阅读说明：本技术 一种基于泰勒展开的数字阵列单脉冲测角方法 (Digital array monopulse angle measurement method based on Taylor expansion ) 是由 陈新亮 梁振楠 刘泉华 盖季妤 曾涛 于 2020-05-25 设计创作，主要内容包括：本发明公开了一种基于泰勒展开的数字阵列单脉冲测角方法,该方法充分发挥数字阵列化处理方式灵活,能够对各个阵元的输出进行任意加权处理的特点,基于泰勒展开原理对和、差波束加权矢量进行优化设计,从而获得比传统单脉冲测角方法更加陡峭的鉴角曲线(单脉冲比),有效提升了目标角度测量精度。(The invention discloses a digital array monopulse angle measurement method based on Taylor expansion, which fully exerts the characteristics that the digital array processing mode is flexible, and the output of each array element can be subjected to arbitrary weighting processing, and carries out optimization design on sum and difference beam weighting vectors based on the Taylor expansion principle, thereby obtaining a steeper angle discrimination curve (monopulse ratio) than that of the traditional monopulse angle measurement method, and effectively improving the target angle measurement precision.)

1. A digital array monopulse angular measurement method for Taylor expansion is characterized by comprising the following steps:

step 1, assuming that the phased array radar is a one-dimensional linear array, wherein antenna units are non-uniformly arranged, and all the antenna units are isotropic array elements;

step 2, assuming a certain angle theta at the far field_tNext there is a desired signal s_t(t) obtaining the receiving signal of the antenna array by incidence of plane wave:

x＝a(θ_t)s_t+n (1)

where x represents the complex vector of the echo data received by the array, a (θ)_t) Representing an array steering vector, and n represents a complex vector of Gaussian white noise;

and 3, performing guided vector Taylor expansion, specifically:

will make an angle theta_tAnd the beam pointing direction theta₀The difference is approximately zero, and the pointing angle theta of the radar beam is equal to theta according to the Taylor expansion principle₀To complete the steering vector a (theta)_t) Taylor expansion, ignoring higher order terms:

x＝(a(θ₀)+b(θ₀)(θ_t-θ₀))s_t+n (2)

wherein the content of the first and second substances,

selecting a certain weighting vector w to carry out weighting summation processing on the signals, and obtaining:

y_Drepresenting the weighted summed output signals of the array; for simplicity of operation, the weight vector w and the steering vector a (θ) of the beam center are required₀) Orthogonal, i.e. w^Ha(θ₀) Neglecting the influence of the noise term, equation (3) reduces to 0:

y_D＝w^Hb(θ₀)(θ_t-θ₀)s_t(4)

step 4, selecting a weight vector, specifically:

from the perspective of improving the estimation accuracy of the target angle, the principle of selecting the array weighting vector w is to make the output signal y after the array weighting summation_DThe signal-to-noise ratio of (a) is maximum, and the weight vector is obtained as:

step 5, estimating a signal amplitude parameter of the expected signal, specifically:

unknown signal amplitude parameter s_tEstimated by beamforming and channel signal data, and the path signal data is written as:

wherein, a^H(θ₀)a(θ_t) Is the antenna beam pointing theta₀At angle, the antenna array is at theta_tResponse at angle, approximately θ₀Response at an angle, i.e. a^H(θ₀)a(θ_t)≈a^H(θ₀)a(θ₀)；

Ignoring the effect of the noise term, equation (6) reduces to:

y_S≈a^H(θ₀)a(θ₀)s_t(7)

the amplitude parameter s_tThe estimated values of (c) are written as:

step 6, estimating a target angle, specifically:

determining an array weighting vector w and estimating a signal magnitude parameter s_tThen, formula (5) and formula (8) are substituted into formula (4), to obtain:

order to

Technical Field

The invention belongs to the technical field of angle measurement, and particularly relates to a digital array monopulse angle measurement method based on Taylor expansion.

Background

Monopulse angle measurement, also known as simultaneous beam comparison angle measurement, is an angular localization technique for a radiation source or "target" reflecting electromagnetic energy, which uses simultaneously generated "sum" and "difference" beams to measure target angles within a beam width range, and has been widely used in radar systems. The single-pulse angle measurement accuracy is derived from the root mean square error of the single-pulse sum-difference ratio and is respectively related to the signal-to-noise ratio of the echo signal, the 3dB beam width and the normalized single-pulse sum-difference ratio slope. In the design process of the phased array radar, the radar with the three parameters comprehensively considered obtains the optimal monopulse angle measurement performance, wherein the signal-to-noise ratio and the 3dB beam width of echo signals are related to a sum beam directional diagram, and the monopulse slope and the difference slope are respectively related to the sum beam directional diagram and the difference beam directional diagram. Therefore, to obtain the best single-pulse goniometric performance, the sum and difference beam patterns need to be optimized.

Conventional phased array radars obtain sum and difference beams through a single pulse sum and difference network: the outputs of the sub-arrays are added to form a sum beam, and the outputs of the left and right (or upper and lower) quadrant arrays are subtracted to form a difference beam. Obviously, a single pulse sum and difference network defines the optimum range of the sum and difference patterns. Meanwhile, the sum beam pattern is related to the radar detection performance, and the sum beam pattern determined by the antenna aperture is always kept unchanged in order to ensure the radar detection performance. Therefore, for the conventional phased array radar, the improvement of the monopulse angular measurement performance brought by optimizing the poor beam pattern is very limited.

At present, the sum and difference beams are obtained by the advanced digital array radar by replacing a single pulse sum and difference network through a digital beam forming technology, a great degree of freedom is provided for optimizing the sum and difference beam directional diagram by a digital processing mode, digital weighting processing is allowed to be carried out on the output of each sub-array, the sum and difference beams are flexibly formed, and the radar system can obtain the optimal single pulse angle measurement precision while the detection performance is ensured. Therefore, further research is needed to optimize the single-pulse sum and difference patterns so that the digital array obtains the best single-pulse angle measurement performance.

Disclosure of Invention

In view of this, the present invention provides a digital array monopulse angle measurement method for taylor expansion, which can reduce the angle measurement error and improve the angle measurement accuracy.

A digital array monopulse angle measurement method for Taylor expansion comprises the following steps:

step 1, assuming that the phased array radar is a one-dimensional linear array, wherein antenna units are non-uniformly arranged, and all the antenna units are isotropic array elements;

step 2, assuming a certain angle theta at the far field_tNext there is a desired signal s_t(t) obtaining the receiving signal of the antenna array by incidence of plane wave:

x＝a(θ_t)s_t+n (1)

where x represents the complex vector of the echo data received by the array, a (θ)_t) Representing the array steering vector, n representing the complex of Gaussian white noise

Vector quantity;

and 3, performing guided vector Taylor expansion, specifically:

will make an angle theta_tAnd the beam pointing direction theta₀The difference is approximately zero, and the pointing angle theta of the radar beam is equal to theta according to the Taylor expansion principle₀To complete the steering vector a (theta)_t) Taylor expansion, ignoring higher order terms:

x＝(a(θ₀)+b(θ₀)(θ_t-θ₀))s_t+n (2)

wherein the content of the first and second substances,

selecting a certain weighting vector w to carry out weighting summation processing on the signals, and obtaining:

y_Drepresenting the weighted summed output signals of the array; for simplicity of operation, the weight vector w and the steering vector of the beam center are required

a(θ₀) Orthogonal, i.e. w^Ha(θ₀) Neglecting the influence of the noise term, equation (3) reduces to 0:

y_D＝w^Hb(θ₀)(θ_t-θ₀)s_t(4)

step 4, selecting a weight vector, specifically:

from the angle of improving the estimation precision of the target angle, the principle of selecting the array weighting vector w is to enable the arrayThe column weighted summed output signal y_DThe signal-to-noise ratio of (a) is maximum, and the weight vector is obtained as:

step 5, estimating a signal amplitude parameter of the expected signal, specifically:

unknown signal amplitude parameter s_tEstimated by beamforming and channel signal data, and the path signal data is written as:

wherein, a^H(θ₀)a(θ_t) Is the antenna beam pointing theta₀At angle, the antenna array is at theta_tResponse at angle, approximately θ₀Response at an angle, i.e. a^H(θ₀)a(θ_t)≈a^H(θ₀)a(θ₀)；

Ignoring the effect of the noise term, equation (6) reduces to:

y_S≈a^H(θ₀)a(θ₀)s_t(7)

the amplitude parameter s_tThe estimated values of (c) are written as:

step 6, estimating a target angle, specifically:

determining an array weighting vector w and estimating a signal magnitude parameter s_tThen, formula (5) and formula (8) are substituted into formula (4), to obtain:

order toFrom top to bottomThe target angle can be estimated by the following formula:

the invention has the following beneficial effects:

according to the digital array monopulse angle measurement method based on Taylor expansion, the characteristics that a digital array processing mode is flexible and output of each array element can be subjected to arbitrary weighting processing are fully exerted, and sum and difference beam weighting vectors are optimally designed based on the Taylor expansion principle, so that a steeper angle identification curve (monopulse ratio) than that of a traditional monopulse angle measurement method is obtained, and the target angle measurement accuracy is effectively improved.

Drawings

Fig. 1 is a signal processing flow chart according to an embodiment of the present invention.

Fig. 2(a) and 2(b) are sum and difference patterns comparisons of the method of the present invention and a conventional method, respectively.

FIG. 3 is a comparison of the angle curve of the method of the present invention and the conventional method.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

Step 1, calculating relative position vectors of the antenna array. The phased array radar is assumed to be a one-dimensional linear array, the number of the antenna units is M, the antenna units are arranged in a non-uniform mode, and all the antenna units are isotropic array elements. The phase center of the m-th antenna element is denoted as d_mBalance of vector

d＝[d₁,d₂,…,d_m,…,d_M-1,d_M]^T(1)

Is the absolute position vector of the antenna element. The average value of all unit phase centers of the antenna is

Referred to as the phase center of the antenna array. The phase centers of the units of the antenna are oppositeOffset in the center of the array phase

Formed vector

Referred to as the relative position vector of the antenna elements.

And step 2, obtaining a target echo signal. Assume a certain angle theta in the far field_tNext there is a desired signal s_t(t) incident as a plane wave, the m-th antenna element receiving a signal of

x_m(t)＝s_t(t-τ_m(θ_t))+n_m(t)m＝1,2,…M (4)

Wherein, tau_m(θ_t) Is the time delay of the signal arriving at the m-th antenna element relative to the phase center of the antenna array, n_m(t) is white gaussian noise received by the mth antenna element.

Suppose a desired signal s_tFor narrow band signals, the time delay can be approximated as the phase shift of the center frequency of the desired signal, and equation (14) is rewritten as:

x_m(t)＝a_m(θ_t)s_t(t)+n_m(t) m＝1,2,…M (5)

wherein the content of the first and second substances,

c represents the speed of light, f₀Representing the center frequency of the desired signal.

Order to

Where x represents the complex vector of the echo data received by the array, a (θ)_t) Representing array steering vector, n representing complex vector of Gaussian white noise, and narrow-band signal echo data received by the array can be represented as

x＝a(θ_t)s_t+n (7)

And 3, performing guiding vector Taylor expansion. According to the working principle of the array radar, the target angle to be detected is located in the range of the main lobe of the radar detection wave beam, so that the target angle theta_tAnd the beam pointing direction theta₀The difference is small and can be approximated as (theta)_t-θ₀) → 0. According to Taylor expansion principle, the pointing angle theta of radar beam is theta₀To complete the steering vector a (theta)_t) The taylor expansion, ignoring higher order terms, yields:

a(θ_t)≈a(θ₀)+b(θ₀)(θ_t-θ₀) (8)

wherein the content of the first and second substances,substituting the data expression (17) received by the array radar to obtain

x＝(a(θ₀)+b(θ₀)(θ_t-θ₀))s_t+n (9)

A certain weighting vector w is selected to carry out weighting summation processing on the signals, and the signal can be obtained

y_DRepresenting the weighted summed output signals of the array. For simplicity of operation, the weight vector w and the steering vector a (θ) of the beam center are required₀) Orthogonal, i.e. w^Ha(θ₀) The influence of the noise term can be ignored under the condition that the signal-to-noise ratio is sufficient, and the expression (10) can be reduced to 0

y_D＝w^Hb(θ₀)(θ_t-θ₀)s_t(11)

Therefore, only the weight vector w needs to be selected reasonably, and the complex envelope s of the signal is estimated_tThe target angle θ can be estimated from the above equation_t。

And 4, selecting a weight vector. From the perspective of improving the estimation accuracy of the target angle, the principle of selecting the array weighting vector w is to make the output signal y after the array weighting summation_DHas the largest signal-to-noise ratio, obtains a weight vector of

And 5, estimating the complex envelope of the expected signal. Unknown signal amplitude parameter s_tCan be estimated by beamforming and channel signal data, and channel signal data writing

Wherein, a^H(θ₀)a(θ_t) Is the antenna beam pointing theta₀At angle, the antenna array is at theta_tThe response at an angle can be approximated as θ₀Response at an angle, i.e. a^H(θ₀)a(θ_t)≈a^H(θ₀)a(θ₀)。

If the signal-to-noise ratio is sufficient, the influence of the noise term is ignored, and equation (13) can be simplified to

y_S≈a^H(θ₀)a(θ₀)s_t(14)

The amplitude parameter s_tCan be written as

And 6, estimating a target angle. Determining an array weighting vector w and estimating a signal magnitude parameter s_tThen, formula (12) and formula (15) are substituted for formula (11), and the following can be obtained:

order toThe target angle can be estimated by the above formula:

the following gives a simulation example applying the method, and specific simulation parameters are shown in table 1.

TABLE 1 Uniform array simulation parameters

The sum-difference antenna patterns of the conventional difference-sum-ratio method and the proposed method are shown in fig. 2. As can be seen, the same sum path weight vector is chosen for both methods, and therefore the sum pattern remains the same. The two methods use different difference path weighting vectors, so that difference directional diagrams have differences. The difference directional diagram of the method is higher in value in the range of the main lobe of the sum directional diagram than that of the difference directional diagram of the traditional difference sum ratio method, and the method has a steeper angle identification curve.

The curve of the angle profile (single pulse ratio) obtained by the two methods in the range of-1 to 1 degrees is shown in fig. 3, and it is obvious from the figure that the angle profile obtained by the method is steeper than that obtained by the traditional sum-of-difference ratio method. The angle measurement precision is inversely proportional to the single pulse ratio K, and the larger the single pulse ratio is, the higher the angle measurement precision is. Therefore, the proposed method possesses a higher measurement accuracy than the conventional method.

The method is suitable for digital arrays, is a method for accurately measuring the target angle, and reduces the angle measurement error and improves the angle measurement precision compared with the traditional method. In addition, the angle measurement method has no restriction on the arrangement of the antenna array elements and is suitable for non-uniform arrays.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.