Direction of arrival estimation method and apparatus, electronic device, and storage medium

CN117761612BActive Publication Date: 2026-10-30PURPLE MOUNTAIN LAB
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Patent Information

Application Number
CN202311548413.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-11-17
Publication Date
2026-10-30
Estimated Expiration
2043-11-17

AI Technical Summary

Technical Problem

[0004]本发明提供一种波达方向估计方法、装置、电子设备及存储介质,用以解决现有的DOA估计方法中在定位场景的维度为三维的情况下,为保证定位精度,定位速度将大幅降低的缺陷,该方法基于蚁群算法中的初始蚁群和反向蚁群,能够有效提高蚁群算法的收敛性能,这样一来,在基于该蚁群算法,对阵列信号对应的方向谱函数进行谱峰搜索的过程中,可快速且准确地估计阵列信号对应的波达方向,整个过程有效提升了DOA估计的定位精度和速度

Benefits of technology

[0023]本发明提供的波达方向估计方法、装置、电子设备及存储介质,通过获取阵列信号对应的方向谱函数;根据蚁群算法中的初始蚁群和反向蚁群,确定方向谱函数对应的谱峰;根据谱峰,估计阵列信号对应的波达方向。该方法基于蚁群算法中的初始蚁群和反向蚁群,能够有效提高蚁群算法的收敛性能,这样一来,在基于该蚁群算法,对阵列信号对应的方向谱函数进行谱峰搜索的过程中,可快速且准确地估计阵列信号对应的波达方向,整个过程有效提升了DOA估计的定位精度和速度,进而满足高精度低时延的定位要求。

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Abstract

The application provides a DOA estimation method and device, electronic equipment and storage medium, the method comprises the following steps: obtaining the direction spectrum function corresponding to the array signal; determining the spectrum peak corresponding to the direction spectrum function according to the initial ant colony and the reverse ant colony in the ant colony algorithm; and estimating the DOA corresponding to the array signal according to the spectrum peak. The method can effectively improve the convergence performance of the ant colony algorithm based on the initial ant colony and the reverse ant colony in the ant colony algorithm, so that the DOA corresponding to the array signal can be quickly and accurately estimated in the process of searching the spectrum peak of the direction spectrum function corresponding to the array signal based on the ant colony algorithm, the positioning accuracy and speed of the DOA estimation are effectively improved in the whole process, and the positioning requirements of high accuracy and low time delay are met.
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Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method, apparatus, electronic device, and storage medium for estimating direction of arrival. Background Technology

[0002] Direction of Arrival (DOA) estimation is a classic positioning technique widely used in electronics, communications, radar, and sonar. When a transmitter emits a signal, a receiver receives that signal. Due to the rectilinear propagation of electromagnetic waves, the receiver can estimate the location of the transmitter by measuring the angle at which the signal arrives. To improve the accuracy of DOA estimation, advanced signal processing techniques and algorithms are typically employed, such as millimeter-wave beamforming and massively multi-input multiple-output (MIMO) technology.

[0003] Existing DOA estimation methods use a grid method to determine the extreme values ​​of the directional spectrum function for localization. However, in the case of a three-dimensional localization scene, the localization speed will be significantly reduced in order to ensure localization accuracy. Summary of the Invention

[0004] This invention provides a direction-of-arrival (DOA) estimation method, apparatus, electronic device, and storage medium to address the shortcomings of existing DOA estimation methods, where the positioning speed is significantly reduced in three-dimensional scenarios to ensure positioning accuracy. This method, based on the initial ant colony and reverse ant colony in the ant colony algorithm, effectively improves the convergence performance of the algorithm. Thus, during the peak search of the spectral function corresponding to the array signal based on this ant colony algorithm, the DOA of the array signal can be estimated quickly and accurately. The entire process effectively improves the positioning accuracy and speed of DOA estimation.

[0005] This invention provides a direction-of-arrival estimation method, comprising:

[0006] Obtain the directional spectrum function corresponding to the array signal;

[0007] Based on the initial ant colony and reverse ant colony in the ant colony algorithm, the spectral peak corresponding to the directional spectral function is determined; wherein, each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal;

[0008] Based on the spectral peaks, the direction of arrival (DOA) of the array signal is estimated.

[0009] According to a direction-of-arrival (DOA) estimation method provided by the present invention, the step of determining the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm includes: S1, determining a first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectral function in the ant colony algorithm; S2, determining a second ant colony based on the first ant colony and the directional spectral function, and updating the first ant colony to the second ant colony; S3, repeating step S2 until a preset number of times is reached, and determining the spectral peak corresponding to the directional spectral function based on the finally obtained second ant colony.

[0010] According to a direction-of-arrival estimation method provided by the present invention, determining the first ant colony based on the initial ant colony, the reverse ant colony, and the direction spectrum function in the ant colony algorithm includes: determining the initial pheromone corresponding to the initial ant under the same signal based on the direction spectrum function, and determining the reverse pheromone corresponding to the reverse ant under the same signal; determining the ant corresponding to the larger pheromone among the initial pheromone and the reverse pheromone as the target ant under the same signal; and constructing the first ant colony based on the target ants corresponding to each of the signals.

[0011] According to a direction-of-arrival estimation method provided by the present invention, determining a second ant colony based on a first ant colony and the direction spectrum function includes: determining a first pheromone matrix corresponding to the first ant colony based on the direction spectrum function; and determining the second ant colony based on the first pheromone matrix and the first ant colony.

[0012] According to a direction-of-arrival estimation method provided by the present invention, determining the second ant colony based on the first pheromone matrix and the first ant colony includes: determining the state transition probability matrix corresponding to the first ant colony based on the first pheromone matrix; for each state transition probability in the state transition probability matrix, if the state transition probability is less than a preset probability threshold, then locally updating the first ant corresponding to the state transition probability based on a step size parameter to obtain the second ant colony; if the state transition probability is greater than or equal to the preset probability threshold, then globally updating the first ant corresponding to the state transition probability based on the maximum first pheromone in the first pheromone matrix to obtain the second ant colony.

[0013] According to a direction-of-arrival estimation method provided by the present invention, the step of locally updating the first ant corresponding to the state transition probability based on the step size parameter to obtain the second ant colony includes: determining the step size parameter based on the current iteration number; and updating the first ant corresponding to the state transition probability based on the step size parameter to obtain the second ant colony.

[0014] According to a direction-of-arrival estimation method provided by the present invention, the step of globally updating the first ant corresponding to the state transition probability based on the largest first pheromone in the first pheromone matrix to obtain the second ant colony includes: determining pheromone coefficients based on the current iteration number; updating the first pheromone matrix based on the pheromone coefficients to obtain the second pheromone matrix; determining the ant corresponding to the larger pheromone among the largest first pheromone and the largest second pheromone as the queen ant, wherein the largest second pheromone belongs to the second pheromone matrix; and updating the first ant corresponding to the state transition probability based on the weight coefficient corresponding to the queen ant to obtain the second ant colony.

[0015] According to a direction-of-arrival estimation method provided by the present invention, determining the pheromone coefficient based on the current iteration number includes: obtaining the historical pheromone coefficient corresponding to the previous iteration number; if the historical pheromone coefficient is less than or equal to a preset minimum coefficient, then determining the preset minimum coefficient as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than or equal to a preset maximum coefficient, then determining the preset maximum coefficient as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than the preset minimum coefficient and less than the preset maximum coefficient, then determining the pheromone coefficient corresponding to the current iteration number based on the previous iteration number and the historical pheromone coefficient.

[0016] The present invention also provides a direction-of-arrival estimation device, comprising:

[0017] The acquisition module is used to acquire the directional spectrum function corresponding to the array signal;

[0018] The spectral peak determination module is used to determine the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm; wherein, each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal;

[0019] The direction-of-arrival (DOA) estimation module is used to estimate the DOA corresponding to the array signal based on the spectral peaks.

[0020] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement any of the above-described direction-of-arrival estimation methods.

[0021] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the direction-of-arrival estimation method as described above.

[0022] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements any of the above-described direction-of-arrival estimation methods.

[0023] The present invention provides a direction-of-arrival (DOA) estimation method, apparatus, electronic device, and storage medium. This method acquires the directional spectrum function corresponding to an array signal; determines the spectral peaks corresponding to the directional spectrum function based on the initial ant colony and reverse ant colony in an ant colony algorithm; and estimates the DOA corresponding to the array signal based on the spectral peaks. This method, based on the initial ant colony and reverse ant colony in the ant colony algorithm, effectively improves the convergence performance of the algorithm. Thus, during the spectral peak search of the directional spectrum function corresponding to the array signal based on this ant colony algorithm, the DOA corresponding to the array signal can be estimated quickly and accurately. The entire process effectively improves the positioning accuracy and speed of DOA estimation, thereby meeting the requirements for high-precision, low-latency positioning. Attached Figure Description

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

[0025] Figure 1 This is one of the flowcharts illustrating the direction-of-arrival estimation method provided by the present invention;

[0026] Figure 2 This is the second flowchart of the direction of arrival estimation method provided by the present invention;

[0027] Figure 3 This is a schematic diagram of the direction of arrival estimation device provided by the present invention;

[0028] Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0030] To better understand the embodiments of the present invention, the relevant content involved in the embodiments of the present invention will first be described:

[0031] The first device generates a demodulation reference signal (DMRS) for the second device and sends the DMRS to the second device. The second device may use an antenna array to receive the DMRS sent by the first device, extract the DMRS, and determine the array signal.

[0032] Optionally, the first device may generate the DMRS reference signal for the second device based on the 4th Generation Mobile Communication Technology (4G) protocol standard, the 5th Generation Mobile Communication Technology (5G) protocol standard, or other protocol standards.

[0033] The 4G protocol standard refers to a series of protocols used in 4G communication; the 5G protocol standard refers to a series of protocols used in 5G communication. These protocol standards can include physical layer protocols, data link layer protocols, and network layer protocols, etc.

[0034] The DMRS reference signal refers to the reference signal used for correlation demodulation of the Physical Uplink Shared Channel (PUSCH) and Physical Uplink Control Channel (PUCCH) in Long Term Evolution (LTE) technology.

[0035] An antenna array refers to an antenna array composed of two or more individual antennas operating at the same frequency, fed and spatially arranged according to certain requirements. The antenna radiating elements that constitute an antenna array are called array elements. Optionally, the antenna arrays involved in the embodiments of the present invention are mainly uniform area arrays and / or uniform circular arrays.

[0036] Optionally, the first and second devices mentioned above may include: computers, mobile terminals, and wearable devices, etc.

[0037] It should be noted that the execution subject involved in the embodiments of the present invention can be a direction-of-arrival estimation device or an electronic device, wherein the electronic device is the second device mentioned above.

[0038] The embodiments of the present invention will be further described below using an electronic device as an example.

[0039] like Figure 1 The diagram shown is one of the flowcharts of the direction-of-arrival estimation method provided by the present invention, which may include:

[0040] 101. Obtain the directional spectrum function corresponding to the array signal.

[0041] Taking a uniform circular array as an example, the signal received by an electronic device using a uniform circular array is: x * (t) represents a K×1 dimensional vector used to characterize the signals received by K (K≥2) array elements in a uniform circular array, x * (t) is an analog signal, and for this analog signal x * (t) is converted from analog to digital to obtain a digital signal x. * (n), x * (n) represents a K×1 dimensional vector, which is then used to analyze the digital signal x. * Extracting from (n) yields the array signal y(n), where y(n) represents a K×1 dimensional vector, which is the effective array signal actually received by the electronic device.

[0042] The electronic device determines the directional spectrum function corresponding to the array signal y(n), which can be expressed as:

[0043] Where K represents the number of elements on a uniform circular array; w H This represents the conjugate transpose of the weighted vector w of the array signal; The array manifold matrix representing a uniform circular array. θ represents the pitch angle, and θ represents the azimuth angle.

[0044] It should be noted that if the electronic device uses a uniform area array, the direction spectrum function corresponding to the array signal is determined in the same way. The direction spectrum function corresponding to the uniform area array can be expressed as:

[0045]

[0046] Wherein, MN (MN≥2) represents the number of array elements on a uniform surface array; The array manifold matrix represents a uniform area array.

[0047] The electronic device acquires the directional spectrum function corresponding to the array signal in order to subsequently determine the spectral peaks corresponding to the directional spectrum function.

[0048] 102. Determine the spectral peaks corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm.

[0049] It should be noted that the Ant Colony Algorithm (ACA) is a swarm intelligence biomimetic algorithm used to solve various optimization problems, that is, an algorithm that simulates the foraging behavior of ants.

[0050] The initial ant colony in the ant colony algorithm described above is also called the original ant colony, which includes multiple initial ants. The number of these initial ants is the same as the number of signals in the array signal.

[0051] A reverse ant colony refers to an ant colony composed of the reverse ants corresponding to each of the initial ants in the initial ant colony; that is, the reverse ant colony includes multiple reverse ants.

[0052] In the initial ant colony, each initial ant corresponds to a signal in the array signal, and each initial ant is used to represent the first incident angle of the corresponding signal; in the reverse ant colony, each reverse ant corresponds to a signal in the array signal, and each reverse ant is used to represent the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal.

[0053] Optionally, the incident angle may include: pitch angle And the azimuth angle θ.

[0054] The electronic device first initializes the preset ant colony parameters, which may include: the number of ants Z (Z≥2), the number of iterations T, and the probability transition constant C0, etc.

[0055] Optionally, the number of ants Z can be the number of array elements MN on a uniform surface array mentioned above, or the number of array elements K on a uniform circular array; no specific limitation is made here.

[0056] The initial ant colony can be represented as: iAnts = [iants1, ..., iants] z ,...,iants Z ];

[0057] in, This represents the z-th initial ant in the initial ant colony, used to characterize the pitch angle of the z-th signal in the corresponding array signal. and azimuth

[0058] A reverse ant colony can be represented as: nAnts = [nants1, ..., nants] z ,...,nants Z ];

[0059] in, This represents the z-th reverse ant in the reverse ant colony, used to characterize the reverse pitch angle of the z-th signal in the corresponding array signal. and reverse azimuth angle nants z It is an ant z The corresponding reverse ants, i.e., iants z and nants z These are the ants that correspond to the same signal in different ant colonies within an array of signals.

[0060] The electronic device employs an initial ant colony from the ant colony algorithm, combined with a back-learning strategy. First, it determines the corresponding back-learning ant colony. Then, based on the initial and back-learning ant colonies, it determines the extrema of the directional spectral function, which represents the spectral peak of the directional spectral function. Introducing the back-learning strategy effectively improves the convergence performance of the ant colony algorithm.

[0061] 103. Based on the spectral peaks, estimate the direction of arrival (DOA) of the array signal.

[0062] Electronic devices can quickly and accurately estimate the direction of arrival (DOA) of array signals based on the spectral peaks corresponding to the directional spectral function jointly determined by the initial ant colony and the reverse ant colony in the ant colony algorithm.

[0063] The final positioning result can be expressed as:

[0064] Wherein, iantsearch(·) represents the ant colony algorithm involved in the embodiments of the present invention; Indicates the direction of arrival (DOA) of the array signal estimated by the electronic device; This represents the directional spectrum function mentioned above, which is optional. It can be or No specific limitations are specified here.

[0065] In this embodiment of the invention, the directional spectrum function corresponding to the array signal is obtained; the spectral peak corresponding to the directional spectrum function is determined based on the initial ant colony and reverse ant colony in the ant colony algorithm; and the direction of arrival (DOA) corresponding to the array signal is estimated based on the spectral peak. This method, based on the initial ant colony and reverse ant colony in the ant colony algorithm, can effectively improve the convergence performance of the ant colony algorithm. Thus, during the spectral peak search of the directional spectrum function corresponding to the array signal based on this ant colony algorithm, the DOA corresponding to the array signal can be estimated quickly and accurately. The entire process effectively improves the positioning accuracy and speed of DOA estimation. Furthermore, it can meet the high-precision, low-latency positioning requirements in 4G, 5G, or other scenarios.

[0066] In some embodiments, the electronic device determines the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm, which may include: S1, the electronic device determines a first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectral function in the ant colony algorithm; S2, the electronic device determines a second ant colony based on the first ant colony and the directional spectral function, and updates the first ant colony to the second ant colony; S3, the electronic device repeats step S2 until a preset number of times is reached, and determines the spectral peak corresponding to the directional spectral function based on the finally obtained second ant colony.

[0067] The first ant colony refers to the first generation of ant colonies, which includes multiple first ants.

[0068] The second ant colony refers to the updated first ant colony, which can be understood as the second generation of ant colony, including multiple second ants.

[0069] The preset number of times refers to the number of times the ant moves (i.e., the number of iterations T). It can be set before the electronic device leaves the factory or it can be user-defined. It is generally set according to experience value. For example, the preset number of times can be set to 100.

[0070] The electronic device can determine the spectral peak of the directional spectral function based on the first ant colony. During the process of determining the spectral peak of the directional spectral function, the first ant colony is updated, and the spectral peak of the directional spectral function is determined based on the first ant colony before and after the update. The specific process is as follows: In step S1, the electronic device, based on the ant colony algorithm, can first determine the initial ant colony and the reverse ant colony, and then construct a new ant colony, namely the first ant colony, based on the initial ant colony, the reverse ant colony, and the directional spectral function; In step S2, the electronic device updates the first ant colony based on the first ant colony and the directional spectral function to obtain a second ant colony, and updates the first ant colony to the second ant colony; In step S3, the electronic device repeats step S2 until a preset number of times is reached, and determines the spectral peak corresponding to the directional spectral function based on the finally obtained second ant colony.

[0071] For example, assuming the preset number of updates is 3, after the electronic device determines the first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectrum function in the ant colony algorithm, it first determines the second ant colony based on the first ant colony and the directional spectrum function; then it determines the third ant colony based on the second ant colony and the directional spectrum function; and then it determines the fourth ant colony based on the third ant colony and the directional spectrum function. At this point, the number of ant colony updates has reached the preset number of updates, and the electronic device can perform spectral peak search based on the fourth ant colony.

[0072] It should be noted that, in the process of determining the spectral peak corresponding to the directional spectral function based on the final obtained second ant colony, the electronic device can determine the largest second ant in the final obtained second ant colony as the spectral peak corresponding to the directional spectral function.

[0073] In some embodiments, the electronic device determines the first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectrum function in the ant colony algorithm. This may include: the electronic device determining the initial pheromone corresponding to the initial ant under the same signal based on the directional spectrum function, and determining the reverse pheromone corresponding to the reverse ant under the same signal; the electronic device determining the ant corresponding to the larger pheromone among the initial pheromone and the reverse pheromone as the target ant under the same signal; and the electronic device constructing the first ant colony based on the target ants corresponding to each of the signals.

[0074] Pheromones are used to characterize the function value of the directional spectral function.

[0075] For each initial ant in the initial ant colony, the electronic device can determine the initial pheromone corresponding to the initial ant based on the directional spectrum function, taking the z-th initial ant in the initial ant colony as an example. z For example, iants z The corresponding initial pheromone can be expressed as: τ′ z =calObjFun(iants) z ), z = 1,...,Z, where calObjFun(·) represents the directional spectrum function; simultaneously, for each reverse ant in the reverse ant colony, the electronic device can determine the reverse pheromone corresponding to the reverse ant based on the directional spectrum function, taking the z-th reverse ant in the reverse ant colony as an example. z For example, nants z The corresponding reverse pheromone can be represented as: τ″ z =calObjFun(nants) z ), z = 1,...,Z; then, the electronic device will τ′ z and τ″ z Compare and choose τ′ z and τ″ zThe electronic device identifies the ant corresponding to the largest pheromone in the signal and determines it as the target ant. Based on this, the device can identify the target ant for each signal and construct a first ant colony based on all target ants.

[0076] The first ant colony can be represented as: Ants = [ants1, ..., ants] z ,...,ants Z ];

[0077] in, This represents the z-th ant in the first ant colony, used to characterize the pitch angle of the z-th signal in the corresponding array signal. and azimuth θ z For the z-th signal in the array signal, if the initial ant... z The corresponding initial pheromone τ′ z Greater than reverse ant nants z The corresponding reverse pheromone τ″ z ,but and If the initial ants z The corresponding initial pheromone τ′ z Smaller than reverse ant nants z The corresponding reverse pheromone τ″ z ,but and If the initial ants z The corresponding initial pheromone τ′ z Equal to reverse ants z The corresponding reverse pheromone τ″ z Then the initial ants z and reverse ants z The pitch angle and azimuth angle corresponding to any ant are determined as the pitch angle corresponding to the first ant. and azimuth θ z ,Right now, and or, and

[0078] It should be noted that calObjFun(·) refers to the directional spectrum function mentioned above.

[0079] In some embodiments, the electronic device determines the second ant colony based on the first ant colony and the directional spectrum function, which may include: the electronic device determining the first pheromone matrix corresponding to the first ant colony based on the directional spectrum function; and the electronic device determining the second ant colony based on the first pheromone matrix and the first ant colony.

[0080] The first pheromone matrix refers to the matrix formed by the first pheromones of each first ant in the first ant colony.

[0081] The electronic device can determine the initial pheromone corresponding to each initial ant in the initial ant colony and the reverse pheromone corresponding to each reverse ant in the reverse ant colony based on the aforementioned directional spectrum function, construct the first ant colony, and then determine the first pheromone corresponding to each first ant in the first ant colony to construct the first pheromone matrix corresponding to the first ant colony. This first pheromone matrix can be represented as: τ=[τ1,...,τ z ,...,τ Z ], where τ z τ represents the first pheromone corresponding to the z-th first ant in the first ant colony. z Used to characterize τ′ z and τ″ z The larger pheromone in the first pheromone matrix; then, the electronic device can determine the second ant colony based on the first pheromone matrix and the first ant colony.

[0082] In some embodiments, the electronic device determines the second ant colony based on the first pheromone matrix and the first ant colony, which may include: the electronic device determining the state transition probability matrix corresponding to the first ant colony based on the first pheromone matrix; for each state transition probability in the state transition probability matrix, if the state transition probability is less than a preset probability threshold, the electronic device locally updates the first ant corresponding to the state transition probability according to the step size parameter to obtain the second ant colony; if the state transition probability is greater than or equal to the preset probability threshold, the electronic device globally updates the first ant corresponding to the state transition probability according to the maximum first pheromone in the first pheromone matrix to obtain the second ant colony.

[0083] The state transition probability matrix can be expressed as: C = [c1,...,c z ,...,c Z ];c z =τ z / τ max τ represents the state transition probability for the z-th ant in the first ant colony; max This represents the largest first pheromone in the first pheromone matrix.

[0084] The preset probability threshold, also known as the probability transition constant, can be represented by C0.

[0085] For each first ant in the first ant colony, the electronic device can determine the maximum first pheromone in the first pheromone matrix, and then determine the state transition probability of each first ant based on the first pheromone corresponding to each first ant and the maximum first pheromone. Next, the electronic device can construct a state transition probability matrix C = [c1,...,c...] for the first ant colony based on the state transition probabilities of each first ant. z ,...,c Z ].

[0086] For the state transition probability matrix C = [c1,...,c z ,...,c Z The state transition probabilities in the data are given below. Taking the state transition probability c corresponding to the z-th ant in the first ant colony as an example, the electronic device will use c... z Compare with the preset probability threshold C0: If c z If C < C0, the electronic device will perform a local update on the z-th first ant based on the step size parameter to obtain the second ant colony; if c z If ≥C0, the electronic device will perform a global update on the z-th first ant based on the maximum first pheromone in the first pheromone matrix to obtain the second ant colony.

[0087] In some embodiments, the electronic device locally updates the first ant corresponding to the state transition probability according to the step size parameter to obtain the second ant colony. This may include: the electronic device determining the step size parameter according to the current iteration number; the electronic device updating the first ant corresponding to the state transition probability according to the step size parameter to obtain the second ant colony.

[0088] The step size parameter, also known as the local update parameter, can be expressed as: t′ represents the current iteration number, t′≤T, where T is the preset number mentioned above. As the iteration number increases, the step size parameter λ(t′) becomes smaller and smaller, so that the result of the local update (i.e., the second ant colony) becomes more and more accurate. This process can be called the step size parameter update process.

[0089] The state transition probability c corresponding to the z-th first ant in the first ant colony z For example, the electronic device can determine the step size parameter λ(t′) based on the current iteration number t′, and then perform a local update on the z-th first ant, which can be expressed as:

[0090]

[0091] in, Let represent the pitch angle of the z-th signal in the array signal corresponding to the z-th ant in the first ant colony. θ represents the pitch angle after a local update.z Let θ′ represent the azimuth angle of the z-th signal in the array corresponding to the z-th ant in the first ant colony. z This represents the azimuth angle after local update; λ(t′) represents the step size parameter; rand(·) represents a function that generates random numbers with values ​​between 0 and 1; a1, b1, a2, and b2 all represent preset ant colony parameters. For example, a1 has a value of 2, b1 has a value of -1, a2 has a value of 2, and b2 has a value of -1.

[0092] In other words, the electronic device targets the z-th first ant in the first ant colony. Perform a partial update to obtain the first ant after the partial update.

[0093] Optional, if If it is less than 0, then let Equal to 0; if If it is greater than π / 2, then let It equals π / 2; if θ′ z If it is less than -π, then let θ′ z Equal to -π; if θ′ z If it is greater than π, then let θ′ z It equals π. This process can be called the boundary constraint process.

[0094] Furthermore, the electronic device can construct a second ant colony based on all the locally updated ants.

[0095] In some embodiments, the electronic device globally updates the first ant corresponding to the state transition probability based on the largest first pheromone in the first pheromone matrix to obtain a second ant colony. This process may include: the electronic device determining pheromone coefficients based on the current iteration number; the electronic device updating the first pheromone matrix based on the pheromone coefficients to obtain a second pheromone matrix; the electronic device identifying the ant corresponding to the larger of the largest first pheromone and the largest second pheromone as the queen ant, and the largest second pheromone belonging to the second pheromone matrix; and the electronic device updating the first ant corresponding to the state transition probability based on the weight coefficient corresponding to the queen ant to obtain a second ant colony.

[0096] The pheromone coefficient, also known as the adaptive pheromone evaporation coefficient, can be represented by ρ(t′).

[0097] The first ant corresponding to the largest first pheromone in the first pheromone matrix can be called the first queen ant.

[0098] The weighting coefficient refers to the weight of the queen ant's influence on the ants, and can be represented by w.

[0099] The electronic device can determine the pheromone coefficient ρ(t′) based on the current iteration number t′, and use ρ(t′) to update the first pheromone matrix to obtain the second pheromone matrix. Taking the z-th ant in the first ant colony as an example... z For example, update ants z The corresponding first pheromone τ z , can be represented as: z = 1, ..., Z; where, This represents the updated first pheromone; due to calObjFun(ants) z )=τ z Then the above expression can be reformulated as: Furthermore, the electronic device can construct a second pheromone matrix based on all the updated first pheromones.

[0100] Next, the electronic device compares the largest first pheromone in the first pheromone matrix with the largest second pheromone in the second pheromone matrix, and selects the larger of the two. The ant corresponding to the larger pheromone is then identified as the queen ant. In other words, the pheromone of the first ant (i.e., the first queen ant) ​​corresponding to the largest first pheromone is compared with the pheromone of the second ant corresponding to the largest second pheromone: if the pheromone of the first queen ant is greater than that of the second ant, then the first queen ant is identified as the queen ant; if the pheromone of the first queen ant is less than that of the second ant, then the second ant is identified as the queen ant, and the first queen ant is relegated to a regular first ant; if the pheromone of the first queen ant is equal to that of the second ant, then either the first queen ant or the second ant is identified as the queen ant.

[0101] The state transition probability c corresponding to the z-th first ant in the first ant colony z For example, the electronic device can perform a global update on the first ant of the z-th ant based on the weight coefficient w corresponding to the queen ant, which can be expressed as:

[0102]

[0103] in, Represents the pitch angle after a global update; θ″ z represents the azimuth angle after global update; w represents the weight coefficient corresponding to the queen ant. The larger w is, the more the ants tend to move closer to the queen ant, and the faster the ant colony algorithm can converge. The smaller w is, the easier it is to ensure population diversity and find the global optimum. θ represents the elevation angle of the array signal corresponding to the queen ant; queenγ1 and γ2 represent the azimuth angle of the array signal corresponding to the queen ant; both γ1 and γ2 represent global update parameters; a3, b3, a4, and b4 represent preset ant colony parameters. For example, γ1 is 90°, γ2 is 360°, a3 is 1, b3 is -1, a4 is 1, and b4 is -1.

[0104] In other words, the electronic device targets the z-th first ant in the first ant colony. Perform a global update to obtain the first ant after the global update.

[0105] Optional, if If it is less than 0, then let Equal to 0; if If it is greater than π / 2, then let It equals π / 2; if θ″ z If it is less than -π, then let θ″ z Equal to -π; if θ″ z If it is greater than π, then let θ″ z It equals π. This process is the boundary constraint process.

[0106] Furthermore, the electronic device can build a second ant colony based on all the globally updated ants.

[0107] Furthermore, in the process of locally updating the first ant corresponding to the state transition probability to obtain the second ant colony, the first pheromone matrix can also be updated using the pheromone coefficient ρ(t′) to obtain the second pheromone matrix. The process of updating the first pheromone is the same as the process of updating the first pheromone during global update, and will not be elaborated here.

[0108] In some embodiments, the electronic device determines the pheromone coefficient based on the current iteration number, which may include: the electronic device acquiring the historical pheromone coefficient corresponding to the previous iteration number; if the historical pheromone coefficient is less than or equal to a preset minimum coefficient, the electronic device determines the preset minimum coefficient as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than or equal to a preset maximum coefficient, the electronic device determines the preset maximum coefficient as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than the preset minimum coefficient and less than the preset maximum coefficient, the electronic device determines the pheromone coefficient corresponding to the current iteration number based on the previous iteration number and the historical pheromone coefficient.

[0109] Here, the preset minimum coefficient refers to the minimum value of the pheromone coefficient ρ(t′), which can be expressed as ρ. min express.

[0110] The preset maximum coefficient refers to the maximum value of the pheromone coefficient ρ(t′), which can be expressed as ρ. maxexpress.

[0111] In determining the pheromone coefficient, the electronic device first obtains the historical pheromone coefficient corresponding to the previous iteration number and compares it with a preset minimum coefficient. If the historical pheromone coefficient is less than or equal to the preset minimum coefficient, the preset minimum coefficient is determined as the pheromone coefficient corresponding to the current iteration number. If the historical pheromone coefficient is greater than the preset minimum coefficient, it is compared with a preset maximum coefficient. If the historical pheromone coefficient is greater than or equal to the preset maximum coefficient, the preset maximum coefficient is determined as the pheromone coefficient corresponding to the current iteration number. If the historical pheromone coefficient is less than the preset maximum coefficient but greater than the preset minimum coefficient, the pheromone coefficient corresponding to the current iteration number is determined based on the previous iteration number and the historical pheromone coefficient.

[0112] For example, the pheromone coefficient can be expressed as:

[0113]

[0114] Where t represents the previous iteration number; ρ(t) represents the historical pheromone coefficient corresponding to the previous iteration number t; t′ represents the current iteration number, and t′=t+1; ρ(t′) represents the pheromone coefficient corresponding to the current iteration number t′; ρ min Indicates the preset minimum coefficient; ρ max This indicates the preset maximum coefficient.

[0115] Electronic devices can adaptively update the pheromone coefficient as the number of iterations increases. For example, during global / local updates, the pheromone coefficient can be increased in the early stages of the update to accelerate the convergence of the ant colony algorithm; while in the later stages of the update, the pheromone coefficient can be decreased to make the ant colony algorithm more stable. This process can be called the pheromone coefficient update process.

[0116] The embodiments of the present invention will be further illustrated with reference to the following examples:

[0117] For example, such as Figure 2 The diagram shown is a second schematic flowchart of the direction-of-arrival estimation method provided by this invention. From... Figure 2 As can be seen from this, the processing flow of the electronic device is as follows: 1. Initialize the preset ant colony parameters; 2. Introduce the reverse learning strategy; 3. Determine the first pheromone matrix and the first generation queen ant; 4. Determine the state transition probability c. z5. Based on the state transition probability and the probability transition constant C0, select the update method (local update or global update) to update the ants; 6. Boundary constraints; 7. Update the pheromone and queen ant; 8. Update the step size parameter and pheromone coefficient; 9. Determine whether the preset number of times has been reached. If the preset number of times has not been reached, repeat steps 4-8; if the preset number of times has been reached, output the result, that is, the direction of arrival of the array signal estimated by the electronic device.

[0118] The direction-of-arrival estimation device provided by the present invention is described below. The direction-of-arrival estimation device described below can be referred to in correspondence with the direction-of-arrival estimation method described above.

[0119] like Figure 3 The diagram shown is a schematic representation of the direction-of-arrival estimation device provided by the present invention, which may include:

[0120] The acquisition module 301 is used to acquire the directional spectrum function corresponding to the array signal;

[0121] The spectral peak determination module 302 is used to determine the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm; wherein, each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal;

[0122] The direction of arrival estimation module 303 is used to estimate the direction of arrival of the array signal based on the spectral peak.

[0123] Optionally, the spectral peak determination module 302 is specifically used for: S1, determining a first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectral function in the ant colony algorithm; S2, determining a second ant colony based on the first ant colony and the directional spectral function, and updating the first ant colony to the second ant colony; S3, repeating step S2 until a preset number of times is reached, and determining the spectral peak corresponding to the directional spectral function based on the finally obtained second ant colony.

[0124] Optionally, the spectral peak determination module 302 is specifically used to determine the initial pheromone corresponding to the initial ant under the same signal based on the directional spectral function, and to determine the reverse pheromone corresponding to the reverse ant under the same signal; to determine the ant corresponding to the larger pheromone among the initial pheromone and the reverse pheromone as the target ant under the same signal; and to construct the first ant colony based on the target ants corresponding to each of the signals.

[0125] Optionally, the spectral peak determination module 302 is specifically used to determine the first pheromone matrix corresponding to the first ant colony based on the directional spectral function; and to determine the second ant colony based on the first pheromone matrix and the first ant colony.

[0126] Optionally, the spectral peak determination module 302 is specifically used to determine the state transition probability matrix corresponding to the first ant colony based on the first pheromone matrix; for each state transition probability in the state transition probability matrix, if the state transition probability is less than a preset probability threshold, then the first ant corresponding to the state transition probability is locally updated according to the step size parameter to obtain the second ant colony; if the state transition probability is greater than or equal to the preset probability threshold, then the first ant corresponding to the state transition probability is globally updated according to the maximum first pheromone in the first pheromone matrix to obtain the second ant colony.

[0127] Optionally, the peak determination module 302 is specifically used to determine the step size parameter based on the current iteration number; and to update the first ant corresponding to the state transition probability based on the step size parameter to obtain the second ant colony.

[0128] Optionally, the spectral peak determination module 302 is specifically used to determine the pheromone coefficient based on the current iteration number; update the first pheromone matrix based on the pheromone coefficient to obtain the second pheromone matrix; determine the ant corresponding to the larger pheromone among the largest first pheromone and the largest second pheromone as the queen ant, and the largest second pheromone belongs to the second pheromone matrix; update the first ant corresponding to the state transition probability based on the weight coefficient corresponding to the queen ant to obtain the second ant colony.

[0129] Optionally, the spectral peak determination module 302 is specifically used to obtain the historical pheromone coefficient corresponding to the previous iteration number; if the historical pheromone coefficient is less than or equal to a preset minimum coefficient, then the preset minimum coefficient is determined as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than or equal to a preset maximum coefficient, then the preset maximum coefficient is determined as the pheromone coefficient corresponding to the current iteration number; if the historical pheromone coefficient is greater than the preset minimum coefficient and less than the preset maximum coefficient, then the pheromone coefficient corresponding to the current iteration number is determined based on the previous iteration number and the historical pheromone coefficient.

[0130] like Figure 4The diagram shows the structure of an electronic device provided by the present invention. This electronic device may include a processor 410, a communication interface 420, a memory 430, and a communication bus 440. The processor 410, communication interface 420, and memory 430 communicate with each other via the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute a direction-of-arrival (DOA) estimation method. This method includes: obtaining the directional spectrum function corresponding to the array signal; determining the spectral peak corresponding to the directional spectrum function based on the initial ant colony and the reverse ant colony in the ant colony algorithm; wherein each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first angle of incidence of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second angle of incidence of the corresponding signal; the first angle of incidence corresponding to the initial ant under the same signal is different from the second angle of incidence corresponding to the reverse ant under the same signal; and estimating the DOA corresponding to the array signal based on the spectral peak.

[0131] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0132] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the direction-of-arrival estimation method provided by the above methods. The method includes: obtaining the directional spectrum function corresponding to the array signal; determining the spectral peak corresponding to the directional spectrum function based on the initial ant colony and the reverse ant colony in the ant colony algorithm; wherein each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal; and estimating the direction of arrival corresponding to the array signal based on the spectral peak.

[0133] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the direction-of-arrival estimation method provided by the above methods. The method includes: acquiring a directional spectrum function corresponding to an array signal; determining a spectral peak corresponding to the directional spectrum function based on an initial ant colony and a reverse ant colony in an ant colony algorithm; wherein each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize a first angle of incidence of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize a second angle of incidence of the corresponding signal; the first angle of incidence corresponding to an initial ant under the same signal is different from the second angle of incidence corresponding to a reverse ant under the same signal; and estimating the direction of arrival corresponding to the array signal based on the spectral peak.

[0134] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. 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 the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0135] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A direction-of-arrival estimation method, characterized in that, include: Obtain the directional spectrum function corresponding to the array signal; Based on the initial ant colony and reverse ant colony in the ant colony algorithm, the spectral peak corresponding to the directional spectral function is determined; wherein, each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal; Based on the spectral peaks, the direction of arrival (DOA) of the array signal is estimated.

2. The method according to claim 1, characterized in that, The step of determining the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm includes: S1. Determine the first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectrum function in the ant colony algorithm; S2. Based on the first ant colony and the directional spectrum function, determine the second ant colony, and update the first ant colony to the second ant colony; S3. Repeat step S2 until the preset number of times is reached, and determine the spectral peak corresponding to the directional spectral function based on the final obtained second ant colony.

3. The method according to claim 2, characterized in that, The step of determining the first ant colony based on the initial ant colony, the reverse ant colony, and the directional spectrum function in the ant colony algorithm includes: Based on the directional spectrum function, determine the initial pheromone corresponding to the initial ant under the same signal, and determine the reverse pheromone corresponding to the reverse ant under the same signal; The ant corresponding to the larger pheromone in the initial pheromone and the reverse pheromone is identified as the target ant under the same signal; The first ant colony is constructed based on the target ant corresponding to each of the signals.

4. The method according to claim 2, characterized in that, The step of determining the second ant colony based on the first ant colony and the directional spectral function includes: Based on the directional spectral function, determine the first pheromone matrix corresponding to the first ant colony; The second ant colony is determined based on the first pheromone matrix and the first ant colony.

5. The method according to claim 4, characterized in that, The step of determining the second ant colony based on the first pheromone matrix and the first ant colony includes: Based on the first pheromone matrix, determine the state transition probability matrix corresponding to the first ant colony; For each state transition probability in the state transition probability matrix, if the state transition probability is less than a preset probability threshold, then according to the step size parameter, the first ant corresponding to the state transition probability is locally updated to obtain the second ant colony. If the state transition probability is greater than or equal to the preset probability threshold, then the first ant corresponding to the state transition probability is globally updated according to the maximum first pheromone in the first pheromone matrix to obtain the second ant colony.

6. The method according to claim 5, characterized in that, The step of locally updating the first ant colony corresponding to the state transition probability based on the step size parameter to obtain the second ant colony includes: The step size parameter is determined based on the current iteration number; Based on the step size parameter, the first ant corresponding to the state transition probability is updated to obtain the second ant colony.

7. The method according to claim 5, characterized in that, The step of globally updating the first ant corresponding to the state transition probability based on the maximum first pheromone in the first pheromone matrix to obtain the second ant colony includes: Determine the pheromone coefficient based on the current iteration number; The first pheromone matrix is ​​updated based on the pheromone coefficients to obtain the second pheromone matrix; The ant corresponding to the larger of the largest first pheromone and the largest second pheromone is identified as the queen ant, and the largest second pheromone belongs to the second pheromone matrix; Based on the weight coefficient corresponding to the queen ant, the first ant corresponding to the state transition probability is updated to obtain the second ant colony.

8. The method according to claim 7, characterized in that, The step of determining the pheromone coefficient based on the current iteration number includes: Obtain the historical pheromone coefficient corresponding to the previous iteration number; If the historical pheromone coefficient is less than or equal to a preset minimum coefficient, then the preset minimum coefficient is determined as the pheromone coefficient corresponding to the current iteration number; If the historical pheromone coefficient is greater than or equal to the preset maximum coefficient, then the preset maximum coefficient is determined as the pheromone coefficient corresponding to the current iteration number; If the historical pheromone coefficient is greater than the preset minimum coefficient and less than the preset maximum coefficient, then the pheromone coefficient corresponding to the current iteration number is determined based on the previous iteration number and the historical pheromone coefficient.

9. A direction-of-arrival estimation device, characterized in that, include: The acquisition module is used to acquire the directional spectrum function corresponding to the array signal; The spectral peak determination module is used to determine the spectral peak corresponding to the directional spectral function based on the initial ant colony and the reverse ant colony in the ant colony algorithm; wherein, each initial ant in the initial ant colony corresponds to a signal in the array signal, and each initial ant is used to characterize the first incident angle of the corresponding signal; each reverse ant in the reverse ant colony corresponds to a signal in the array signal, and each reverse ant is used to characterize the second incident angle of the corresponding signal; the first incident angle corresponding to the initial ant under the same signal is different from the second incident angle corresponding to the reverse ant under the same signal; The direction-of-arrival (DOA) estimation module is used to estimate the DOA corresponding to the array signal based on the spectral peaks.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the direction-of-arrival estimation method as described in any one of claims 1 to 8.

11. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the direction-of-arrival estimation method as described in any one of claims 1 to 8.

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