CN118884358A - Angle measurement method, device, terminal and medium based on sparse array - Google Patents
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Abstract
本申请公开了一种基于稀疏阵列的测角方法、装置、终端及介质,测角方法包括以下步骤:构建MIMO雷达虚拟稀疏阵列,包括若干连续且间距相同的均匀阵元,其他阵元为稀疏阵元,稀疏阵元的间距是均匀阵元间距的整数倍;取出均匀阵元获得的目标信息,计算目标信号的幅度和相位值,得出不同阵元对应的目标相位连续线性变化规律;根据上述规律对稀疏阵列进行补齐,计算稀疏阵列中缺失阵元对应的目标信息,将稀疏阵列转换为均匀阵列;将补齐后的虚拟阵列乘以窗函数后进行目标的角度计算。本申请利用已有通道的信号规律,预测空缺处的阵元信号,从而将稀疏阵列转变为近似半波长的间距均匀阵列,通道加权后,再进行目标测角计算,提高测角准确度。
The present application discloses an angle measurement method, device, terminal and medium based on a sparse array. The angle measurement method includes the following steps: constructing a MIMO radar virtual sparse array, including a number of continuous uniform array elements with the same spacing, and other array elements are sparse array elements, and the spacing of the sparse array elements is an integer multiple of the spacing of the uniform array elements; taking out the target information obtained by the uniform array elements, calculating the amplitude and phase values of the target signal, and obtaining the continuous linear change law of the target phase corresponding to different array elements; filling the sparse array according to the above law, calculating the target information corresponding to the missing array elements in the sparse array, and converting the sparse array into a uniform array; multiplying the filled virtual array by a window function to calculate the angle of the target. The present application uses the signal law of the existing channel to predict the array element signal at the vacant position, thereby converting the sparse array into a uniform array with a spacing of approximately half a wavelength, and then performing target angle measurement calculation after channel weighting to improve the angle measurement accuracy.
Description
技术领域Technical Field
本申请涉及雷达技术领域,特别涉及一种基于稀疏阵列的测角方法、装置、终端及介质。The present application relates to the field of radar technology, and in particular to an angle measurement method, device, terminal and medium based on a sparse array.
背景技术Background Art
随着自动驾驶技术蓬勃发展,毫米波雷达的应用愈加广泛。由于技术水平的不断迭代,毫米波雷达也在朝4D、高分辨方向发展,其实质的关键技术就是多通道技术,通过虚拟出更大的天线阵列,以实现角度的高分辨,同时也能提升探测距离。虚拟阵列具体实施方案分为两种,一种为均匀阵列,一种为稀疏阵列。均匀阵列为了满足测角的范围,基本采用半波长的间距,但是要实现1°到2°的分辨率,就需要非常多的通道,也就是需要更高的硬件配置,极大增加了成本。稀疏阵列即虚拟的阵列内,不同的阵元,一部分采用半波长的间距,一部分采用更大间距,这样用较少的天线和硬件配置即可以实现较高的分辨率。但虚拟的稀疏阵列一直没有很好的方法进行角度计算,所得测角往往准确度不高。With the vigorous development of autonomous driving technology, the application of millimeter-wave radar is becoming more and more extensive. Due to the continuous iteration of technology, millimeter-wave radar is also developing in the direction of 4D and high resolution. Its key technology is multi-channel technology, which virtualizes a larger antenna array to achieve high angle resolution and improve the detection distance. There are two specific implementation plans for virtual arrays, one is a uniform array and the other is a sparse array. In order to meet the range of angle measurement, the uniform array basically adopts a half-wavelength spacing, but to achieve a resolution of 1° to 2°, a lot of channels are required, which means that higher hardware configuration is required, which greatly increases the cost. In a sparse array, different array elements in a virtual array use a half-wavelength spacing and a larger spacing, so that a higher resolution can be achieved with fewer antennas and hardware configurations. However, there has been no good way to calculate the angle of a virtual sparse array, and the resulting angle measurement is often not accurate.
发明内容Summary of the invention
本申请提供了一种基于稀疏阵列的测角方法、装置、终端及介质,其优点是能够提高稀疏阵列测角的准确度。The present application provides a sparse array-based angle measurement method, device, terminal and medium, which have the advantage of being able to improve the accuracy of sparse array angle measurement.
本申请的技术方案如下:The technical solution of this application is as follows:
一方面,本申请提供一种基于稀疏阵列的测角方法,其特征在于,包括以下步骤:On the one hand, the present application provides an angle measurement method based on a sparse array, characterized in that it includes the following steps:
S1:构建MIMO雷达虚拟稀疏阵列,其中,稀疏阵列中,包括若干连续且间距相同的均匀阵元,其他阵元为稀疏阵元,稀疏阵元的间距是均匀阵元间距的整数倍;S1: construct a MIMO radar virtual sparse array, wherein the sparse array includes a number of continuous uniform array elements with the same spacing, and the other array elements are sparse array elements, and the spacing of the sparse array elements is an integer multiple of the spacing of the uniform array elements;
S2:取出均匀阵元获得的目标信息,计算目标信号的幅度和相位值,得出不同阵元对应的目标相位连续线性变化规律;S2: Take out the target information obtained by the uniform array element, calculate the amplitude and phase value of the target signal, and obtain the continuous linear change law of the target phase corresponding to different array elements;
S3:根据上述规律对稀疏阵列进行补齐,计算稀疏阵列中缺失阵元对应的目标信息,将稀疏阵列转换为均匀阵列;S3: Completing the sparse array according to the above rules, calculating the target information corresponding to the missing array elements in the sparse array, and converting the sparse array into a uniform array;
S4:将补齐后的虚拟阵列乘以窗函数后进行目标的角度计算。S4: Multiply the padded virtual array by the window function and calculate the angle of the target.
进一步的,所述稀疏阵列中,均匀阵元的阵元间距d为半波长。Furthermore, in the sparse array, the array element spacing d of the uniform array elements is half a wavelength.
进一步的,步骤S2中,获得目标相位连续线性变化规律还包括:计算均匀阵元中相邻阵元的平均相位差。Furthermore, in step S2, obtaining the target phase continuous linear variation rule further includes: calculating the average phase difference between adjacent array elements in the uniform array element.
进一步的,步骤S3中,缺失阵元的获取步骤为: 稀疏阵列和间距相同口径也相同的均匀阵列相比,稀疏阵列缺少的阵元即为缺失阵元。Furthermore, in step S3, the step of obtaining the missing array elements is as follows: when the sparse array is compared with a uniform array with the same spacing and the same caliber, the array elements missing from the sparse array are the missing array elements.
进一步的,步骤S4中,利用泰勒加权对补齐后的虚拟阵列进行处理。Furthermore, in step S4, Taylor weighting is used to process the padded virtual array.
又一方面,本申请提供一种稀疏阵列的测角装置,包括:On the other hand, the present application provides a sparse array angle measuring device, comprising:
稀疏阵列构建单元,用于构建MIMO雷达虚拟稀疏阵列,其中,稀疏阵列中,包括若干连续且间距相同的均匀阵元,其他阵元为稀疏阵元,稀疏阵元的间距是均匀阵元间距的整数倍;A sparse array construction unit is used to construct a MIMO radar virtual sparse array, wherein the sparse array includes a number of continuous uniform array elements with the same spacing, and the other array elements are sparse array elements, and the spacing of the sparse array elements is an integer multiple of the spacing of the uniform array elements;
拟合单元,用于取出均匀阵元获得的目标信息,计算目标信号的幅度和相位值,得出不同阵元对应的目标相位连续线性变化规律;The fitting unit is used to extract the target information obtained by the uniform array element, calculate the amplitude and phase value of the target signal, and obtain the continuous linear change law of the target phase corresponding to different array elements;
补齐单元,用于根据上述规律对稀疏阵列进行补齐,计算稀疏阵列中缺失阵元对应的目标信息,将稀疏阵列转换为均匀阵列;A filling unit is used to fill the sparse array according to the above rules, calculate the target information corresponding to the missing array elements in the sparse array, and convert the sparse array into a uniform array;
测角单元,用于对补齐后的虚拟阵列乘以窗函数后进行目标的角度计算。The angle measuring unit is used to calculate the angle of the target after multiplying the padded virtual array by the window function.
又一方面,本申请提供一种MIMO雷达信号处理终端,包括处理器和存储器,所述存储器存储有计算机程序,所述计算机程序被处理器调用执行时,实现如上所述的基于稀疏阵列的测角方法。On the other hand, the present application provides a MIMO radar signal processing terminal, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is called and executed by the processor, the sparse array-based angle measurement method as described above is implemented.
又一方面,本申请提供一种计算机可读介质,其特征在于,所述计算机可读介质中存储有计算机程序,所述计算机程序被计算机调用执行时,实现如上所述的基于稀疏阵列的测角方法。On the other hand, the present application provides a computer-readable medium, characterized in that a computer program is stored in the computer-readable medium, and when the computer program is called and executed by a computer, the angle measurement method based on the sparse array as described above is implemented.
综上所述,本申请的有益效果有:利用已有通道的信号规律,预测空缺处的阵元信号,从而将稀疏阵列转变为近似半波长的间距均匀阵列,通道加权后,再进行目标测角计算,通常情况,测角是将各个通道的目标信号进行DBF计算等,利用本申请方法后,目标信号计算结果主峰光滑连续,单一目标时有且仅有一个极大值点,该极大值点且是最大值点,判断简单清晰,其他极大值点为系统性噪声,强度稳定且与主峰有较大差异。未采用本申请方法时,DBF计算后,单一目标时主峰上存在多个极大值点,多个极大值点相差不大,容易将一个目标识别成多个目标,或者在测量两个以上目标时造成混乱。In summary, the beneficial effects of the present application are as follows: using the signal law of the existing channels to predict the array element signals at the vacant positions, thereby transforming the sparse array into a uniform array with a spacing of approximately half a wavelength, and after the channels are weighted, the target angle measurement calculation is performed. Normally, the angle measurement is to perform DBF calculation on the target signals of each channel, etc. After using the method of the present application, the main peak of the target signal calculation result is smooth and continuous, and there is only one maximum point for a single target, and this maximum point is also the maximum value point, and the judgment is simple and clear. Other maximum points are systematic noise, and the intensity is stable and has a large difference from the main peak. When the method of the present application is not used, after the DBF calculation, there are multiple maximum points on the main peak for a single target, and the multiple maximum points are not much different, which makes it easy to identify one target as multiple targets, or cause confusion when measuring more than two targets.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本申请一具体实施例中天线的虚拟阵列示意图;FIG1 is a schematic diagram of a virtual array of antennas in a specific embodiment of the present application;
图2是本申请一具体实施例中雷达天线测角原理示意图;FIG2 is a schematic diagram of the angle measurement principle of a radar antenna in a specific embodiment of the present application;
图3是本申请一具体实施例中虚拟阵列对于缺失阵列补零、DBF计算结果示意图;FIG3 is a schematic diagram of a virtual array filling zeros for a missing array and DBF calculation results in a specific embodiment of the present application;
图4是本申请一具体实施例中虚拟阵列对于缺失阵列补零后加窗函数、DBF计算结果示意图;FIG4 is a schematic diagram of a window function and DBF calculation result after a virtual array fills a missing array with zeros in a specific embodiment of the present application;
图5是本申请一具体实施例中虚拟阵列相位值示意图;FIG5 is a schematic diagram of a virtual array phase value in a specific embodiment of the present application;
图6是本申请一具体实施例中对虚拟阵列缺失阵元补全后、加窗函数、DBF计算结果示意图;FIG6 is a schematic diagram of a window function and DBF calculation result after missing elements of a virtual array are completed in a specific embodiment of the present application;
图7是本申请一具体实施例中一种基于稀疏阵列的测角方法的步骤示意图。FIG. 7 is a schematic diagram of the steps of an angle measurement method based on a sparse array in a specific embodiment of the present application.
具体实施方式DETAILED DESCRIPTION
下面结合附图详细说明本申请的具体实施方式。The specific implementation of the present application is described in detail below with reference to the accompanying drawings.
本申请一具体实施例提供一种基于稀疏阵列的测角方法,如图7,包括以下步骤:A specific embodiment of the present application provides an angle measurement method based on a sparse array, as shown in FIG7 , comprising the following steps:
S1:构建MIMO雷达虚拟稀疏阵列,其中,稀疏阵列中,包括若干连续且间距相同的均匀阵元,其他阵元为稀疏阵元,稀疏阵元的间距是均匀阵元间距的整数倍;设均匀阵元的间距为d,稀疏阵列中,均匀阵元的阵元间距d为半波长。S1: Construct a MIMO radar virtual sparse array, wherein the sparse array includes a number of continuous uniform array elements with the same spacing, and the other array elements are sparse array elements, and the spacing of the sparse array elements is an integer multiple of the spacing of the uniform array elements; let the spacing of the uniform array elements be d, and in the sparse array, the array element spacing d of the uniform array elements is half a wavelength.
第一个阵元到最后一个阵元的距离称为口径。The distance from the first array element to the last array element is called the aperture.
S2:取出均匀阵元获得的目标信息,计算目标信号的幅度和相位值,得出不同阵元对应的目标相位连续线性变化规律;获得目标相位连续线性变化规律还包括:计算均匀阵元中相邻阵元的平均相位差。S2: taking out the target information obtained by the uniform array element, calculating the amplitude and phase value of the target signal, and obtaining the continuous linear change law of the target phase corresponding to different array elements; obtaining the continuous linear change law of the target phase also includes: calculating the average phase difference of adjacent array elements in the uniform array element.
S3:根据上述规律对稀疏阵列进行补齐,计算稀疏阵列中缺失阵元对应的目标信息,将稀疏阵列转换为均匀阵列;缺失阵元的获取步骤为:稀疏阵列和间距相同口径也相同的均匀阵列相比,稀疏阵列缺少的阵元即为缺失阵元。S3: Completing the sparse array according to the above rules, calculating the target information corresponding to the missing elements in the sparse array, and converting the sparse array into a uniform array; the step of obtaining the missing elements is: comparing the sparse array with a uniform array with the same spacing and the same caliber, the missing elements in the sparse array are the missing elements.
S4:将补齐后的虚拟阵列乘以窗函数后进行目标的角度计算。具体的,利用泰勒加权对补齐后的虚拟阵列进行处理。S4: multiplying the padded virtual array by the window function to calculate the angle of the target. Specifically, Taylor weighting is used to process the padded virtual array.
以下以一个具体应用场景对本实施例所提方法进行详细说明。The method proposed in this embodiment is described in detail below using a specific application scenario.
该场景中,以具有3个发射天线和4个接收天线的MIMO雷达为例,接收天线的间距为半个波长即0.5λ,所以接收天线的坐标为(0,0),(0.5λ,0),(λ,0),(1.5λ,0),发射天线的坐标为(0, 8λ),(2λ, 8λ),(8λ, 8λ)。In this scenario, a MIMO radar with three transmitting antennas and four receiving antennas is taken as an example. The spacing between the receiving antennas is half a wavelength, i.e., 0.5λ. Therefore, the coordinates of the receiving antennas are (0, 0), (0.5λ, 0), (λ, 0), (1.5λ, 0), and the coordinates of the transmitting antennas are (0, 8λ), (2λ, 8λ), (8λ, 8λ).
采用MIMO(multiple input multiple output)技术,虚拟天线阵列为12个天线阵元,如图1所示,图1中黑色实心点为天虚拟阵列中的天线阵元。坐标依次为(0,0),(0.5λ,0),(λ,0),(1.5λ,0),(2λ,0),(2.5λ,0),(3λ,0),(3.5λ,0),(8λ,0),(8.5λ,0),(9λ,0),(9.5λ,0)。Using MIMO (multiple input multiple output) technology, the virtual antenna array consists of 12 antenna elements, as shown in Figure 1. The black solid points in Figure 1 are the antenna elements in the virtual antenna array. The coordinates are (0, 0), (0.5λ, 0), (λ, 0), (1.5λ, 0), (2λ, 0), (2.5λ, 0), (3λ, 0), (3.5λ, 0), (8λ, 0), (8.5λ, 0), (9λ, 0), and (9.5λ, 0).
当目标的距离远大于远场条件时,目标到各个接收天线的角度θ认为近似一样。如图2所示,R1,R2,R3,R4为不同的接收天线,箭头方向为目标返回的信号路径方向,Δd为信号的路程差值,各个接收天线信号的相位差即为Δd/λ, λ为载频的波长。又因为Δd=Lsinθ,L为虚拟阵元间距,即各个接收天线信号之间的相位差为Lsinθ/λ。目标角度一定的情形下,间距相同接收天线之间信号信号相位差一样。同时因为目标到接收的距离相对较远,微小距离差异,信号幅度几乎一样。由此可以推导出相同间距相邻位置处接收天线的幅度和相位。When the distance of the target is much greater than the far-field condition, the angle θ from the target to each receiving antenna is considered to be approximately the same. As shown in Figure 2, R1, R2, R3, and R4 are different receiving antennas, the direction of the arrow is the direction of the signal path returned by the target, Δd is the distance difference of the signal, and the phase difference of the signals of each receiving antenna is Δd/λ, λ is the wavelength of the carrier frequency. And because Δd=Lsinθ, L is the virtual array element spacing, that is, the phase difference between the signals of each receiving antenna is Lsinθ/λ. When the target angle is constant, the phase difference of the signals between the receiving antennas with the same spacing is the same. At the same time, because the distance from the target to the receiver is relatively far, the signal amplitude is almost the same with a small distance difference. From this, the amplitude and phase of the receiving antennas at adjacent positions with the same spacing can be derived.
对图1所示的缺失阵元,进行补零,并进行DBF(Digital Beamforming)计算,结果如图3所示,单一目标会出现多个峰值,无法判断目标For the missing array elements shown in Figure 1, zero padding is performed and DBF (Digital Beamforming) calculation is performed. The result is shown in Figure 3. A single target will have multiple peaks, and the target cannot be determined.
对图1所示的缺失阵元,进行补零,并进行DBF(Digital Beamforming)计算,并加权后,结果如图4所示,效果改善明显,但仍旧达不到预期。For the missing array elements shown in Figure 1, zero padding is performed, DBF (Digital Beamforming) calculation is performed, and weighting is performed. The result is shown in Figure 4. The effect is significantly improved, but still does not meet expectations.
假设目标的坐标为(10,50),假定目标的回波信号模值为1,依据目标和接收天线虚拟阵列中阵元距离关系,计算目标的回波信号如下:Assuming the coordinates of the target are (10,50), and assuming the modulus of the target's echo signal is 1, the target's echo signal is calculated based on the distance relationship between the target and the array elements in the virtual array of the receiving antenna as follows:
0.7191 - 0.6949i,0.9884 - 0.1517i,0.8944 + 0.4472i,0.4718 + 0.8817i,-0.1256 + 0.9921i,-0.6757 + 0.7372i,-0.9774 + 0.2113i,-0.9199 - 0.3921i, -0.9414 + 0.3374i,-0.9633 - 0.2686i,-0.6311 - 0.7757i,-0.0670 - 0.9978i。0.7191 - 0.6949i, 0.9884 - 0.1517i, 0.8944 + 0.4472i, 0.4718 + 0.8817i, -0.1256 + 0.9921i, -0.6757 + 0.7372i, -0.9774 + 0.2113i, -0.9199 -0.3921i, -0.9414 + 0.3374i, -0.9633 - 0.2686i, -0.6311 - 0.7757i, -0.0670 - 0.9978i.
取目标信号的相位值,列出相位值如图5所示,由于信号连续变化后会超过正负π,所以会出现折叠,虚线框中是根据相位规律,推导出的相位值。Take the phase value of the target signal and list the phase values as shown in Figure 5. Since the signal will exceed positive and negative π after continuous changes, folding will occur. The dotted box is the phase value derived according to the phase law.
根据推算出的相位值和信号的模值,补全目标信号如下:According to the calculated phase value and the modulus value of the signal, the target signal is completed as follows:
0.7191 - 0.6949i,0.9884 - 0.1517i,0.8944 + 0.4472i,0.4718 + 0.8817i,-0.1256 + 0.9921i,-0.6757 + 0.7372i,-0.9774 + 0.2113i,-0.9199 - 0.3921i,-0.5248 - 0.8512i,0.0635 - 0.9980i,0.6284 - 0.7779i,0.9623 - 0.2720i,0.9434 +0.3316i,0.5784 + 0.8158i,0.0008 + 1.0000i,-0.5770 + 0.8168i,-0.9414 +0.3374i,-0.9633 - 0.2686i,-0.6311 - 0.7757i,-0.0670 - 0.9978i。0.7191 - 0.6949i, 0.9884 - 0.1517i, 0.8944 + 0.4472i, 0.4718 + 0.8817i, -0.1256 + 0.9921i, -0.6757 + 0.7372i, -0.9774 + 0.2113i, -0.9199 - 0.3921i, -0.5248 - 0.8512i, 0.0635 - 0.9980i, 0.6284 - 0.7779i, 0.9623 - 0.2720i, 0.9434 + 0.3316i, 0.5784 + 0.8158i, 0.0008 + 1.0000i, -0.5770 + 0.8168i, -0.9414 +0.3374i, -0.9633 - 0.2686i, -0.6311 - 0.7757i, -0.0670 - 0.9978i.
对阵列进行补全后,对20个通道加如下权值0.2220,0.3086,0.4670,0.6737,0.9034,1.1346,1.3498,1.5330,1.6679,1.7400,1.7400,1.6679,1.5330,1.3498,1.1346,0.9034,0.6737,0.4670,0.3086,0.2220。然后用DBF计算,得到测角结果,如图6,可见测角效果明显提高。After completing the array, the following weights are added to the 20 channels: 0.2220, 0.3086, 0.4670, 0.6737, 0.9034, 1.1346, 1.3498, 1.5330, 1.6679, 1.7400, 1.7400, 1.6679, 1.5330, 1.3498, 1.1346, 0.9034, 0.6737, 0.4670, 0.3086, 0.2220. Then DBF is used to calculate and get the angle measurement results, as shown in Figure 6. It can be seen that the angle measurement effect is significantly improved.
由于实际雷达测角过程中,就算经过校准,每个阵元得到的相位依然存在噪声等误差,所以需要连续多个间距一样的阵元,获取平均相位差,以便保证预测的准确性,同时其他稀疏阵元可以用于验证推测值,保证补值准确。In the actual radar angle measurement process, even after calibration, the phase obtained by each array element still has errors such as noise, so multiple array elements with the same spacing are required to obtain the average phase difference in order to ensure the accuracy of the prediction. At the same time, other sparse array elements can be used to verify the estimated value to ensure the accuracy of the supplementary value.
本申请又一具体实施例提供一种稀疏阵列的测角装置,包括:Another specific embodiment of the present application provides a sparse array angle measuring device, comprising:
稀疏阵列构建单元,用于构建MIMO雷达虚拟稀疏阵列,其中,稀疏阵列中,包括若干连续且间距相同的均匀阵元,其他阵元为稀疏阵元,稀疏阵元的间距是均匀阵元间距的整数倍;A sparse array construction unit is used to construct a MIMO radar virtual sparse array, wherein the sparse array includes a number of continuous uniform array elements with the same spacing, and the other array elements are sparse array elements, and the spacing of the sparse array elements is an integer multiple of the spacing of the uniform array elements;
拟合单元,用于取出均匀阵元获得的目标信息,计算目标信号的幅度和相位值,得出不同阵元对应的目标相位连续线性变化规律;The fitting unit is used to extract the target information obtained by the uniform array element, calculate the amplitude and phase value of the target signal, and obtain the continuous linear change law of the target phase corresponding to different array elements;
补齐单元,用于根据上述规律对稀疏阵列进行补齐,计算稀疏阵列中缺失阵元对应的目标信息,将稀疏阵列转换为均匀阵列;A filling unit is used to fill the sparse array according to the above rules, calculate the target information corresponding to the missing array elements in the sparse array, and convert the sparse array into a uniform array;
测角单元,用于对补齐后的虚拟阵列乘以窗函数后进行目标的角度计算。The angle measuring unit is used to calculate the angle of the target after multiplying the padded virtual array by the window function.
本申请又一具体实施例提供一种MIMO雷达信号处理终端,包括处理器和存储器,所述存储器存储有计算机程序,所述计算机程序被处理器调用执行时,实现如上所述的基于稀疏阵列的测角方法。Another specific embodiment of the present application provides a MIMO radar signal processing terminal, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is called and executed by the processor, the sparse array-based angle measurement method as described above is implemented.
本申请又一具体实施例提供一种计算机可读介质,其特征在于,所述计算机可读介质中存储有计算机程序,所述计算机程序被计算机调用执行时,实现如上所述的基于稀疏阵列的测角方法。Another specific embodiment of the present application provides a computer-readable medium, characterized in that a computer program is stored in the computer-readable medium, and when the computer program is called and executed by a computer, the angle measurement method based on the sparse array as described above is implemented.
以上所述的仅是本申请的优选实施方式,应当指出,对于本领域的普通技术人员来说,在不脱离本申请创造构思的前提下,还可以做出若干变形和改进,这些都属于本申请的保护范围。The above is only a preferred implementation of the present application. It should be pointed out that a person skilled in the art can make several modifications and improvements without departing from the inventive concept of the present application, and these all fall within the scope of protection of the present application.
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