CN111220942B - Near-field calibration method for amplitude-phase consistency of receiving transducer array - Google Patents

Abstract

The invention provides a near-field calibration method for amplitude-phase consistency of a receiving transducer array. Firstly, incident signals collected in different directions by a receiving array on a rotary table are subjected to focused beam forming processing to obtain a series of direction-of-arrival estimates; then, establishing a covariance matrix of the received signals in a frequency domain, and establishing an amplitude-phase consistency error estimation model; selecting small-angle incident angle signals, respectively assuming the neighborhood angles as ideal incident angles, and estimating error estimation results corresponding to angles in the neighborhood according to an amplitude-phase consistency error estimation model; and finally, compensating the array according to the error result, selecting data of two known angle intervals according to preset parameters of a test, evaluating the estimated deviation of the angle intervals, determining the amplitude-phase consistency error according to the minimum value of the deviation, and finishing calibration. The invention can improve the amplitude-phase consistency and direction-finding performance of the array without an auxiliary information source.

Description

A Near Field Calibration Method for Amplitude and Phase Consistency of Receive Transducer Array

technical field

The invention relates to a method for calibrating and measuring an array antenna, in particular to a near-field calibration method for receiving transducer array amplitude and phase consistency.

Background technique

In signal direction of arrival estimation, it is necessary to use the beamforming method to scan the incoming wave azimuth, and the direction finding performance of some beamforming algorithms greatly depends on the amplitude and phase information between the array elements. Due to the long-term use of the receiving transducer array, the array The difference in element processing technology and environmental changes will inevitably lead to the inconsistency of the amplitude and phase between the array elements of the underwater acoustic transducer, which will further lead to the decrease of the direction finding accuracy and the increase of the side lobe level of the beam pattern.

The existing calibration methods for the amplitude-phase consistency of receiving transducer arrays usually need to obtain azimuth information with the help of auxiliary sources, and most of them use a plane wave assumption model. However, the passive calibration method with the help of auxiliary sources is more likely to introduce errors, and the hypothetical model of the plane wave is only applicable to the far field. Dimensions have high requirements, which are often difficult to meet. In addition, due to the large number of sampling points of the time-domain signal in one period, when it comes to covariance matrix calculations, the existing calibration methods are mostly performed in the time domain, and the amount of calculation is relatively large.

Near-field focused beamforming is based on the spherical wave assumption and can focus on the position of the sound source. Compared with the plane wave assumption model, it can ensure accurate direction finding results when the distance from the emitting sound source is relatively close, which provides convenience for measurement conditions. Especially when calibrating a transducer array with a large aperture and a large number of elements, it has natural advantages over traditional calibration methods.

Contents of the invention

The purpose of the present invention is to provide a near-field calibration method for the amplitude-phase consistency of the receiving transducer array that can improve the amplitude-phase consistency of the receiving transducer array under the condition of limited calibration site size and no auxiliary signal source.

The purpose of the present invention is achieved like this:

(1) Establish a near-field focused beamforming model. The incident signals collected by the receiving array on the rotary platform in different directions are processed by focused beamforming to obtain a series of direction-of-arrival estimates;

(2) Establish the received signal covariance matrix in the frequency domain, and establish the amplitude-phase consistency error estimation model;

(3) Select the small-angle incident angle signal, set its neighborhood angles as ideal incident angles, and estimate the amplitude-phase error corresponding to the angle in the neighborhood according to the amplitude-phase consistency error estimation model;

(4) Compensate the array according to the error result, select the data of two known angular intervals according to the preset parameters, evaluate the deviation of the estimated angular interval, determine the amplitude and phase consistency error according to the minimum value of the deviation, and complete the calibration.

The present invention may also include:

1. The near-field focusing model described is:

为在第n个采样时刻下，接收信号在阵元m与参考阵元之间的相位差。Among them, V(θ) is the beam output corresponding to the incident direction θ, M is the number of array elements to be estimated, x _m is the signal received by the mth array element,

is the phase difference of the received signal between element m and the reference element at the nth sampling moment.

2. Step (2) specifically includes:

Establish the magnitude-phase consistency error estimation model, Γ and Φ are respectively used as the magnitude and phase vectors of the array:

Γ=diag[ρ ₁ ,ρ ₂ ,…,ρ _M ]

分别为第m个阵元的幅度和相位向量，并且ρ₁＝1,

where ρ _m and

are the magnitude and phase vectors of the mth array element respectively, and ρ ₁ =1,

Then the ideal received signal and the received signal with errors are expressed as:

X ₀ (t)=AS(t)+N(t)

X(t)=ΓΦ(AS(t)+N(t))

S(t)＝[s ₁ (t),s ₂ (t),…,s _M (t)] ^T (s ₁ (t)=s ₂ (t),…,=s _M (t))

N(t)＝[n ₁ (t),n ₂ (t),...,n _M (t)] ^T

Among them, X ⁰ (t) and X(t) are the ideal received signal and the actual received signal matrix; S(t) is the transmitted signal matrix composed of the source transmitted signal, and N(t) is the noise composition received by each array element The noise matrix of , where the noise is set to Gaussian white noise;

The ideal signal X ⁰ (t) and the actual signal X(t) received by each array element are transformed into the frequency domain by Fourier transform to obtain X ⁰ _fre (f) and X _fre (f), and the spectrum peaks closest to zero frequency are extracted respectively X ⁰ _P and X _P :

X _fre (f)＝[x ₁ (f), x ₂ (f),…, x _M (f)] ^T

X _P ＝[P ₁ ,P ₂ ,…,P _M ] ^T

和R_X：And construct the ideal covariance matrix and the actual covariance matrix

and R _x :

为：The amplitude-phase consistency error matrix Ω and the amplitude-phase consistency error ρ of each array element and

for:

3. In step (3), select the received signal with a small incident angle of θ ₀ , and traverse K angles in the neighborhood in the neighborhood with an angle range of ε, so that the ideal angle θ _s satisfies θ _s (k)∈ (θ ₀ -ε,θ ₀ +ε), calculate the amplitude-phase consistency error Ω(k) of each angle in the corresponding neighborhood.

4. Step (4) is specifically:

分别补偿阵列，选择两入射角间隔为Δθ的接收信号，其中参数Δθ₀根据回转台获得，分别估计这两组信号的波达方向并计算其角度间隔Δθ(k)，考察对角度间隔估计的偏差e(k)＝|Δθ₀-Δθ(k)|，若在角度邻域(θ₀-ε,θ₀+ε)内存在唯一极小值,则

理想角度为

换能器阵列各阵元的幅相误差为

和

For each channel amplitude error ρ _m (k) and phase error of group k

Compensate the array separately, select two received signals whose incident angle interval is Δθ, and the parameter Δθ ₀ is obtained according to the turntable, estimate the direction of arrival of these two groups of signals and calculate their angular interval Δθ(k), and investigate the estimation of the angular interval Deviation e(k)=|Δθ ₀ -Δθ(k)|, if there is a unique minimum value in the angle neighborhood (θ ₀ -ε,θ ₀ +ε), then

The ideal angle is

The amplitude and phase errors of each element of the transducer array are

and

Compared with the prior art, the invention has the beneficial effects of using the angle interval information provided by the turntable for calibration without the need of an auxiliary signal source, and the test is simple and practical. Compared with the plane wave assumption model, the near-field focused beamforming processing method based on the spherical wave assumption is more accurate in estimation results, which can overcome the problem that the traditional calibration method is difficult to meet the size of the calibration site, and has strong versatility. In addition, the calibration method of the present invention can complete the construction of the covariance matrix in a snapshot in the frequency domain, which effectively reduces the amount of calculation, and the frequency domain processing enables the signal to extract effective information without low-pass filtering after demodulation .

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is a schematic diagram of angular interval estimation deviation;

Figure 3a is a schematic diagram before and after amplitude calibration between array elements;

Figure 3b is a schematic diagram before and after phase calibration between array elements;

Fig. 4 is the beamforming diagram before and after calibration of the amplitude-phase consistency error.

detailed description

The following examples describe the present invention in more detail.

1 to 4, the receiving transducer array amplitude-phase consistency near-field calibration method of the present invention mainly includes the following steps:

(1) The incident signals collected by the receiving array on the turntable in different directions are processed by focused beamforming to obtain a series of direction-of-arrival estimates;

(2) Establish the received signal covariance matrix in the frequency domain, and establish the amplitude-phase consistency error estimation model;

(3) Select the small-angle incident angle signal, assume its neighborhood angles as ideal incident angles, and estimate the amplitude-phase error corresponding to the angle in the neighborhood according to the amplitude-phase consistency error estimation model;

(4) Compensate the array according to the error result, select the data of two known angular intervals according to the test preset parameters, evaluate the deviation of the estimated angular interval, determine the amplitude-phase consistency error according to the minimum value of the deviation, and complete the calibration.

As the carrier of the receiving array to be calibrated, the turntable can collect signals incident in different directions, obtain the incident angle interval of any two sets of sampling data, estimate the direction of arrival of multiple sets of data through focused beamforming, and select the data with small incident angles Traversing its angular neighborhood, using the covariance matrix algorithm to calculate the amplitude and phase errors, investigating the estimated deviation of the compensated array for data with two known incident angle intervals, adjusting the neighborhood range through the existence of the deviation minimum, and finally determining Amplitude-phase consistency error, the calibration process is shown in Figure 1.

The near-field focusing model involved in step (1) is:

为在第n个采样时刻下，接收信号在阵元m与参考阵元之间的相位差；Among them, V(θ) is the beam output corresponding to the incident direction θ, M is the number of array elements to be estimated, x _m is the signal received by the mth array element,

is the phase difference of the received signal between element m and the reference element at the nth sampling moment;

为：The near-field focusing model established above is based on the spherical wave assumption. Unlike the plane wave, it is necessary to perform phase compensation for each sampling moment of the received signal to achieve focusing.

for:

Where d _m is the distance between the mth array element and the reference array element, λ is the wavelength of the sound wave, and r _n is the corresponding focusing distance at the nth sampling moment.

Step (2) Establish the amplitude-phase consistency error estimation model, Γ and Φ are used as the amplitude-phase vectors of the array respectively:

Γ=diag[ρ ₁ ,ρ ₂ ,…,ρ _M ]

分别为第m个阵元的幅度和相位向量，并且有ρ₁＝1,

where ρ _m and

are the magnitude and phase vectors of the mth array element respectively, and have ρ ₁ =1,

Then the ideal received signal and the received signal with errors can be expressed as:

X ₀ (t)=AS(t)+N(t)

X(t)=ΓΦ(AS(t)+N(t))

S(t)＝[s ₁ (t),s ₂ (t),…,s _M (t)] ^T (s ₁ (t)=s ₂ (t),…,=s _M (t))

N(t)＝[n ₁ (t),n ₂ (t),...,n _M (t)] ^T

Among them, X ⁰ (t) and X(t) are matrices based on the ideal received signal and the actual received signal. S(t) is the transmitted signal matrix composed of the signal transmitted by the source, and N(t) is the noise matrix composed of the noise received by each array element, where the noise is assumed to be Gaussian white noise;

The ideal signal X ⁰ (t) received by each array element (the amplitude and phase consistency error of each array element is consistent) and the actual signal X(t) are transformed into the frequency domain by Fourier transform to obtain X ⁰ _fre (f) and X _fre ( f), respectively extracting the spectrum peaks X ⁰ _P and X _P closest to the zero frequency:

X _fre (f)＝[x ₁ (f), x ₂ (f),…, x _M (f)] ^T

X _P ＝[P ₁ ,P ₂ ,…,P _M ] ^T

和R_X：And construct the ideal covariance matrix and the actual covariance matrix

and R _x :

为：The amplitude-phase consistency error matrix Ω and the amplitude-phase consistency error ρ of each array element and

for:

In step (3), select the received signal with a small incident angle of θ ₀ , and traverse K angles in the neighborhood in the neighborhood of angle range ε, so that the ideal angle θ _s satisfies θ _s (k)∈(θ ₀ -ε,θ ₀ +ε), calculate the amplitude-phase consistency error Ω(k) of each angle in the corresponding neighborhood.

分别补偿阵列，选择两入射角间隔为Δθ的接收信号，其中参数Δθ₀根据回转台获得，分别估计这两组信号的波达方向并计算其角度间隔Δθ(k)，考察对角度间隔估计的偏差e(k)＝|Δθ₀-Δθ(k)|，若在角度邻域(θ₀-ε,θ₀+ε)内存在唯一极小值,则

理想角度为

换能器阵列各阵元的幅相误差为

和

Step (4) for each channel amplitude error ρ _m (k) and phase error of group k

Compensate the array separately, select two received signals whose incident angle interval is Δθ, and the parameter Δθ ₀ is obtained according to the turntable, estimate the direction of arrival of these two groups of signals and calculate their angular interval Δθ(k), and investigate the estimation of the angular interval Deviation e(k)=|Δθ ₀ -Δθ(k)|, if there is a unique minimum value in the angle neighborhood (θ ₀ -ε,θ ₀ +ε), then

The ideal angle is

The amplitude and phase errors of each element of the transducer array are

and

存在幅相一致性误差情况下使得第150组数据的波束图的旁瓣级升高并导致波达方向估计偏差为0.9°。以0.9°对附近邻域进行搜索，由于设定的理想值为0.8°，则选择邻域为0.7°～0.9°进行遍历，每次遍历增量为0.01°，共21个角度，通过幅相一致性误差估计模型计算得到21组阵元间幅度相位误差，根据21组幅相误差对阵列补偿前，为结果更加明显应选择入射角较大的数据，适当选择两角度间隔为24°的两组数据，选择第100组数据和第140组数据，在每一组幅相误差补偿后，记录对两组数据的波达方向估计结果。经过处理，得到对应不同组数据的角度间隔估计误差。由图2可知，第11组幅相误差对阵列补偿后具有最佳的估计结果，对应的入射角度为0.8°与理想角度参考值一致，并且在邻域内具有唯一的极小值，因此阵列的幅度相位误差可以确定，幅相误差真实值与估计值的对比如图3a和图3b，阵列校准前后对第150组数据进行处理得到的波束图如图4。经过校准，阵列的测向精度得到了提高，波束图的旁瓣得到了抑制。The simulation test analysis of the near-field calibration method for the amplitude-phase consistency of the receiving transducer array is carried out. The array to be calibrated is a uniform linear array with the number of elements M=100, and the distance between elements d=3.75mm. Since the array is installed in The incident angle interval between each data is known on the turntable, the set rotation range of the turntable is -90°～90°, the rotation speed is 0.6°/s, the distance between the signal source and the receiving array is 10m in the near-field range, and the transmission High-frequency narrow-band pulse signal, in which the center frequency of the transmitted signal is 200kHz, and the pulse width is 0.1ms. The receiving array receives the signal at the same time as the signal is transmitted, and the cycle is 1s. There are 300 sets of received signals in total, and the angular interval between each adjacent two sets of data is 0.6°, where the incident angle of the 150th set of data is the ideal reference value and is set to 0.8°. Introducing amplitude and phase errors, the amplitude error of each array element satisfies ρ～N(1,0.3 ² ), and the phase error satisfies

In the case of amplitude-phase consistency error, the sidelobe level of the beam pattern of the 150th set of data increases and causes a deviation of 0.9° in the estimated direction of arrival. Search the nearby neighborhood at 0.9°. Since the ideal value set is 0.8°, select the neighborhood to traverse from 0.7° to 0.9°. Each traverse increment is 0.01°, a total of 21 angles, through the amplitude and phase The consistency error estimation model calculates the amplitude and phase errors between 21 groups of array elements. Before the array is compensated according to the 21 groups of amplitude and phase errors, the data with a larger incident angle should be selected for the result to be more obvious, and the two angles with an interval of 24° should be selected appropriately. Group data, select the 100th group of data and the 140th group of data, after each group of amplitude and phase error compensation, record the DOA estimation results of the two groups of data. After processing, angle interval estimation errors corresponding to different sets of data are obtained. It can be seen from Figure 2 that the 11th group of amplitude and phase errors has the best estimation result after array compensation, and the corresponding incident angle is 0.8°, which is consistent with the ideal angle reference value, and has a unique minimum value in the neighborhood, so the array’s The amplitude and phase error can be determined. The comparison between the real value and the estimated value of the amplitude and phase error is shown in Figure 3a and Figure 3b. The beam pattern obtained by processing the 150th set of data before and after array calibration is shown in Figure 4. After calibration, the direction finding accuracy of the array is improved and the side lobes of the beam pattern are suppressed.

In summary, the present invention provides a near-field calibration method for amplitude-phase consistency of a receiving transducer array. Calibration can be completed without an auxiliary source, especially when calibrating a transducer array with a large aperture and a large number of elements, the near-field spherical wave model used can overcome the current situation that the size of the calibration site is difficult to meet the measurement requirements . Constructing a covariance matrix in the frequency domain simplifies the frequency modulation steps and calculation complexity, and the invention improves the amplitude-phase consistency and direction-finding performance of the array, is easy to operate, and is suitable for engineering applications.

Claims (4)

1. A near field calibration method for receiving the amplitude-phase consistency of a transducer array is characterized by comprising the following steps:

(1) Establishing a near-field focusing beam forming model, and carrying out focusing beam forming processing on incident signals acquired by a receiving array on a rotary table in different directions to obtain a series of direction-of-arrival estimations;

(2) Establishing a covariance matrix of a received signal in a frequency domain, and establishing an amplitude-phase consistency error estimation model;

establishing an amplitude-phase consistency error estimation model, wherein gamma and phi respectively serve as amplitude-phase vectors of the array and comprise:

Γ＝diag[ρ ₁ ,ρ ₂ ,…,ρ _M ]

where ρ is _m And

amplitude and phase vectors of the m-th array element, respectively, and p ₁ ＝1,

The ideal received signal and the received signal with errors are expressed as:

X ₀ (t)＝AS(t)+N(t)

X(t)＝ΓΦ(AS(t)+N(t))

S(t)＝[s ₁ (t),s ₂ (t),…,s _M (t)] ^T (s ₁ (t)＝s ₂ (t),…,＝s _M (t))

N(t)＝[n ₁ (t),n ₂ (t),…,n _M (t)] ^T

wherein, X ⁰ (t) and X (t) are matrices of ideal received signals and actual received signals; s (t) is a transmitting signal matrix formed by transmitting signals by an information source, N (t) is a noise matrix formed by noise received by each array element, wherein the noise is Gaussian white noise;

ideal signal X received by each array element ⁰ (t) Fourier transforming the actual signal X (t) to a frequency domain to obtain X ⁰ _fre (f) And X _fre (f) Respectively extracting the nearest frequency spectrum peak value X from the zero frequency ⁰ _P And X _P ：

X _fre (f)＝[x ₁ (f),x ₂ (f),…,x _M (f)] ^T

X _P ＝[P ₁ ,P ₂ ,…,P _M ] ^T

And constructing an ideal covariance matrix and an actual covariance matrix

And R _X ：

Amplitude-phase consistency error matrix omega and amplitude-phase consistency errors rho and

comprises the following steps:

(3) Selecting small-angle incident angle signals, setting the neighborhood angles of the small-angle incident angle signals as ideal incident angles, and estimating the amplitude-phase error corresponding to the angles in the neighborhood according to an amplitude-phase consistency error estimation model;

(4) And according to the error result compensation array, selecting data of two known angle intervals according to preset parameters, evaluating the deviation estimated for the angle intervals, determining amplitude-phase consistency errors according to the minimum deviation value, and finishing calibration.

2. The method of claim 1, wherein the near field focused beam forming model comprises:

wherein V (theta) is the beam output corresponding to the incident direction theta, M is the array element number of the array to be estimated, and x _m For the signal received by the m-th array element,

is the phase difference of the received signal between the array element m and the reference array element at the nth sampling time.

3. The method of claim 2 wherein in step (3) the angle of incidence is selected to be a small angle θ ₀ Traversing K angles in the neighborhood with the angle range of epsilon to ensure that the ideal angle theta _s Satisfies theta _s (k)∈(θ ₀ -ε,θ ₀ + epsilon), the amplitude-phase consistency error omega (k) for each angle in the neighborhood is calculated.

4. The method of claim 3, wherein the step (4) is specifically as follows:

for k groups of channel amplitude errors rho _m (k) And phase error

Respectively compensating the arrays, selecting two incidence angles with a delta theta interval ₀ In which the parameter delta theta ₀ Obtained from the rotary table, the directions of arrival of the two sets of signals are estimated, the angular interval delta theta (k) is calculated, and the deviation e (k) = | delta theta (k) of the angular interval estimation is considered ₀ - Δ θ (k) | if in angular neighborhood (θ) ₀ -ε,θ ₀ + ε) has a unique minimum value, then

The ideal angle is

The amplitude-phase error of each array element of the transducer array is

And

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