CN116879835A - Method and device for estimating direction of arrival of projection minimum maximum concave function - Google Patents
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Abstract
The invention discloses a method and a device for estimating the direction of arrival of a projection minimum maximum concave function, which are characterized by comprising the following steps: s1, obtaining an antenna array multiple measurement matrix; s2, performing singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimensions and noise; s3, constructing a direction-of-arrival estimation optimization model of a projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction; s4, solving a direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information; and S5, obtaining an accurate estimated angle according to the sparse solution containing the angle information. By adopting the technical scheme of the invention, more accurate angle positioning can be realized.
Description
Technical Field
The invention belongs to the technical field of signal processing, and relates to a method and a device for estimating the direction of arrival of a projection minimum maximum concave function.
Background
Direction of arrival estimation and angular positioning of a signal source are of vital importance in array signal processing, which refers to measuring the angle of arrival of a signal source relative to an antenna array. Accurate direction of arrival estimation and angular localization are critical for wireless communication, radar, sonar, sound source localization, etc. applications, which can provide critical information about signal source location, motion state, and environmental information. By optimizing the angle positioning algorithm and technology, more accurate signal source positioning can be realized, and the system performance and application effect are improved. Conventional angular positioning techniques include beamforming and subspace methods such as MUSIC and ESPRIT algorithms. The subspace method utilizes the statistical characteristics of the observed data to obtain the direction of arrival estimation and realize angle positioning, so that sufficient observed data and a sufficient number of uncorrelated signal sources are needed for accurate estimation and angle positioning.
With the advent of different signal estimation theory, some limitations have been better addressed. In this context, many innovative methods of direction of arrival estimation and angular positioning have been proposed, such as in net, off-net and no net direction of arrival estimation and angular positioning. By dividing the signal space into specific grids, the angular positioning problem is then translated into a challenging optimization problem. And searching for spectral peaks by means of different norm constraint rules, these methods typically useNorms, & gt>Norm (0)<p<1) Lorentz norm and Lorentz norm, etc>The norm, however, results in the objective function being a non-convex function, which has some difficulty in mathematical solution and cannot guarantee that the optimal solution is a globally optimal solution. MC (Minimax Concave) function although the objective function can be made convex by parameter setting, linear operation is requiredThe operators are non-singular matrices. Unfortunately, in direction of arrival estimation or angular positioning applications, this condition is difficult to meet.
Disclosure of Invention
The invention aims to provide a method and a device for estimating the direction of arrival of a projection minimum maximum concave function, which realize the direction of arrival estimation by adopting a method based on a projection minimum maximum concave function (PMC), wherein the function can be maximally approximatedNorms, and at B H And in the case of the non-singular matrix, the objective function is made to be a convex function only through parameter setting. The method utilizes the projection minimum and maximum concave functions to construct the optimization problem of the direction of arrival estimation, thereby better promoting the sparsity of the signals to be recovered on the space grid. By means of this optimization strategy, a more accurate angular positioning can be achieved.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a projection minimum maximum concave function direction of arrival estimation method comprises the following steps:
s1, obtaining an antenna array multiple measurement matrix;
s2, performing singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimensions and noise;
s3, constructing a direction-of-arrival estimation optimization model of a projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
s4, solving a direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and S5, obtaining an accurate estimated angle according to the sparse solution containing the angle information.
Preferably, in step S1, an antenna array multiple measurement matrix is obtained according to a preset antenna array model.
Preferably, in step S4, the direction of arrival estimation optimization model is solved by a near-end gradient descent method, and a lean solution including angle information is obtained.
Preferably, in step S5, an accurate estimated angle is obtained by searching for the position of the spectral peak according to the thinning-out including the angle information.
The invention also provides a device for estimating the direction of arrival of the projection minimum and maximum concave functions, which comprises the following steps:
the acquisition module is used for acquiring an antenna array multiple measurement matrix;
the decomposition module is used for carrying out singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimension and noise;
the construction module is used for constructing a direction-of-arrival estimation optimization model of the projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
the computing module is used for solving the direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and the estimation module is used for obtaining an accurate estimation angle according to the sparse solution containing the angle information.
Preferably, the acquiring module is configured to acquire an antenna array multiple measurement matrix according to a preset antenna array model.
Preferably, the calculation module is used for solving the direction-of-arrival estimation optimization model through a near-end gradient descent method to obtain a lean solution containing angle information.
Preferably, the estimation module is configured to obtain an accurate estimated angle by searching for a peak position according to the sparse solution containing the angle information.
The invention has the following beneficial effects:
(1) Solves the existing baseNorm (0)<p<1) Lorentz norm and Lorentz norm, etc>The problem of non-convex sparse optimization of the norm direction of arrival estimation and angle positioning method reduces the challenge in solving. The inventionThe method for estimating the direction of arrival of the minimum and maximum concave functions of the projection is a convex sparse optimization problem, and creatively solves the problem of difficult objective function solving.
(2) On the premise of ensuring that the objective function is easy to solve, the projection minimum and maximum concave function method used by the method can not only improve the estimation precision, but also accurately obtain the amplitude of an incoming wave signal, and can also obtain extremely high arrival direction estimation precision under the conditions of low signal-to-noise ratio and a small amount of snapshots.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of direction of arrival estimation based on a uniform linear array;
FIG. 2 is a flow chart of a method for estimating the direction of arrival of a projected minimum concave function according to an embodiment of the present invention;
FIG. 3 is a diagram of the error simulation result of the method for estimating the direction of arrival of the minimum concave function in the embodiment of the invention;
fig. 4 is a diagram of a success rate simulation result of the method for estimating the direction of arrival of the minimum concave function in the projection of the embodiment of the invention.
Fig. 5 is a diagram of simulation results of the root mean square error of the method for estimating the direction of arrival of the minimum and maximum concave function according to the embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1:
as shown in fig. 1, the uniform linear array-based direction of arrival estimation system is composed of an antenna array, a signal processing unit and an angle estimation algorithm. An antenna array is a device for receiving incoming wave signals, and is generally composed of a group of antennas which are equidistantly arranged or an antenna array structure which is designed according to requirements. These antennas receive signals from a signal source and transmit them to a signal processing unit. The signal processing unit receives the signal from the antenna and amplifies, filters and digitizes it. It is responsible for converting the received analog signal into a digital signal for subsequent processing and analysis. The arrival direction is finally estimated by the arrival direction estimation algorithm provided by the invention.
As shown in fig. 2, an embodiment of the present invention provides a method for estimating a direction of arrival of a projection minimum-maximum concave function, including the following steps:
s1, obtaining an antenna array multiple measurement matrix;
s2, performing singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimensions and noise;
s3, constructing a direction-of-arrival estimation optimization model of a projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
s4, solving a direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and S5, obtaining an accurate estimated angle according to the sparse solution containing the angle information.
As an implementation manner of the embodiment of the present invention, in step S1, assuming that the antenna array is a uniform linear array formed by M omni-directional antennas, a distance d between adjacent array elements of the uniform linear array is a half of a wavelength λ, and at a time t, an output y of the antenna array may be expressed as:
wherein K represents the number of the information sources,representing the phase difference of the kth far-field narrowband signal source acting on the uniform linear array, and taking the first array element as the origin of coordinates, s k (t) is the sampling value of the kth source at time t,/and>in order to uniformly guide the matrix of the linear array,is the additive noise of the system at time t. For T sample snapshots, the output matrix of the antenna array may be denoted +.>
According to the uniform linear array arrangement structure, the steering matrix thereof can be expressed as:
as an implementation manner of the embodiment of the present invention, in step S2, in order to reduce the influence of noise on the estimation of the direction of arrival and reduce the computational complexity, singular value decomposition is performed on the output matrix Y of the antenna array, so as to obtain y=u Σv H WhereinAnd->Are unitary matrices, +.>Comprises K major elements and (M-K) minor elements; according to the singular value size, a new antenna array output matrix can be obtained> I K Is a unit matrix; obtaining Y after linear transformation SV ＝AS sv +N sv ，S sv ＝SVD K ，N sv ＝NVD K 。
In step S3, the incoming wave direction of the spatial domain signal is divided, the sparsity is presented in the incoming wave direction of the spatial domain signal with respect to the spatial angle position, and the signal space-90 ° to 90 ° can be divided into N equal-divided grids according to the signal estimation theory, and N > K, θ= { θ are satisfied 1 ,…,θ N The } represents all possible angles of incidence in the signal space, the overcomplete dictionary matrix B, may be represented as The original signal s (t) can be expressed as +.o after the overcomplete dictionary matrix B>Wherein the method comprises the steps of
The direction of arrival estimation optimization model of the projection minimum maximum concave function is constructed and can be modeled as follows:
wherein,,for the signal to be reconstructed, μ is the regularization parameter, balance residual and constraint term +.> The specific expression of the minimum and maximum concave function is as follows:
wherein, gamma is an adjusting parameter, and the smaller gamma is, the closer to l 0 A norm; b (B) + Moore-Penrose generalized inverse matrix for B; v is an intermediate variable of the molo envelope.
As an implementation manner of the embodiment of the present invention, in step S4, the above direction of arrival estimation optimization model is rewritten as:
order theWhen (when)When F (Z) is a Z convex function, wherein +.>Is B H B strictly positive eigenvalues.
When the above conditions are met, the optimization problem is convex optimization, and a global optimal solution can be obtained by using a near-end gradient descent method, specifically:
f (Z) is at Z k The points are taylor expanded:
wherein Z is k For the iteration value of Z at the kth time,<·,·>representing the inner product of two matrices, beta being the step size, controlling the convergence rate, G k For F (Z) at Z k The derivative at (a) is specifically:
wherein soft is the near-end operator:
wherein Q is a near-end operator intermediate variable, Q * For the optimal solution of the near-end operator, Z (i, i) is the ith row of Z, Q * (i) is Q * Is the i-th row of (a).
Wherein, β ε (0, 2/(λ) max (B H B)+μγ -1 ))，λ max (B H B) Is B H Maximum eigenvalue of B. When Z k+1 -Z k || F /||Z k || F When ε is less than or equal to ε or the maximum number of iterations is reached, the algorithm may be considered to converge to a global minimum, ε is an error parameter, typically 10 -6 。
In step S5, the optimal solution Z obtained in step S4 is used as an implementation manner of the embodiment of the present invention * Fetch/line 2 And searching the position of the spectrum peak according to the norm, and obtaining corresponding angle information according to the signal space grid division rule.
Further, in order to verify the beneficial effects of the invention, the embodiment of the invention verifies the effects through simulation experiments. Assuming that the antenna array is composed of a uniform linear array with 8 omni-directional array elements, the distance d between adjacent array elements of the uniform linear array is half of the wavelength lambda, the signal space is divided into grids at an angle interval of 1 DEG from-90 DEG to 90 DEG, and the Root Mean Square Error (RMSE) is adopted to represent the estimation performance of the direction of arrival of the invention, and the specific formula is as follows:
wherein K is the number of far-field narrowband sources, P is the number of repeated tests of Monte Carlo,for the estimated value of the kth far-field narrowband source in the p-th repetition test, theta k In order to avoid the influence of random errors, the number of monte carlo repetition tests of all experimental results is 500 in the embodiment of the present invention.
Fig. 3 is a diagram of the error simulation result of a method for estimating the direction of arrival of the projection minimum maximum concave function. The signal-to-noise ratio (SNR) range is set to be-5 dB-20 dB, the snapshot quantity T=10, and the far-field narrowband source is set to be [ -12+rand,30+rand]Rand means randomly generating a random number distributed in the range of 0 to 1. 1)The method comprises the following steps: adopts->Taking norms as sparse constraint terms, and solving an objective function by adopting a quasi-Newton method; 2)/>The method comprises the following steps: adopts->The norm is used as a sparse constraint term, and singular value decomposition is carried out on the output of the antenna array so as to achieve the effects of data dimension reduction and noise reduction; 3) SFW-L21 method: with weighting +.>The norms were solved using a convex optimization toolbox (CVX) of MATLAB as sparse induction terms. From the results in the figure, it can be seen that: compared with other algorithms, the embodiment of the invention is better than other three algorithms within the range of-5 dB to 20 dB.
Fig. 4 is a diagram of the result of success rate simulation of a method for estimating the direction of arrival of a projection minimum-maximum concave function, and the specific parameter settings are the same as those of fig. 3. From the figures it can be seen that: the success rate of the estimation of the direction of arrival provided by the embodiment of the invention is obviously higher than that of other three methods, and almost reaches 100% identification at 0 dB; the success rate reaches about 60% at-5 dB. This demonstrates the advantage of the proposed method at low signal to noise ratio.
Fig. 5 is a diagram of simulation results of the root mean square error of the projection minimum maximum concave function direction of arrival estimation method as a function of the number of snapshots. The signal-to-noise ratio (SNR) is fixed at 15dB, the far-field narrowband signal source is set as [ -12+rand,30+rand ], rand represents randomly generating a random number distributed in the range of 0-1, and the snapshot number T is set as 4-50. From the figures it can be seen that: the SFW-L21 method has the worst performance under a small number of snapshots, and the performance is similar to the method provided by the embodiment of the invention along with the increase of the number of the snapshots; the performance of the other two methods increases with the number of shots; the method provided by the embodiment of the invention has obvious advantages under a small number of snapshots.
Example 2:
the embodiment of the invention also provides a device for estimating the direction of arrival of the projection minimum concave function, which comprises the following steps:
the acquisition module is used for acquiring an antenna array multiple measurement matrix;
the decomposition module is used for carrying out singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimension and noise;
the construction module is used for constructing a direction-of-arrival estimation optimization model of the projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
the computing module is used for solving the direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and the estimation module is used for obtaining an accurate estimation angle according to the sparse solution containing the angle information.
As an implementation manner of the embodiment of the present invention, the obtaining module is configured to obtain an antenna array multiple measurement matrix according to a preset antenna array model.
As one implementation mode of the embodiment of the invention, the calculation module is used for solving the direction-of-arrival estimation optimization model through a near-end gradient descent method to obtain the sparse solution containing the angle information.
As an implementation manner of the embodiment of the present invention, the estimation module is configured to obtain an accurate estimated angle by searching for a spectral peak position according to a sparse solution including angle information.
The above embodiments are merely illustrative of the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, but various modifications and improvements made by those skilled in the art to which the present invention pertains are made without departing from the spirit of the present invention, and all modifications and improvements fall within the scope of the present invention as defined in the appended claims.
Claims (8)
1. A projection minimum maximum concave function direction of arrival estimation method is characterized by comprising the following steps:
s1, obtaining an antenna array multiple measurement matrix;
s2, performing singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimensions and noise;
s3, constructing a direction-of-arrival estimation optimization model of a projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
s4, solving a direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and S5, obtaining an accurate estimated angle according to the sparse solution containing the angle information.
2. The method of estimating a direction of arrival of a projection minimum-maximum-concave function according to claim 1, wherein in step S1, an antenna array multiple measurement matrix is obtained according to a predetermined antenna array model.
3. The method for estimating a direction of arrival of a projected minimum-concave function according to claim 2, wherein in step S4, a direction of arrival estimation optimization model is solved by a near-end gradient descent method to obtain a sparse solution containing angle information.
4. The method for estimating a direction of arrival of a projection minimum and maximum concave function according to claim 3, wherein in step S5, an accurate estimated angle is obtained by searching for a position of a spectral peak according to a thinning solution containing angle information.
5. A projection minimum maximum concave function direction of arrival estimation device, comprising:
the acquisition module is used for acquiring an antenna array multiple measurement matrix;
the decomposition module is used for carrying out singular value decomposition on the antenna array multiple measurement matrix to obtain a multiple measurement matrix with reduced dimension and noise;
the construction module is used for constructing a direction-of-arrival estimation optimization model of the projection minimum maximum concave function according to the multiple measurement matrixes after dimension reduction and noise reduction;
the computing module is used for solving the direction-of-arrival estimation optimization model to obtain a sparse solution containing angle information;
and the estimation module is used for obtaining an accurate estimation angle according to the sparse solution containing the angle information.
6. The apparatus for estimating a direction of arrival of a projected minimum and maximum notch function according to claim 5, wherein the obtaining module is configured to obtain an antenna array multiple measurement matrix according to a predetermined antenna array model.
7. The projection minimum and maximum concave function direction of arrival estimation device according to claim 6, wherein the calculation module is configured to solve the direction of arrival estimation optimization model by a near-end gradient descent method to obtain a sparse solution containing angle information.
8. The projection minimum and maximum concave function direction of arrival estimation apparatus according to claim 7, wherein the estimation module is configured to obtain an accurate estimated angle by searching for a spectral peak position according to a lean solution containing angle information.
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