KR101032299B1 - Self-calibration for direction finding in multi-baseline interferometer system - Google Patents

Abstract

PURPOSE: A method for detecting a self calibration direction in a multi-base line interferometer system is provided to reduce mismatch errors. CONSTITUTION: A phase difference between antenna devices is estimated. The measurement value of the phase difference is calculated. An azimuth is estimated.

Description

Self-calibration direction detection in multibaseline interferometer systems {SELF-CALIBRATION FOR DIRECTION FINDING IN MULTI-BASELINE INTERFEROMETER SYSTEM}

The present invention relates to a multibaseline interferometer system, and more particularly, to a self-calibration direction detection method in a multibaseline interferometer system.

A simple interferometer antenna system is a single baseline based direction detection system in which two identical antennas are arranged at regular intervals. The direction detection system consisting of two antennas has 180 degree ambiguity. Practical interferometer systems often solve 180 degree ambiguity problems using other systems such as amplitude monopulse direction detection or circular monopulse arrays.

In general, passive interferometer systems covering wideband frequencies require two or more antennas and one or more baselines. This is because the solution of the angle of arrival equation can provide more than one angle of arrival information. This type of interferometer system is called a multibaseline type and consists of two or more different antenna elements, arranged in a straight line with different antenna spacing. It is possible to use multibaselines to cover wideband frequencies, and all direction detection ambiguities are eliminated by deriving the relationship between baselines.

However, a large number of antenna elements are required to construct a multibaseline, and when the separation distance between the antenna elements is more than half the wavelength of the incident signal, a grating lobe is generated in addition to the desired angle to completely eliminate ambiguity. It is impossible. In the case of a direction detection system, a slight inaccurate phase degrades the system's accuracy and reduces the resolution at which the signal can be estimated separately. Therefore, array calibration in adaptive beamformers and direction detection systems is very important.

Various arrays of high-resolution direction detection algorithms from MUSIC and Min-Norm show excellent performance under ideal conditions in array signal processing. However, in real arrays with phase and amplitude mismatch, correction and modeling methods are needed. Conventionally, most of them are applied to uniform linear arrays to correct gain and phase and estimate the direction angle of the incident signal. However, since the position of the array sensor can be arbitrarily arranged, there are many constraints. Although the Gauss-Newton method repeatedly estimates the direction angle by correcting gain and phase, the convergence time may be very long depending on the initial value. In addition, when the sensor gain and the phase mismatch is severe, there is a problem that can be the error of the estimated direction angle because it can converge to the local minimum value.

It is an object of the present invention to provide a self-calibrating direction detection method in a multibaseline interferometer system.

를 추정하는 단계와, k₂,k₃,k₄를 각각 변경하여 측정한 측정값

를 하기 수학식 8에 대입하여

를 계산하는 단계와, 하기 수학식 9로부터

를 계산하여 최소값을 제공하는 k₂,k₃ 내지 k_m을 선정하는 단계와, 상기 선정된 k₂,k₃ 내지 k_m을 하기 수학식 10에 대입하여 방위각

를 추정하는 단계를 포함하고, 수학식 8은

이고, 수학식 9는

이고, 수학식 10은

인 것으로 구성될 수 있다. 여기에서, 상기 안테나 소자 간 이격비는, 트리플 베이스라인인 경우에 제1 안테나 소자와 제2 안테나 소자간의 간격 d₁₂가 1.5이고, 제1 안테나 소자와 제3 안테나 소자 간의 간격 d₁₃가 3.9이고, 제1 안테나 소자와 제4 안테나 소자 간의 간격 d₁₄가 6.0 또는 6.1인 것으로 구성될 수 있다. 그리고 전처리 단계로서 초기 도래각을 추정하는 단계를 더 포함하도록 구성될 수 있다. 이때, 상기 전처리 단계로서 초기 도래각을 추정하는 단계는, 하기의 공분상 행렬을 이용하여 초기 도래각을 추정하는 것을 특징으로 하고, 공분산 행렬 Rx는,

,여기에서,

,

인 것으로 구성될 수 있다.Self-calibration direction detection method in a multibaseline interferometer system according to the above object of the present invention, the phase difference between the antenna elements

Estimating, and measured values of k ₂ , k ₃ , k ₄ , respectively

By substituting Equation 8 below

Calculating the following equation, and

To the calculated and the step of selecting the k _2, k ₃ k to _m which provides the minimum value, the selected k _2, k ₃ To k _m in Equation 10

Estimating Equation 8,

Equation 9 is

Equation 10 is

It may be configured to be. Here, in the case of the triple baseline, the separation ratio between the antenna elements is a distance d ₁₂ between the first antenna element and the second antenna element is 1.5, and a distance d ₁₃ between the first antenna element and the third antenna element is 3.9. The distance d ₁₄ between the first antenna element and the fourth antenna element may be 6.0 or 6.1. And estimating the initial angle of arrival as a preprocessing step. At this time, estimating the initial angle of arrival as the pre-processing step, characterized in that to estimate the initial angle of arrival using the following covariance matrix, the covariance matrix Rx,

,From here,

,

It may be configured to be.

According to the self-calibration direction detection method in the multibaseline interferometer system as described above, there is an effect of significantly reducing the mismatch error by using a covariance matrix-based self-calibration algorithm.

1 is a conceptual diagram of a multibaseline interferometer according to an embodiment of the present invention.
2A to 2C are graphs showing a comparison of sample RMS performance of an interferometer and a self-calibration technique according to sector spacing according to an embodiment of the present invention.
3A to 3B are graphs illustrating a change in sample bias according to a signal-to-noise ratio according to an embodiment of the present invention.
4A to 4B are graphs illustrating a change in a sample standard deviation according to a signal-to-noise ratio according to an embodiment of the present invention.
5A to 5B are graphs illustrating RMS change according to a signal-to-noise ratio according to an embodiment of the present invention.
6A to 6C are graphs showing statistical performance comparisons according to amplitude mismatch increase according to an embodiment of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. Like reference numerals are used for like elements in describing each drawing.

The terms first, second, A, B, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the first component may be referred to as the second component, and similarly, the second component may also be referred to as the first component. And / or < / RTI > includes any combination of a plurality of related listed items or any of a plurality of related listed items.

When a component is referred to as being "connected" or "connected" to another component, it may be directly connected to or connected to that other component, but it may be understood that other components may be present in between. Should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that there is no other component in between.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

Hereinafter, preferred embodiments according to the present invention will be described with reference to the accompanying drawings.

1 is a conceptual diagram of a multibaseline interferometer according to an embodiment of the present invention.

Figure 1 shows a triple baseline using four antenna elements, which consists of an array with d ₁₂ , d ₁₃ , and d ₁₄ spacing between antennas. The azimuth angle is represented by the angle θ formed between the end fire and the signal. Assuming that the incident signal is a plane wave, as shown in Fig. 1, the signals are sequentially received from the antenna 4, and the time delay τ between the antennas is determined by a phase detector with a phase difference φ _ij = w τ _ij = 2π f τ _ij And is given by Equation 1 by modulo 2π.

Where φ _j | ≤π, 0 ≤θ≤π, k _j = 0, ± 1, ± 2,... k _j is an integer and lambda is the wavelength of the incident signal.

If the separation distance between antennas in Equation 1 is greater than half wavelength, φ _ij according to k value even if the incident angle θ is different It can be seen that a value has several of the same values, which is said to have ambiguity. Thus, if the separation distance between antennas is more than half wavelength, the phase difference φ _ij And an integer k _j Additional techniques are needed to minimize liver ambiguity.

In order to examine the correlation between the accuracy (or resolution) and the ambiguity from the separation distance between the antenna elements, Equation 1 is expressed as Equation 2 as the relation between d λ and the incident angle θ.

The parameters to be considered in the design of the array antenna are the angle of arrival, the signal frequency, the bandwidth, the accuracy of the estimated angle of arrival, and the ambiguity resolution ability. The design can be regarded as an optimization problem with several independent variables. First, the algorithm is described using a linear array antenna composed of three antenna elements, and then, it is shown that it can be extended to four cases.

Considering the dual baseline linear arrangement in FIG. 1, the phase differences φ ₁₂ and φ ₁₃ are expressed as in Equations 3 and 4 by using Equation 2.

,

, 0≤θ≤π이고, k ₂ 와 k ₃가 갖는 정수값의 범위는 다음과 같이 다시 표현될 수 있다.here,

,

, 0 ≦ θ ≦ π, and the range of integer values of k ₂ and k ₃ may be re-expressed as follows.

| k ₂ | ≤ d ₁₂ / λ + 1/2, | k ₃ | ≤ d ₁₃ / λ + 1/2

If the system of equations is solved from equations (3) and (4) to remove (2π / λ) cos θ, the relationship between φ ₁₂ and φ ₁₃ is expressed as shown in equations (5) and (6).

Φ ₁₄ is obtained in the same manner as in Equation 7 below.

When ( k ₂ , k ₃ ) pairs are found, azimuth angle θ is estimated by substituting k ₂ and k ₃ values into equations (3) and (4).

를 추정하는 단계와, k₂, k₃, k₄를 각각 변경하여 측정한 측정값

를 하기 수학식 8에 대입하여

를 계산하는 단계와, 하기 수학식 9로부터

를 계산하여 최소값을 제공하는 k₂, k₃ 내지 k_m을 선정하는 단계와, 상기 선정된 k₂, k₃ 내지 k_m을 하기 수학식 10에 대입하여 방위각

를 추정하는 단계를 포함하도록 구성된다.Next, the self-calibration direction detection method in the multibaseline interferometer system according to the present invention will be described. Self-calibration direction detection method is the phase difference between antenna elements

Estimating, k ₂ , measured value by changing k ₃ and k ₄ respectively

By substituting Equation 8 below

Calculating the following equation, and

K ₂ , which provides the minimum value by computing selecting k ₃ to k _m , wherein k ₂ , k ₃ To k _m in Equation 10

Estimating.

Here, Equations 8 to 10 are as follows.

Here, in the case of the triple baseline, the separation ratio between the antenna elements is a distance d ₁₂ between the first antenna element and the second antenna element is 1.5, and a distance d ₁₃ between the first antenna element and the third antenna element is 3.9. The distance d ₁₄ between the first antenna element and the fourth antenna element is preferably 6.0 or 6.1.

And estimating the initial angle of arrival as a preprocessing step. At this time, the step of estimating the initial angle of arrival as the pre-processing step, characterized in that to estimate the initial angle of arrival using the following covariance matrix, the covariance matrix Rx is expressed by the following equation (11).

,

이다.From here,

,

to be.

2A to 2C are graphs showing a comparison of sample RMS performance of an interferometer and a self-calibration technique according to sector spacing according to an embodiment of the present invention.

In the present invention, a random array linear array consisting of four elements is used to investigate statistical performance, and z 1 = [0 0 0] ' , z 2 = [1.5 0 0] ' , z 3 = [3.9 0 0] ' , z 4 = [6.1 0 0] is adopted as the position vector of each antenna element, and the unit is assumed to be the wavelength of the incident signal. Considering the reliability of statistical features, 1,000 independent trials were performed. In the equation (19), the L value is 100 or 200 for the discrete integration of the spatial sector.

First, the angle of arrival of the incident signal was assumed to be 50 °, and ± 10 dB was taken as the amplitude mismatch. In order to investigate the more accurate performance of the self-calibration algorithm, we investigated the performance change according to the sector spacing in the absence of noise. Statistical performance results are shown in FIG. 2 in terms of sample mean square error (RMS). From Fig. 2, the sector intervals of ± 2 ° and ± 5 ° show much better performance in terms of RMS than the interferometer method, while the sector intervals of ± 7 ° show inferior performance to the interferometer technique. Giving. The self-calibration technique is a non-linear technique, and the performance depends greatly on the initial estimated angle and the sector spacing. The self-calibration technique provides a very good performance when the sector spacing is small around the angle of arrival. The simulation results show that the smaller the appropriate sector spacing is, the better the self-correction capability of the phase mismatch error can be achieved when selected within ± 5 °. It should be noted that the self-calibration technique shows 100% resolution regardless of the magnitude of the phase mismatch error, while the interferometer method shows a low resolution according to the phase mismatch error.

In order to investigate the performance change according to the signal-to-noise ratio after selecting the proper sector interval of the self-calibration method within ± 5 °, the statistical characteristics of the case where SNR = 10 dB and -10 dB were obtained after 1,000 independent trials. , In terms of sample standard deviation and RMS, respectively, are shown in FIGS. 3A to 5B. The self-calibration technique from FIGS. 3A-5B shows consistently good performance regardless of signal-to-noise ratio, while the interferometer method shows poor performance with a large increase in sample standard deviation when the signal-to-noise ratio is small. Moreover, an interesting result is that the self calibration technique is not sensitive to the magnitude of the phase mismatch error. It can be seen that the self-calibration technique always provides consistently good performance regardless of the magnitude of the phase mismatch error and the signal-to-noise ratio. In order to investigate how the self-calibration technique is less sensitive to phase mismatch error, but shows the performance of amplitude mismatch, the simulation results are shown in FIGS. It was. As the magnitude of the amplitude mismatch increases, the interferometer approach shows a significant increase in both bias and standard deviation. In particular, it can be seen that the sample standard deviation is greatly increased by more than two times, which means that the interferometer algorithm is very sensitive to amplitude mismatch. On the other hand, it can be seen that the self-calibration technique provides statistical performance when amplitude mismatch is within ± 10 dB even though amplitude mismatch is increased.

3A to 3B are graphs illustrating a change in sample bias according to a signal-to-noise ratio according to an embodiment of the present invention.

It can be seen from FIGS. 3A-3B that the spatial sector self-calibration technique provides very good calibration capability almost consistently regardless of the magnitude of the signal-to-noise ratio, amplitude mismatch and phase mismatch once the appropriate sector spacing has been determined.

4A to 4B are graphs illustrating a change in a sample standard deviation according to a signal-to-noise ratio according to an embodiment of the present invention.

4A to 4B also show consistent good calibration capability.

5A to 5B are graphs illustrating RMS change according to a signal-to-noise ratio according to an embodiment of the present invention.

It can be seen from FIGS. 5A-5B that the spatial sector self-calibration technique can also provide very good calibration capability almost consistently regardless of the magnitude of the signal-to-noise ratio, amplitude mismatch and phase mismatch once the appropriate sector spacing is established. .

6A to 6C are graphs showing statistical performance comparisons according to amplitude mismatch increase according to an embodiment of the present invention.

6A to 6C are also the same as above.

Although described with reference to the above embodiments, those skilled in the art will understand that various modifications and changes can be made without departing from the spirit and scope of the invention as set forth in the claims below. Could be.

Claims (4)

A self-calibrating direction detection method of a multibaseline interferometer system comprising a phase detector for detecting a phase of each antenna element and a direction detector for performing a direction detection algorithm.
A phase difference between the antenna elements from the phase of each antenna element detected by the phase detector by the direction detector

Estimating;
The direction finder k ₂ , measured value by changing k ₃ and k ₄ respectively

By substituting Equation 8 below

Calculating;
The direction finder from Equation 9

K ₂ , which provides the minimum value by computing selecting k ₃ to k _m ;
The direction detector is selected k ₂ , azimuth angle by substituting k ₃ to k _m in Equation 10

Estimating
Equation 8 is

ego,
Equation 9 is

ego,
Equation 10 is

Self-calibration direction detection method in a multibaseline interferometer system, characterized in that. The method of claim 1, wherein the separation ratio between the antenna elements,
In the case of the triple baseline, the distance d ₁₂ between the first antenna element and the second antenna element is 1.5,
The distance d ₁₃ between the first antenna element and the third antenna element is 3.9,
Self-calibrating direction detection method in a multibaseline interferometer system, characterized in that the distance d ₁₄ between the first antenna element and the fourth antenna element is 6.0 or 6.1. The method of claim 1,
Self-calibrating direction detection method in a multibaseline interferometer system, said direction detector further comprising estimating an initial angle of arrival as a preprocessing step. The method of claim 3, wherein the direction detector estimates an initial angle of arrival as a preprocessing step,
It is characterized by estimating the initial angle of arrival using the following conjugate phase matrix,
The covariance matrix Rx is

, And here,

,

Self-calibration direction detection method in a multibaseline interferometer system, characterized in that.

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