KR102400510B1 - Method for detecting multi targets using radar and apparatus for the same - Google Patents

Abstract

A method and apparatus for detecting multiple targets using radar are disclosed. A method for detecting multiple targets includes transmitting first signals using M _t transmit antennas included in the device, and M _r receiving antennas included in the device for first signals reflected by the multiple targets and generating a first function for estimating the velocity and azimuth of each of the multiple targets using the first signals and the reflected first signals.

Description

Method and apparatus for detecting multiple targets using radar

The present invention relates to a technique for detecting multiple targets, and more particularly, to a technique for estimating the distance, azimuth, and velocity of multiple targets using a frequency modulated continuous wave (FMCW) multiple input multiple output (MIMO) radar. it's about

Radar can be used to detect multiple targets ahead in vehicles that support autonomous driving functions. The distance, azimuth, and velocity of each of the multiple targets may be estimated using the vehicle-mounted radar. To detect multiple targets, a pulse radar, a continuous wave radar, a frequency modulated continuous wave (FMCW) radar, a frequency shift keying (FSK) radar, etc. may be used.

Using information obtained through radar and a multiple signal classification (MUSIC) algorithm, the distance, azimuth, and velocity of multiple targets can be estimated. The MUSIC algorithm has high computational complexity and is greatly affected by noise. Due to this, the result estimated by the MUSIC algorithm may have many errors. Therefore, it may be inappropriate to apply the current MUSIC algorithm to a vehicle supporting the autonomous driving function, so an algorithm that can be used in a vehicle supporting the autonomous driving function (for example, an algorithm used for detection of multiple targets) is required. .

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method and apparatus for detecting multiple targets using a frequency modulated continuous wave (FMCW) multiple input multiple output (MIMO) radar.

A method for detecting multiple targets according to a first embodiment of the present invention for achieving the above object includes transmitting first signals using M _t transmission antennas included in the apparatus, reflected by the multiple targets receiving the first signals through M _r receiving antennas included in the device; a first for estimating the velocity and azimuth of each of the multiple targets using the first signals and the reflected first signals generating a 1 function, estimating the velocity and azimuth that maximize the result of the first function as the velocity and azimuth of a first one of the multiple targets closest to the device, caused by the first target generating a second function by removing interference from the first function, and estimating the velocity and azimuth that maximize the result of the second function as the velocity and azimuth of a second one of the multiple targets; , the distance between the device and the second target is equal to or greater than the distance between the device and the first target, and each of M _t and M _r is a natural number equal to or greater than 2 .

Here, the first signals transmitted through the M _t transmit antennas may be orthogonal to each other.

Here, the first function may be generated based on the 2D MUSIC algorithm.

Here, the first function is a first matrix formed by the velocities and azimuths of the multiple targets, a Hermitian matrix for the first matrix, a second matrix formed by the noise subspace, and for the second matrix It can be configured as a Hermitian matrix.

In this case, M _t × M _r virtual array elements may be implemented by the M _t transmit antennas and the M _r receive antennas, and the first function functions to generate the M _t × M _r virtual array elements. It may be generated based on the first signals transmitted and received through and the reflected first signals.

Here, generating the second function includes generating a first matrix based on the velocity and azimuth of the first target, generating a projected matrix by projecting the first matrix onto an orthogonal area, and The method may further include generating the second function by performing eigenvalue decomposition on a sample covariance matrix of the projected matrix.

Here, the operating method includes generating a first matrix based on a velocity and an azimuth of the first target, a first matrix including a bit frequency indicating a distance between the device and the first target using the first matrix The method may further include generating two signals, and estimating a result of FFT on the second signal as a distance between the device and the first target.

A detection apparatus according to a second embodiment of the present invention for achieving the above object includes a processor, M _t transmit antennas for transmitting first signals under the control of the processor, and the multiple targets under the control of the processor. M _r receive antennas receiving first signals reflected by generating a first function for estimating the velocity and azimuth of each of the multiple targets using the obtained first signals, and determining the velocity and azimuth that maximizes the result of the first function among the multiple targets closest to the device Estimating the velocity and azimuth of a first target, generating a second function by removing interference caused by the first target from the first function, and determining the velocity and azimuth that maximizes the result of the second function and estimating the velocity and azimuth of a second target among multiple targets, wherein a distance between the device and the second target is greater than or equal to a distance between the device and the first target, and each of M _t and M _r is a natural number greater than or equal to 2 am.

Here, the first function is a first matrix formed by the velocities and azimuths of the multiple targets, a Hermitian matrix for the first matrix, a second matrix formed by the noise subspace, and for the second matrix It can be configured as a Hermitian matrix.

In this case, M _t × M _r virtual array elements may be implemented by the M _t transmit antennas and the M _r receive antennas, and the first function functions to generate the M _t × M _r virtual array elements. It may be generated based on the first signals transmitted and received through and the reflected first signals.

wherein, when generating the second function, the one or more instructions generate a first matrix based on the velocity and azimuth of the first target, and generate a projected matrix by projecting the first matrix onto an orthogonal area. and generate the second function by performing an eigenvalue decomposition on a sample covariance matrix of the projected matrix.

wherein the one or more instructions generate a first matrix based on a velocity and an azimuth of the first target, and a first matrix comprising a bit frequency indicative of a distance between the device and the first target using the first matrix. generating two signals, and estimating a result of FFT on the second signal as a distance between the device and the first target.

According to the present invention, the detection device may generate a first function for estimating parameters (eg, velocity, azimuth, distance) of multiple targets based on a signal reflected by the multiple targets, the first The velocity and azimuth maximizing the function may be estimated as the velocity and azimuth of a first target closest to the detection device. The detection device may generate the second function by removing the interference caused by the first target from the first function, and may estimate the velocity and azimuth that maximize the second function as the velocity and azimuth of the second target. Since the interference caused by the target is sequentially removed, the detection apparatus can accurately estimate the parameters of each of the multiple targets. In addition, computational complexity for detection of parameters of multiple targets can be reduced.

1 is a conceptual diagram illustrating a first embodiment of a detection apparatus using an FMCW MIMO radar.
2 is a conceptual diagram illustrating a virtual antenna formed by antennas included in a detection device.
3 may be a graph illustrating a result of performing an existing 2D MUSIC algorithm.
4 may be a graph illustrating a result of performing a 2D MUSIC algorithm to which an orthogonal projection-based interference cancellation technique is applied.
5 is a graph showing errors generated by the existing 2D MUSIC algorithm.

Since the present invention can have various changes and can have various embodiments, specific embodiments are illustrated in the drawings and described in detail. However, this is not intended to limit the present invention to specific embodiments, and it should be understood to include all modifications, equivalents and substitutes included in the spirit and scope of the present invention.

Terms such as first, second, etc. may be used to describe various elements, but the elements should not be limited by the terms. The above terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, a first component may be referred to as a second component, and similarly, a second component may also be referred to as a first component. and/or includes a 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 or connected to the other component, but it is understood that other components may exist in between. it should be On the other hand, when it is said that a certain element is "directly connected" or "directly connected" to another element, it should be understood that the other element does not exist in the middle.

The terms used in the present application are only used to describe specific embodiments, and are not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly dictates otherwise. In the present application, terms such as “comprise” or “have” are intended to designate that a feature, number, step, operation, component, part, or combination thereof described in the specification exists, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations 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 to which this invention belongs. Terms such as those defined in a commonly used dictionary should be interpreted as having a meaning consistent with the meaning in the context of the related art, and should not be interpreted in an ideal or excessively formal meaning unless explicitly defined in the present application. does not

Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the accompanying drawings. In describing the present invention, in order to facilitate the overall understanding, the same reference numerals are used for the same components in the drawings, and duplicate descriptions of the same components are omitted.

1 is a conceptual diagram illustrating a first embodiment of a detection apparatus using a frequency modulated continuous wave (FMCW) multiple input multiple output (MIMO) radar.

Referring to FIG. 1 , the detection device may be mounted on a vehicle and may include a processor 110 , a memory 120 , a storage device 130 , M _t transmit antennas, and M _r receive antennas. . Each of M _t and M _r may be a natural number. The processor 110 may execute a program command stored in at least one of the memory 120 and the storage device 130 . The processor 110 may mean a central processing unit (CPU), a graphics processing unit (GPU), or a dedicated processor on which methods according to embodiments of the present invention are performed. Each of the memory 120 and the storage device 130 may be configured of at least one of a volatile storage medium and a non-volatile storage medium. For example, the memory 120 may be configured as at least one of a read only memory (ROM) and a random access memory (RAM).

The detection apparatus may transmit signals using M _t transmit antennas, and signals transmitted from the M _t transmit antennas may be reflected by K targets. K may be a natural number. The M _t transmit antennas may transmit signals having orthogonal waveforms to each other. By adjusting the frequency offset of signals transmitted from the M _t transmit antennas, signals having orthogonal waveforms may be generated. Alternatively, signals having orthogonality may be generated based on the time division method. The signals reflected from the K targets may be acquired at the M _r receive antennas. Signals obtained from the M _r receive antennas may be separated.

를 전송할 수 있다.When different frequency offsets are applied to the M _t transmit antennas, a signal (eg, FMCW signal) transmitted from the m _t th transmit antenna among the M _t transmit antennas may be defined as in Equation 1 below. there is. That is, the detection device uses a transmit antenna to

can be transmitted.

는 m_t번째 송신 안테나에서 전송되는 신호일 수 있다.

는 반송파의 주파수일 수 있다.

는 주파수 오프셋일 수 있다.

은 시간 영역에서 하나의 펄스의 길이일 수 있다.

는 첩 레이트(chirp rate)일 수 있다.

는 K개의 목표물들에 의해 반사될 수 있고, K개의 목표물들에 의해 반사된 신호는 M_r개의 수신 안테나들 중에서 m_r번째 수신 안테나에서 수신될 수 있다. m_r번째 수신 안테나에서 수신된 신호(

)는 아래 수학식 2와 같이 정의될 수 있다. 즉, 검출 장치는 수신 안테나를 통해

를 수신할 수 있다.

may be a signal transmitted from the m _t th transmit antenna.

may be the frequency of the carrier wave.

may be a frequency offset.

may be the length of one pulse in the time domain.

may be a chirp rate.

may be reflected by the K targets, and the signal reflected by the K targets may be received at the m _r th receiving antenna among the M _r receiving antennas. The signal received at the m _r th receiving antenna (

) may be defined as in Equation 2 below. That is, the detection device is transmitted through the receiving antenna.

can receive

는 목표물의 반사 계수, 레인지(range)로 인한 경로 손실, 안테나 이득 등을 고려하여 결정될 수 있다. 수학식 2에서

는 아래 수학식 3과 같이 정의될 수 있다.

may be determined in consideration of a reflection coefficient of a target, a path loss due to a range, an antenna gain, and the like. in Equation 2

can be defined as in Equation 3 below.

는 m_t번째 송신 안테나에서 k번째 목표물까지의 거리일 수 있다.

는 m_r번째 수신 안테나에서 k번째 목표물까지의 거리일 수 있다. 여기서, m_t번째 송신 안테나와 m_r번째 수신 안테나의 가운데에 위치한 가상 안테나에서 신호가 송수신되는 것으로 가정될 수 있다. 즉, M_t개의 송신 안테나들과 M_r개의 수신 안테나들이 사용됨으로써, M_t×M_r개의 가상 어레이 엘리먼트들(virtual array elements)을 포함하는 안테나가 구현될 수 있다.

may be the distance from the m _t th transmit antenna to the k th target.

may be the distance from the m _r th receive antenna to the k th target. Here, it may be assumed that a signal is transmitted/received through a virtual antenna located in the middle between the m _t th transmit antenna and the m _r th receive antenna. That is, by using M _t transmit antennas and M _r receive antennas, an antenna including M _t ×M _r virtual array elements may be implemented.

2 is a conceptual diagram illustrating a virtual antenna formed by antennas included in a detection device.

Referring to FIG. 2 , the detection apparatus may include four transmit antennas and four receive antennas. In this case, a linear array antenna including 16 virtual array elements may be implemented.

는 목표물의 속도일 수 있다. 예를 들어,

는 레이더(예를 들어, 안테나) 방향을 기준으로 목표물의 상대적인 속도일 수 있다. 수학식 3에서

에 의하면, 가상 어레이 엘리먼트들을 포함하는 선형 어레이 안테나에서 신호를 송수신하는 효과를 고려하여, 안테나로부터 목표물까지의 거리가 다시 표현될 수 있다.

는 선형 어레이 안테나에 포함된 가상 어레이 엘리먼트(예를 들어, 기준 엘리먼트)로부터 목표물까지의 거리일 수 있다.

는 m_t번째 송신 안테나와 m_r번째 수신 안테나에 의해 형성되는 가상 어레이 엘리먼트의 상대적인 위칠 수 있다.

는 목표물의 방위각일 수 있고, 선형 어레이 안테나에 포함된 가상 어레이 엘리먼트를 기준으로 결정될 수 있다. 선형 어레이 안테나에 포함된 가상 어레이 엘리먼트의 인덱스가 m이고, 가상 어레이 엘리먼트들 간의 간격이 d인 경우, 수학식 3에서

가 정의될 수 있다.in Equation 3

may be the speed of the target. for example,

may be the relative speed of the target with respect to the radar (eg, antenna) direction. in Equation 3

According to , the distance from the antenna to the target may be expressed again in consideration of the effect of transmitting and receiving signals in the linear array antenna including the virtual array elements.

may be a distance from a virtual array element (eg, a reference element) included in the linear array antenna to the target.

may be a relative position of a virtual array element formed by the m _t th transmit antenna and the m _r th receive antenna.

may be the azimuth of the target, and may be determined based on the virtual array element included in the linear array antenna. When the index of the virtual array element included in the linear array antenna is m and the distance between the virtual array elements is d, in Equation 3

can be defined.

)를 도출할 수 있다. 수학식

는 비트(beat) 주파수 정보를 포함할 수 있다.In order to process the signal of the FMCW MIMO radar, the detection apparatus performs deconvolution and low-pass filtering on the signal transmitted from the transmitting antennas and the signal received at the receiving antenna by performing the following The signal defined in Equation 4 (

) can be derived. formula

may include beat frequency information.

는 T_S마다 샘플링될 수 있고, 샘플링된 신호를 이산 신호로 변환함으로써 아래 수학식 5가 정의될 수 있다.

may be sampled every T _S , and Equation 5 below may be defined by converting the sampled signal into a discrete signal.

When a total of S pulses are used to detect multiple targets, the nth sample signal of the sth pulse belonging to the S pulses may be defined as in Equation 6 below.

가 정의될 수 있다. 가상 어레이 엘리먼트들에서 수신 신호들은 수학식 6에 기초하여 하나의 벡터 형태로 표현될 수 있다. 예를 들어, 가상 어레이 엘리먼트들에서 수신 신호들을 기초로 생성된 벡터는 아래 수학식 7과 같이 정의될 수 있다.in Equation 6

can be defined. In the virtual array elements, the received signals may be expressed in the form of one vector based on Equation (6). For example, a vector generated based on received signals in the virtual array elements may be defined as in Equation 7 below.

는 어레이 응답 벡터(array response vector)일 수 있고,

가 정의될 수 있다.

는 아래 수학식 8과 같이 모든 펄스에 대한 벡터 형태로 표현될 수 있다.

may be an array response vector,

can be defined.

can be expressed in the form of a vector for all pulses as shown in Equation 8 below.

는 아래 수학식 9와 같이 정의될 수 있다.in Equation 8

can be defined as in Equation 9 below.

는 아래 수학식 10과 같이 모든 n에 대한 컬럼(column) 형태로 표현될 수 있다.

can be expressed in the form of a column for all n as shown in Equation 10 below.

■ 2D multiple signal classification (MUSIC) algorithm

에 기초하여 샘플 공분산 행렬을 계산할 수 있고, 샘플 공분산 행렬에 대한 고유 값 분해(eigen-value decomposition)를 수행함으로써 아래 수학식 11을 생성할 수 있다.the detection device

A sample covariance matrix may be calculated based on , and Equation 11 below may be generated by performing eigen-value decomposition on the sample covariance matrix.

는 신호 부공간을 스팬(span)하는 고유 벡터를 기초로 생성된 행렬일 수 있다.

은 잡음 부공간을 스팬하는 고유 벡터를 기초로 생성된 행렬일 수 있다.

이 정의되는 경우, 신호 부공간은 잡음 부공간과 직교할 수 있다. 따라서 아래 수학식 12가 정의될 수 있다.

may be a matrix generated based on an eigenvector spanning a signal subspace.

may be a matrix generated based on an eigenvector spanning the noise subspace.

is defined, the signal subspace may be orthogonal to the noise subspace. Therefore, Equation 12 below can be defined.

을 최대화하는 속도(v)와 방위각(θ)을 추정할 수 있다.The detection device performs a two-dimensional grid search by

It is possible to estimate the velocity (v) and azimuth (θ) maximizing .

■ 2D MUSIC algorithm with interference cancellation based on orthogonal projection

가 최댓값을 가지는 경우, 검출 장치는

가 최댓값을 가지도록 결정된 속도(v)와 방위각(θ)을 목표물의 속도(v)와 방위각(θ)으로 추정할 수 있다. 그러나 잡음 및

의 사이드-로브(side-lobe) 때문에, 검출 장치로부터 상대적으로 멀리 위치한 목표물에 의해 반사된 신호의 감쇄는 클 수 있다. 이 경우, 검출 장치로부터 상대적으로 멀리 위치한 목표물에 의해 반사된 신호의 크기는 검출 장치로부터 상대적으로 가까이 위치한 목표물에 대한 사이드-로브의 크기보다 작을 수 있다. 따라서 목표물에 대한 파라미터들(예를 들어, 거리, 방위각, 속도)을 추정하는 것은 어려울 수 있다.in Equation 12

has a maximum value, the detection device is

The velocity (v) and the azimuth (θ) determined to have a maximum value may be estimated as the velocity (v) and the azimuth (θ) of the target. However, noise and

Due to the side-lobe of the signal, the attenuation of the signal reflected by a target located relatively far from the detection device can be large. In this case, the magnitude of the signal reflected by the target relatively far from the detection device may be smaller than the magnitude of the side-lobe with respect to the target relatively close to the detection device. It can therefore be difficult to estimate parameters (eg, distance, azimuth, velocity) for a target.

의 최댓값을 계산할 수 있고, 최댓값을 사용하여 목표물의 파라미터들을 추정할 수 있고, 추정된 파라미터들을 사용하여 직교 투영법을 수행함으로써 원시 수신 신호 내의 간섭을 제거할 수 있다. 예를 들어, 검출 장치는 검출 장치로부터 가장 가까운 목표물에 의해 야기되는 간섭을 원시 수신 신호에서 제거함으로써 제1 수신 신호를 생성할 수 있다.To solve this problem, the detection device is a function used to estimate parameters of a target based on an original received signal (eg, the signal defined in Equation 2) (eg, Equation 12) function defined in ) can be created. The detection device is defined in Equation 12

can calculate the maximum value of , estimate parameters of the target using the maximum values, and perform orthogonal projection using the estimated parameters to remove interference in the raw received signal. For example, the detection device may generate the first received signal by removing interference caused by a target closest to the detection device from the original received signal.

의 최댓값을 계산할 수 있고, 최댓값(예를 들어, 원시 수신 신호를 기초로 계산된 최댓값보다 작은 최댓값)을 사용하여 목표물의 파라미터들을 추정할 수 있고, 추정된 파라미터들을 사용하여 직교 투영법을 수행함으로써 제1 수신 신호 내의 간섭을 제거할 수 있다. 예를 들어, 검출 장치는 검출 장치로부터 두 번째로 가까운 목표물에 의해 야기되는 간섭을 제1 수신 신호에서 제거함으로써 제2 수신 신호를 생성할 수 있다.After that, the detection device based on the first received signal

It is possible to calculate the maximum value of , and estimate the parameters of the target using the maximum value (eg, a maximum value smaller than the maximum value calculated based on the raw received signal), and perform an orthogonal projection using the estimated parameters. 1 Can cancel interference in the received signal. For example, the detection device may generate the second received signal by canceling interference caused by a target second closest to the detection device from the first received signal.

를 발생시키는 신호를 반사한 목표물에 대한 파라미터들(예를 들어, 속도 및 방위각)이 추정된 경우, 검출 장치는 추정된 파라미터들을 사용하여

를 계산할 수 있고,

와 직교한 영역에 투영된 행렬을 계산할 수 있다.

와 직교한 영역에 투영된 행렬은 아래 수학식 13과 같이 정의될 수 있다.that is, the largest

When parameters (eg, velocity and azimuth) for the target that reflected the signal generating

can be calculated,

We can compute a matrix projected on a region orthogonal to .

A matrix projected on a region orthogonal to can be defined as in Equation 13 below.

)에 기초하여 고유 값 분해를 수행함으로써 수학식 12를 계산할 수 있다. 이 경우, 검출 장치는 가장 큰 세기를 가지는 신호를 반사시키는 목표물의 파라미터들로 인한 간섭 효과를 제거할 수 있고, 간섭 효과가 제거된 상태에서 다음 목표물의 파라미터들을 정확하게 추정할 수 있다. 검출 장치는 앞서 설명된 동작을 K번 반복 수행함으로써 K개 목표물들(예를 들어, 도 1에 도시된 K개 목표물들)의 파라미터들을 추정할 수 있다. 가장 작은 수신 세기를 가지는 목표물(예를 들어, 검출 장치로부터 가장 멀리 떨어진 목표물)의 파라미터들도 정확하게 추정될 수 있다.In addition, the detection device is a sample covariance matrix (eg,

Equation 12 can be calculated by performing eigenvalue decomposition based on ). In this case, the detection apparatus may remove the interference effect due to the parameters of the target that reflects the signal having the greatest intensity, and accurately estimate the parameters of the next target while the interference effect is removed. The detection apparatus may estimate parameters of K targets (eg, K targets illustrated in FIG. 1 ) by repeatedly performing the above-described operation K times. Parameters of a target having the smallest reception strength (eg, a target farthest from the detection device) can also be accurately estimated.

■ 2D root MUSIC algorithm

Since the calculation amount of the two-dimensional grid search is very large, the detection apparatus may estimate the parameters of the target by using the two-dimensional root MUSIC algorithm. The detection apparatus may define two vectors defined in Equation 14 below.

Using the two vectors defined in Equation 14, the denominator of Equation 12 may be defined as Equation 15 below.

는 아래 수학식 16과 같이 정의될 수 있다.

can be defined as in Equation 16 below.

를 최대화하는 파라미터들을 구하는 것은 수학식 15에서

에 대한 방정식의 근을 구하는 것과 동일할 수 있다. 수학식 15는 아래 수학식 17로 변환될 수 있다.of Equation 12

Finding the parameters that maximize

It can be the same as finding the root of the equation for . Equation 15 can be converted to Equation 17 below.

를 계산할 수 있다.The detection device satisfies Equation 18 below

can be calculated.

가 정의되는 경우, 수학식 18의 근들 중에서 속도에 관련된 근은 크기가 1인 단위 원(unit circle)상에 위치할 수 있다. 따라서 K개 목표물들의 속도를 추정하기 위해, 검출 장치는 단위 원에 가장 가까운 K개의 근들(예를 들어,

)을 선택할 수 있고, 아래 수학식 19에 기초하여 K개의 목표물들의 속도를 추정할 수 있다.

is defined, a root related to speed among the roots of Equation 18 may be located on a unit circle having a size of 1. Therefore, to estimate the velocity of K targets, the detection device uses the K roots closest to the unit circle (eg,

) can be selected, and the velocity of K targets can be estimated based on Equation 19 below.

에 기초하여

를 계산할 수 있다. 검출 장치는

를 수학식 17에 대입함으로써 아래 수학식 20을 획득할 수 있다.the detection device

based on

can be calculated. the detection device

By substituting in Equation 17, Equation 20 below can be obtained.

가 정의되는 경우, 수학식 20의 근들 중에서 방위각에 관련된 근은 크기가 1인 단위 원상에 위치할 수 있다. 따라서 K개 목표물들의 방위각을 추정하기 위해, 검출 장치는 수학식 20의 근들 중에서 단위 원에 가장 가까운 K개의 근들을 선택할 수 있고, 아래 수학식 21에 기초하여 K개 목표물들의 방위각을 추정할 수 있다.

is defined, a root related to an azimuth among the roots of Equation 20 may be located on a unit circle having a size of 1. Accordingly, in order to estimate the azimuth angles of the K targets, the detection apparatus may select K roots closest to the unit circle from among the roots of Equation 20, and estimate the azimuth angles of the K targets based on Equation 21 below. .

■ low complexity 2D Root MUSIC Algorithm Based on Approximation

에 대한 함수이고,

가 정의되는 경우,

는

로 표현될 수 있다. 즉,

는 2π 주기를 가지는 주기 함수일 수 있다. 검출 장치는 아래 수학식 22와 같이

를 푸리에 급수(Fourier series)로 표현할 수 있다.Equation 14 is

is a function for

If is defined,

Is

can be expressed as in other words,

may be a periodic function having a period of 2π. The detection device is as shown in Equation 22 below

can be expressed as a Fourier series.

는 아래 수학식 23과 같이 정의될 수 있다.

can be defined as in Equation 23 below.

The detection apparatus may derive Equation 24 below by approximating the determinant of Equation 18 through a Fourier series.

In Equation 24, the polynomial order for z may be “(S-1)×M”. In this case, the polynomial order may increase as S or M increases. When the polynomial order for z in Equation 24 is set to satisfy "N<(S-1)×M", the detection apparatus can efficiently find the roots of Equation 24 having a low polynomial order. The detection apparatus may estimate the velocity of the K targets using the roots of Equation 24 and Equation 19, and estimate the azimuth angles of the K targets using the roots of Equation 24 and Equations 20 and 21 . Since the order of the equation used for azimuth estimation is not high, the detection apparatus can accurately estimate the azimuth without an approximation operation. If necessary, the detection device may estimate the azimuth by performing an approximation operation.

■ Considering the weight low complexity 2D Root MUSIC Algorithm Based on Approximation

를 가중치(

)와 함께 근사화할 수 있다. 예를 들어, 검출 장치는 아래 수학식 25에 기초하여

를 근사화할 수 있다.The detection device is defined in Equation 24

weight (

) can be approximated with For example, the detection device is based on Equation 25 below

can be approximated.

가 만족되는 경우에, 검출 장치는 정확한 근사화를 위해

를 아래 수학식 26과 같이 정의할 수 있다.

is satisfied, the detection device is used to obtain an accurate approximation

can be defined as in Equation 26 below.

는 에르미트 대칭 행렬(Hermitian symmetric matrix)의 디터미넌트일 수 있다. 따라서

는 항상 실수 값을 가질 수 있으며, 수학식 25는 아래 수학식 27과 같이 재정의될 수 있다.

may be a determinant of a Hermitian symmetric matrix. thus

may always have a real value, and Equation 25 may be redefined as Equation 27 below.

The parameters of Equation 27 may be defined as Equation 28 below.

The detection apparatus may calculate the roots of Equation 27 based on Equation 29 below.

"을 만족하는 근들을 효율적으로 계산할 수 있다. 검출 장치는 수학식 27의 근들과 수학식 19를 사용하여 K개의 목표물들의 속도를 추정할 수 있고, 수학식 27의 근들과 수학식 20 및 21을 사용하여 K개의 목표물들의 방위각을 추정할 수 있다. 방위각 추정을 위해 사용되는 방정식의 차수는 높지 않기 때문에, 검출 장치는 근사화 동작 없이 방위각을 정확하게 추정할 수 있다. 필요한 경우, 검출 장치는 근사화 동작을 수행함으로써 방위각을 추정할 수 있다.Therefore, the detection device is "

It is possible to efficiently calculate the roots satisfying " can be used to estimate the azimuth angle of K targets. Since the order of the equation used for azimuth estimation is not high, the detection device can accurately estimate the azimuth without approximation operation. If necessary, the detection device performs the approximation operation You can estimate the azimuth by doing it.

를 계산할 수 있다.

는 아래 수학식 30과 같이 정의될 수 있다.The detection device may estimate a distance between the detection device (eg, an antenna) and the target using the estimated velocity and azimuth. The detection device uses the estimated velocity and azimuth

can be calculated.

can be defined as in Equation 30 below.

와 수학식 10에서 정의된

를 곱함으로써 아래 수학식 31에서 정의된

를 계산할 수 있다.the detection device

and defined in Equation 10

defined in Equation 31 below by multiplying

can be calculated.

)를 정합 필터(matched filter)에 통과시키는 효과가 발생하므로, 목표물 방향으로의 SNR(signal to noise ratio)이 최대가 되도록 수신 벡터가 결합될 수 있다. 따라서 다른 목표물로부터 반사되는 신호는 널링(nulling)될 수 있다.

는 k번째 목표물과 검출 장치(예를 들어, 안테나) 간의 거리에 해당하는 단일 비트 주파수(

)로 인하여 발생하는 단일 톤(tone) 신호를 T_s마다 샘플링한 신호에 잡음이 더해진 신호일 수 있다.

에 대한 FFT(fast Fourier transform)의 결과인 피크 주파수는 비트 주파수일 수 있고, 검출 장치는 아래 수학식 32를 사용하여 k번째 목표물과 검출 장치(예를 들어, 안테나) 간의 거리를 추정할 수 있다.A vector formed by the target's velocity and azimuth (

) is passed through the matched filter, so that the reception vectors can be combined so that the signal to noise ratio (SNR) in the direction of the target is maximized. Accordingly, signals reflected from other targets may be nulled.

is the single bit frequency corresponding to the distance between the kth target and the detection device (eg, antenna)

) may be a signal in which noise is added to a signal obtained by sampling a single tone signal generated every T _s .

A peak frequency that is a result of a fast Fourier transform (FFT) for may be a bit frequency, and the detection device may estimate the distance between the k-th target and the detection device (eg, antenna) using Equation 32 below. .

), 송신 안테나, 및 수신 안테나는 아래 표 1과 같이 정의될 수 있다.Meanwhile, performance according to the above-described embodiments may be as follows. The operating frequency of the detection device (

), a transmit antenna, and a receive antenna may be defined as shown in Table 1 below.

It can be assumed that there are three targets in front of the detection device. The parameters (eg, distance, azimuth, and speed) of the three targets may be defined as shown in Table 2 below.

)은 검출 장치를 기준으로 결정될 수 있다. 목표물의 속도(

)는 검출 장치에 대한 상대 속도일 수 있다. k는 목표물의 인덱스일 수 있다.The distance may be a distance between a detection device (eg, an antenna) and a target. The azimuth of the target (

) may be determined based on the detection device. target speed (

) may be the relative velocity to the detection device. k may be an index of a target.

Signals transmitted from the transmit antennas may be reflected by targets, and the receive antennas may receive signals reflected from the targets. It can be assumed that the strength of signals received at the receiving antennas is inversely proportional to the fourth power of the distance defined in Table 2. Here, additive white Gaussian noise (AWGN) may be present, and the variance value may be set to 8.57×10 ⁻⁴ .

The result of performing the existing 2D MUSIC algorithm based on the parameters defined in Tables 1 and 2 may be as shown in FIG. 3 below. The search interval for the 2D MUSIC algorithm may be “speed grid=40:0.5:100, angle grid=-30:0.5:30”.

3 may be a graph illustrating a result of performing an existing 2D MUSIC algorithm.

Referring to FIG. 3 , since the magnitude of the signal reflected by the target #1 is greater than the magnitude of the signal reflected by the target #3, the signal reflected by the target #1 corresponds to the signal reflected by the target #3. may act as interference. Accordingly, the detection device may not accurately estimate parameters (eg, distance, azimuth, and speed) of target #3.

On the other hand, when the 2D MUSIC algorithm to which the interference cancellation technique based on the orthogonal projection is applied is used, the detection apparatus can estimate the parameters of the target #1 based on the received signal, and remove the interference caused by the target #1 from the received signal. A first signal may be derived, parameters of the target #2 may be estimated based on the first signal, and a second signal in which interference caused by the target #2 may be removed from the first signal may be derived, and a second signal may be derived. 2 It is possible to estimate the parameters of target #3 based on the signal. The result of performing the 2D MUSIC algorithm to which the interference cancellation technique based on the orthogonal projection method is applied may be as shown in FIG. 4 below.

4 may be a graph illustrating a result of performing a 2D MUSIC algorithm to which an orthogonal projection-based interference cancellation technique is applied.

Referring to FIG. 4 , the detection apparatus may accurately estimate the velocity and azimuth of each of the targets #1 to #3, and may estimate the distance of each of the targets #1 to #3 based on the velocity and the azimuth.

Meanwhile, when the existing 2D MUSIC algorithm is used, a complicated calculation process may be required to derive the roots of Equation 12 for a 120×120 grid. In addition, when the existing 2D MUSIC algorithm is used, the detection apparatus may estimate the distance of the target by performing FFT. In this case, an estimation error may occur. For example, the following error may occur when estimating the distance.

5 is a graph showing errors generated by the existing 2D MUSIC algorithm.

의 피크 값이 잘못 결정되는 경우, 검출 장치는 목표물 #1의 비트 주파수가 목표물 #3의 비트 주파수와 동일한 것으로 판단할 수 있다. 이에 따라, 검출 장치는 목표물 #1의 거리를 69.8679m로 판단할 수 있고, 목표물 #2의 거리를 80.0051m로 판단할 수 있고, 목표물 #3의 거리를 69.8679m로 판단할 수 있다. 즉, 검출 장치에 의해 추정된 목표물 #3의 거리는 표 2에 정의된 목표물 #3의 거리와 다를 수 있다.5, in Equation 12

In case the peak value of is erroneously determined, the detection apparatus may determine that the beat frequency of the target #1 is the same as the beat frequency of the target #3. Accordingly, the detection device may determine the distance of the target #1 to be 69.8679m, the distance of the target #2 may be determined to be 80.0051m, and the distance of the target #3 may be determined to be 69.8679m. That is, the distance of the target #3 estimated by the detection device may be different from the distance of the target #3 defined in Table 2.

Meanwhile, the mean squared error (MSE) for the velocity estimated by the existing 2D MUSIC algorithm and the MSE for the velocity estimated by the 2D MUSIC algorithm proposed in the present invention may be shown in Table 3 below.

The MSE for the azimuth estimated by the existing 2D MUSIC algorithm and the MSE for the azimuth estimated by the 2D MUSIC algorithm proposed in the present invention may be shown in Table 4 below.

The methods according to the present invention may be implemented in the form of program instructions that can be executed by various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the computer-readable medium may be specially designed and configured for the present invention, or may be known and available to those skilled in the art of computer software.

Examples of computer-readable media include hardware devices specially configured to store and carry out program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware device described above may be configured to operate as at least one software module to perform the operations of the present invention, and vice versa.

Although it has been described with reference to the above embodiments, it will be understood by those skilled in the art that various modifications and changes can be made to the present invention without departing from the spirit and scope of the present invention as set forth in the claims below. will be able

Claims (12)

A method of operation performed in a device for detecting multiple targets, comprising:
transmitting first signals using M _t transmit antennas included in the apparatus;
receiving the first signals reflected by the multiple targets through M _r receiving antennas included in the apparatus;
generating a first function for estimating velocity and azimuth of each of the multiple targets using the first signals and the reflected first signals;
estimating the velocity and azimuth that maximize the result of the first function as the velocity and azimuth of a first one of the multiple targets that is closest to the device;
generating a first matrix based on a velocity and an azimuth that maximizes a result of the first function;
generating a projected matrix by projecting the first matrix onto an orthogonal region;
generating a second function by performing eigen-value decomposition on a sample covariance matrix of the projected matrix; and
estimating the velocity and azimuth that maximize the result of the second function as the velocity and azimuth of a second target among the multiple targets;
wherein the distance between the device and the second target is greater than or equal to the distance between the device and the first target, and wherein each of M _t and M _r is a natural number greater than or equal to 2 . The method according to claim 1,
and the first signals transmitted through the M _t transmit antennas are orthogonal to each other. The method according to claim 1,
wherein the first function is generated based on a 2D multiple signal classification (MUSIC) algorithm. The method according to claim 1,
wherein the first function consists of the first matrix, a Hermitian matrix for the first matrix, a second matrix formed by a noise subspace, and a Hermitian matrix for the second matrix . The method according to claim 1,
M _t × M _r virtual array elements are implemented by the M _t transmit antennas and the M _r receive antennas, and the first function is transmitted and received through the M _t ×M _r virtual array elements. generated based on first signals and the reflected first signals. delete The method according to claim 1,
The method of operation is
generating a second signal comprising a beat frequency indicative of a distance between the device and the first target using the first matrix; and
and estimating a result of a fast Fourier transform (FFT) on the second signal as a distance between the device and the first target. A device for detecting multiple targets, comprising:
processor;
M _t transmit antennas for transmitting first signals under the control of the processor;
M _r receiving antennas for receiving the first signals reflected by the multiple targets under the control of the processor; and
a memory for storing one or more instructions executed by the processor;
The one or more instructions
generate a first function for estimating a velocity and an azimuth of each of the multiple targets using the first signals and the reflected first signals;
estimating the velocity and azimuth that maximize the result of the first function as the velocity and azimuth of a first one of the multiple targets that is closest to the device;
generate a first matrix based on the velocity and the azimuth of the first target;
use the first matrix to generate a second signal comprising a beat frequency indicative of a distance between the device and the first target;
estimating a result of Fast Fourier Transformation (FFT) on the second signal as a distance between the device and the first target;
generate a second function by canceling interference caused by the first target from the first function; And
estimating the velocity and azimuth maximizing the result of the second function as the velocity and azimuth of a second one of the multiple targets;
and wherein the distance between the device and the second target is greater than or equal to the distance between the device and the first target, and wherein each of M _t and M _r is a natural number greater than or equal to 2 . 9. The method of claim 8,
wherein the first function consists of the first matrix, a Hermitian matrix for the first matrix, a second matrix formed by a noise subspace, and a Hermitian matrix for the second matrix. 9. The method of claim 8,
M _t × M _r virtual array elements are implemented by the M _t transmit antennas and the M _r receive antennas, and the first function is transmitted and received through the M _t ×M _r virtual array elements. generated based on first signals and the reflected first signals. 9. The method of claim 8,
When generating the second function, the one or more instructions include:
generate a projected matrix by projecting the first matrix onto an orthogonal region; And
and generate the second function by performing eigen-value decomposition on a sample covariance matrix of the projected matrix.
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