The elements from the 2nd to the Mth column of ; To obtain The element of the first column of ; is the conjugate transpose operation; is the conjugate operation.

[0111] Furthermore, based on the model gradient direction, the gradient descent method is used to solve the minimum mean square error optimization model to obtain the target parameters to be estimated. Figure 2 , the uniform linear array (uniform linear array receiver) outputs N snapshot signals (multiple array element output signals at each moment), the number of iterations is set to R times (i.e. the maximum number of iterations), then each iteration The sample covariance matrix composed of snapshot signals can be expressed as:

[0112] ;

[0113] in, is the sample covariance matrix at the rth iteration; is the sample covariance matrix at the r-1th iteration; is the sample covariance matrix when r=0; for; Output signal matrix for uniform linear array No. A quick shot A matrix of snapshots; is the maximum number of iterations.

[0114] Furthermore, the reference output signal at the rth iteration is:

[0115] ;

[0116] in, is the reference output signal at the rth iteration; is the matrix element in the first column and first row of the sample covariance matrix at the rth iteration.

[0117] Furthermore, the auxiliary output signal at the rth iteration is:

[0118] ;

[0119] in, is the auxiliary output signal at the rth iteration; The elements from the second row of the first column to the Mth row of the first column of the sample covariance matrix at the rth iteration.

[0120] Furthermore, the noise subspace estimate at the rth iteration is:

[0121] ;

[0122] in, is the noise subspace estimate at the rth iteration; is the identity matrix of M×M dimensions; is the sample covariance matrix at the rth iteration; is a hyperparameter; is the conjugate transpose operation; To take the inverse operation.

[0123] Furthermore, the signal subspace estimation value at the rth iteration is:

[0124] ;

[0125] in, is the signal subspace estimate at the rth iteration; is the identity matrix of M×M dimensions; is the noise subspace estimate at the rth iteration; is the conjugate transpose operation; To take the inverse operation.

[0126] Furthermore, the model gradient direction at the rth iteration is:

[0127] ;

[0128] in, is the model gradient direction at the rth iteration; is the auxiliary output signal at the rth iteration; is the reference output signal at the rth iteration; is the (M-1)×1 dimensional weight vector at the r-1th iteration; is the rth iteration The elements from the 2nd to the Mth column of ; is the rth iteration The element of the first column of ; is the conjugate transpose operation; is the conjugate operation.

[0129] Furthermore, after obtaining the model gradient direction at the rth iteration, the gradient descent method is used to solve the optimization parameter formula, that is:

[0130] ;

[0131] in, is the (M-1)×1 dimensional weight vector at the r+1th iteration; is the (M-1)×1 dimensional weight vector at the rth iteration; is the model gradient direction at the rth iteration; is the update step size.

[0132] Furthermore, the gradient descent method is completed by setting the maximum number of iterations R. The solution of the parameter formula to be optimized based on the above gradient descent method is: , that is, optimizing the solution of the model to obtain the target parameters to be estimated.

[0133] Step 106: Determine the direction of arrival of the target coherent signal based on the target parameters to be estimated.

[0134] Specifically, step 106 may include the following sub-steps S61-S62:

[0135] S61. Constructing a signal spatial spectrum according to the target parameters to be estimated;

[0136] S62: Identify the peak position of the signal spatial spectrum and determine the direction of arrival of the target coherent signal.

[0137] It should be noted that based on the target parameters to be estimated, the signal spatial spectrum is constructed to obtain the DOA (direction of arrival of the target coherent signal) and the number of sources. Specifically, for a uniform linear array, the DOA is limited to between -90° and 90°, that is, .

[0138] Furthermore, the angle is divided into 1° intervals, and the airspace can be divided into 181 grids, that is, the airspace is divided into , the spatial angle is divided into 1801 grids with a division interval of 0.1°, that is, the spatial angle is divided into , according to the weight vector , that is, the target parameters to be estimated and the steering vector The relationship between them is constructed as follows:

[0139] ;

[0140] in, is the signal spatial spectrum; is the conjugate transpose of the target parameter to be estimated; is the guiding vector; To take the modulus.

[0141] Furthermore, by identifying the position and number of the peaks of the signal spatial spectrum, the DOA and the number of sources of the coherent signal source are obtained, that is, the direction of arrival of the target coherent signal and the number of sources of the coherent signal.

[0142] In this embodiment, the present invention utilizes the spatial power spectrum to realize the DOA estimation of the coherent signal while also realizing the accurate estimation of the number of information sources, thereby significantly improving the estimation accuracy and reducing the estimation cost.

[0143] For example, see Figures 3-4 , using a 7-element uniform linear array, the spacing between adjacent antenna elements is half the signal wavelength. Assuming there is a signal source in the far field, due to the multipath propagation effect, 5 coherent signals are generated from the direction is incident on a uniform linear array. The potential target interval is , that is, divided into equal intervals of 0.1°. The hyperparameters in the estimation of the noise subspace are is set to 0.0000001; in the gradient descent technique, the step size and number of iterations R are set to 0.00001 and 8 respectively. Figure 3 The figure shows the signal spatial spectrum of the present invention when the number of snapshots is 200 and the signal-to-noise ratio is -5dB. Figure 3It can be seen that the method can still successfully estimate the DOA of the coherent signal and the number of sources when the signal-to-noise ratio is low; Figure 4 The figure shows the signal spatial spectrum of the present invention when the number of snapshots is 200 and the signal-to-noise ratio is 5dB. Figure 4 It can be seen that the method can successfully estimate the DOA of the coherent signal and the number of sources when the signal-to-noise ratio is slightly improved, and the spectrum peak is sharper than when the signal-to-noise ratio is -5dB.

[0144] For a comparison of technical performance, we can use existing technologies as a reference. Signal direction of arrival (DOA) estimation is a research hotspot in array signal processing, with widespread applications in radar, sonar, wireless communications, and navigation. Due to the increasingly complex electromagnetic propagation environment, signals are prone to generating multipath components due to multipath effects during propagation. These signals are called coherent signals. Traditional multiple signal classification (MUSIC) methods are not suitable for scenarios where coherent signals are present.

[0145] To address the DOA estimation problem in the presence of coherent signals, researchers have proposed decorrelation methods such as the spatially smoothed (SS)-based MUSIC algorithm (SS-MUSIC) and the estimation of signal parameters via rotational invariance techniques (ESPRIT-like). These methods can restore the rank of the signal covariance matrix, enabling the application of subspace-based methods such as the MUSIC algorithm to complete DOA estimation. However, existing DOA estimation methods in the presence of coherent signals are mostly based on decorrelation methods such as spatial smoothing or Toeplitz matrix construction. These methods focus on restoring the rank of the covariance matrix and have certain drawbacks. Specifically, these methods lose the array aperture, significantly reducing the number of signals that can be estimated. SS-MUSIC and ESPRIT-like methods reduce the array aperture by half, thereby halving the number of signals that can be estimated. In addition, the MUSIC-based algorithm requires eigendecomposition of the signal covariance matrix, which has high computational complexity and consumes more hardware resources in practical applications. It also requires prior information on the number of signal sources, making it difficult to apply in practical applications.

[0146] In summary, DOA estimation methods for the presence of coherent signals require a decorrelation calculation step, which results in array aperture loss, thereby reducing the number of signals that can be estimated with the same array, which can easily lead to large estimation errors. At the same time, most existing DOA estimation methods for the presence of coherent signals require an accurate prior number of signal sources. However, in practice, the number of signal sources is unknown and cannot be used as a priori. Instead, a method for estimating the number of signal sources is required. This additional estimation of the number of signal sources undoubtedly increases the complexity of the solution and cannot guarantee an accurate estimate of the number of signal sources. Furthermore, existing optimization models based on minimum mean square error suffer from low accuracy in solving DOA estimation problems for the presence of coherent signals.

[0147] In response to the above problems, the present invention proposes a coherent signal direction of arrival estimation method, which obtains the estimated value of the noise subspace by calculating the sample covariance matrix of the array output signal, and then uses the estimated value of the noise subspace to estimate the signal subspace; then, the relationship between the first column element of the covariance matrix and the weight vector and the relationship between the weight vector and the signal subspace is used to construct an optimization model based on minimum mean square error; finally, the gradient descent method is used to solve the gradient direction of the optimization model, thereby obtaining the DOA estimation and the number of signal sources; compared with the existing DOA estimation method for solving the coherent source, the present invention does not require the calculation step of decoherence, and the estimation error is small, with better estimation performance, so it will not cause array aperture loss. At the same time, the present invention does not require the calculation step of covariance matrix eigendecomposition, so it does not require prior information on the number of signal sources and complex eigendecomposition calculation steps, thereby reducing complexity; in addition, the present invention uses spatial power spectrum to realize coherent signal DOA estimation while also being able to accurately estimate the number of signal sources, significantly improving estimation accuracy and reducing estimation cost.

[0148] In an embodiment of the present invention, the present invention provides a method for estimating the direction of arrival of a coherent signal. First, multiple far-field coherent spatial narrowband source signals at multiple moments are obtained; then, an output signal matrix is ​​constructed based on the multiple far-field coherent spatial narrowband source signals at each moment; based on the output signal matrix, a reference auxiliary output signal and a signal subspace estimation value are determined; a minimum mean square error optimization model is constructed using the reference auxiliary output signal and the signal subspace estimation value; the minimum mean square error optimization model is solved using the gradient descent method to determine the target parameters to be estimated; finally, based on the target parameters to be estimated, the target coherent signal direction of arrival is determined; based on the above scheme, the multiple far-field coherent spatial narrowband source signals obtained at multiple moments are processed to obtain the reference auxiliary output signal and the signal subspace estimation value and construct the minimum mean square error optimization model, which is solved using the gradient descent method to obtain the target coherent signal direction of arrival. This process does not require the prior determination of the number of prior signal sources, nor does it require the consumption of a large amount of computing resources to perform eigendecomposition on the covariance matrix, thereby reducing the estimation cost.

[0149] For better explanation, refer to Figure 5 , showing Figure 5 This is a flow chart of a method for estimating the direction of arrival of a coherent signal provided in Example 2 of the present invention. It should be noted that this embodiment only briefly describes the general process of the method for estimating the direction of arrival of a coherent signal. The specific implementation process of each step can be understood by referring to the relevant content in the aforementioned embodiments. A detailed description is omitted here. It is understood that the present invention is not limited to this.

[0150] 1. When several far-field and coherent spatial narrowband source signals are incident on a uniform linear array receiver from different directions, the antenna array unit receives the spatial narrowband source signals, and the output signal of the antenna array unit is expressed in the form of a vector. Based on the output signal at each different time, an output signal matrix is ​​obtained;

[0151] 2. Based on the output signal matrix, obtain the sample covariance matrix;

[0152] 3. Based on the sample covariance matrix, the autocorrelation function of the reference antenna unit is selected as the reference output signal, and the cross-correlation function between the reference antenna unit and the remaining antenna units is selected as the auxiliary output signal;

[0153] 4. Determine the estimated value of the noise subspace based on the sample covariance matrix;

[0154] 5. Determine an estimate of the signal subspace based on the noise subspace;

[0155] 6. Based on the reference output signal and the auxiliary output signal, the weight vector is used as the parameter to be optimized, and an optimization model based on minimum mean square error (minimum mean square error optimization model) is constructed;

[0156] 7. Based on the minimum mean square error optimization model, obtain the model gradient direction of the minimum mean square error optimization model;

[0157] 8. Based on the model gradient direction, the gradient descent method is used to solve the minimum mean square error optimization model to obtain the target parameters to be estimated;

[0158] 9. Based on the target parameters to be estimated, construct the signal spatial spectrum and obtain the DOA and number of sources of the coherent signal.

[0159] The present invention constructs an optimization model based on minimum mean square error (MMSE) and utilizes gradient descent to solve it, thus avoiding the computational steps required for decorrelation in traditional coherent signal DOA estimation methods and thus avoiding the problem of array aperture loss. Furthermore, the present invention not only eliminates the need for eigendecomposition of the covariance matrix but also eliminates the need for prior information on the number of signal sources, greatly simplifying the complexity of the model solution. Compared with existing optimization models for solving DOA with minimum mean square error (MMSE), the present invention improves estimation accuracy in low signal-to-noise ratio environments.

[0160] See also Figure 6 , Figure 6 This is a structural block diagram of a coherent signal direction-of-arrival estimation system provided in Embodiment 3 of the present invention.

[0161] The present invention provides a coherent signal direction of arrival estimation system, comprising:

[0162] An acquisition module 601 is configured to acquire a plurality of far-field coherent spatial narrowband source signals at a plurality of moments;

[0163] A first construction module 602 is configured to construct an output signal matrix based on a plurality of far-field coherent spatial narrowband source signals at each moment;

[0164] Based on module 603, it is used to determine the reference auxiliary output signal and the signal subspace estimate based on the output signal matrix;

[0165] A second construction module 604 is configured to construct a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value;

[0166] A solution module 605 is used to solve the minimum mean square error optimization model using a gradient descent method to determine the target parameters to be estimated;

[0167] The determination module 606 is configured to determine the direction of arrival of the target coherent signal based on the target parameters to be estimated.

[0168] Furthermore, the first building module 602 is specifically configured to:

[0169] Determining multiple array element output signals at each moment based on multiple far-field coherent spatial narrowband source signals at each moment;

[0170] Arranging multiple array element output signals at each moment to generate an output signal column vector at each moment;

[0171] An output signal matrix is ​​constructed based on the output signal column vectors at each moment.

[0172] Furthermore, the reference auxiliary output signal includes a reference output signal and an auxiliary output signal; based on module 603, specifically used for:

[0173] Based on the output signal matrix, determine the sample covariance matrix;

[0174] Determining a reference output signal and an auxiliary output signal according to matrix elements in the sample covariance matrix;

[0175] Determine a noise subspace estimate based on the sample covariance matrix;

[0176] A signal subspace estimate is determined based on the noise subspace estimate.

[0177] Furthermore, the solution module 605 is specifically configured to:

[0178] Derivate the minimum mean square error optimization model to determine the gradient direction of the model;

[0179] Based on the model gradient direction, the gradient descent method is used to solve the minimum mean square error optimization model, and the target parameters are to be estimated.

[0180] Furthermore, the determination module 606 is specifically configured to:

[0181] Construct the signal spatial spectrum according to the target parameters to be estimated;

[0182] Identify the peak position of the signal spatial spectrum and determine the direction of arrival of the target coherent signal.

[0183] Furthermore, the minimum mean square error optimization model is specifically:

[0184] ;

[0185] in, Optimize the model for minimum mean square error; is the reference output signal; It is the auxiliary output signal; is the signal subspace estimate; is a weight vector of (M-1)×1 dimensions; is the square of the L2 norm; is the transpose operation; is the conjugate transpose operation.

[0186] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described systems and modules can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0187] An embodiment of the present invention further provides a computer device including a memory and a processor, wherein a computer program is stored in the memory; when the computer program is executed by the processor, the processor executes the steps of the coherent signal direction of arrival estimation method as described in the first embodiment above.

[0188] An embodiment of the present invention further provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the steps of the coherent signal direction of arrival estimation method of the first embodiment are implemented.

[0189] An embodiment of the present invention further provides a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, the steps of the coherent signal direction of arrival estimation method as described in the first embodiment are implemented.

[0190] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0191] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0192] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments can still be modified, or some of the technical features thereof can be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating the direction of arrival of a coherent signal, characterized in that: include: Acquire multiple far-field coherent spatial narrowband source signals at multiple times; constructing an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at each moment; determining a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix; Constructing a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value; The minimum mean square error optimization model is solved by using a gradient descent method to determine the target parameters to be estimated; Determining the direction of arrival of the target coherent signal based on the target parameters to be estimated; The reference auxiliary output signal includes a reference output signal and an auxiliary output signal; The determining, based on the output signal matrix, a reference auxiliary output signal and a signal subspace estimation value, comprises: determining a sample covariance matrix based on the output signal matrix; Determining a reference output signal and an auxiliary output signal according to matrix elements in the sample covariance matrix; determining a noise subspace estimate based on the sample covariance matrix; Determining a signal subspace estimate value based on the noise subspace estimate value; The method of solving the minimum mean square error optimization model using the gradient descent method to determine the target parameters to be estimated includes: Derivative the minimum mean square error optimization model to determine the gradient direction of the model; Based on the gradient direction of the model, the minimum mean square error optimization model is solved by using the gradient descent method, and the target parameter is to be estimated; The determining the direction of arrival of the target coherent signal based on the target parameter to be estimated includes: constructing a signal spatial spectrum according to the target parameter to be estimated; The peak position of the signal spatial spectrum is identified to determine the direction of arrival of the target coherent signal.

2. The coherent signal direction of arrival estimation method according to claim 1, characterized in that: The step of constructing an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at various moments includes: Determining a plurality of array element output signals at each moment based on the plurality of far-field coherent spatial narrowband source signals at each moment; Arranging the plurality of array element output signals at each moment to generate an output signal column vector at each moment; An output signal matrix is ​​constructed according to the output signal column vectors at each moment.

3. The coherent signal direction of arrival estimation method according to claim 1, characterized in that: The minimum mean square error optimization model is specifically: ； in, Optimize the model for minimum mean square error; is the reference output signal; It is the auxiliary output signal; is the signal subspace estimate; is a weight vector of (M-1)×1 dimensions; is the square of the L2 norm; is the transpose operation; is the conjugate transpose operation.

4. A coherent signal direction of arrival estimation system, applied to the coherent signal direction of arrival estimation method according to claim 1, characterized in that: include: An acquisition module, used for acquiring multiple far-field coherent spatial narrowband source signals at multiple moments; A first construction module is configured to construct an output signal matrix according to the plurality of far-field coherent spatial narrowband source signals at various moments; Based on a module, for determining a reference auxiliary output signal and a signal subspace estimation value based on the output signal matrix; A second construction module is configured to construct a minimum mean square error optimization model using the reference auxiliary output signal and the signal subspace estimation value; A solution module, configured to solve the minimum mean square error optimization model using a gradient descent method to determine target parameters to be estimated; The determination module is used to determine the direction of arrival of the target coherent signal based on the target parameters to be estimated.

5. A computer device, characterized in that: The invention comprises a memory and a processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the processor executes the steps of the coherent signal direction of arrival estimation method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the method for estimating the direction of arrival of a coherent signal according to any one of claims 1 to 3 is implemented.

7. A computer program product, characterized in that The computer program product includes a computer program stored on a non-transitory computer-readable storage medium, wherein the computer program includes program instructions, wherein when the program instructions are executed by a computer, the computer is caused to execute the coherent signal direction of arrival estimation method according to any one of claims 1 to 3.

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