KR102311970B1 - Apparatus for tracking direction-of-arrival of received signal and method thereof - Google Patents

Abstract

The present invention relates to a device for tracking angle of arrival and method thereof. According to an embodiment of the present invention, the device for tracking angle of arrival includes: an initial angle of arrival determining unit which calculates an estimated state vector from a received signal received at an arbitrary time nT (where n is an arbitrary integer and T is a period of a preset value) and determines the estimated angle of arrival through a calculated estimated state vector; a predicted angle of arrival determining unit which determines the predicted angle of arrival through a predicted state vector corresponding to the arbitrary time nT; and an angle of arrival re-determining unit which determines whether the received signal can be decomposed based on the determined predicted angle of arrival, and re-determines the estimated angle of arrival based on a determination result. Accordingly, the angle of arrival can be adaptively estimated based on whether the received signal can be resolved.

Description

Apparatus and method for tracking the angle of arrival of a received signal

The present invention relates to an apparatus and method for tracking the angle of arrival of a received signal, and more particularly, to a technical idea of tracking the direction-of-arrival (DOA) of signal sources incident on an array antenna system. will be.

Estimation (or tracking) of the angle of arrival of a signal incident on an antenna is used in various fields such as mobile communication, sonar, smart antenna, and radar.

Such methods of estimating the angle of arrival of signals have been studied for the past several decades, focusing on the beamforming method and the subspatial method. It is possible to improve the angle of arrival estimation resolution.

Specifically, various techniques such as multiple signal classification (MUSIC), root-MUSIC, min-Norm, and estimation of signal parameter via rotational invariance technique (ESPRIT) have been proposed as an angle of arrival estimation technique. There is a problem in that complexity increases due to a singular value or eigenvalue decomposition process for forming a signal or noise subspace.

Accordingly, recently, an angle of arrival tracking algorithm combining an efficient subspace technique and a known tracking algorithm has been studied in order to improve computational complexity.

As the above-mentioned angle of arrival tracking algorithm, a new algorithm (hereinafter, PASTd kalman) in which a projection approximation subspace tracking based deation (PASTd) algorithm and a Kalman filtering technique are combined has been proposed.

PASTd kalman was able to reduce the computational complexity when constructing subspaces by avoiding ED and SVD with RLS (recursive least squares) technique. have.

More recently, a new algorithm (hereinafter referred to as AMEND) that replaces the Kalman filter with a luenberger observer as an angle of arrival tracking algorithm has been proposed. In terms of applying the -based method without eigendecomposition) algorithm, there is still a problem that low complexity cannot be implemented.

Korean Patent No. 10-1958337 "Method and apparatus for estimating the angle of arrival of a signal" Korean Patent Registration No. 10-1559270 "A method for estimating the angle of arrival of a sliding vector-based low-computational equally spaced linear array using an autocorrelation matrix and an apparatus therefor"

An object of the present invention is to provide an apparatus and method for tracking an angle of arrival capable of adaptively estimating an angle of arrival based on whether a received signal can be resolved.

An object of the present invention is to provide an angle of arrival tracking apparatus and method capable of implementing very low computational complexity by using a Luenburger observer instead of a Kalman filter for estimating and filtering the angle of arrival.

An object of the present invention is to provide an apparatus and method for tracking an angle of arrival that can further improve performance by optimizing an observer gain in a Luenburger observer.

The apparatus for tracking an angle of arrival according to an embodiment calculates an estimated state vector from a received signal received at an arbitrary time nT (where n is an arbitrary integer and T is a period of a preset value), and through the calculated estimated state vector An initial angle of arrival determiner that determines the estimated angle of arrival, a predicted angle of arrival determiner that determines a predicted angle of arrival through a predicted state vector corresponding to an arbitrary time nT, and whether the received signal can be decomposed based on the determined predicted angle of arrival and a recrystallization unit for determining the angle of arrival and recrystallizing the estimated angle of arrival based on the determination result.

According to one side, the reception signal may be a signal received from at least one signal source at an arbitrary time nT by a plurality of reception antennas disposed at a predetermined interval.

According to one side, the initial angle of arrival calculation unit is based on at least one subspace of a multiple signal classification (MUSIC) algorithm, an estimation of signal parameter via rotational invariance techniques (ESPRIT) algorithm, and a direct signal space construction method (DSPCM) algorithm. The estimated state vector may be calculated based on the technique or the beamforming technique.

According to one side, the prediction state vector corresponding to the arbitrary time nT may be a vector calculated based on the received prediction signal expected to be received at the arbitrary time nT at the time of the previous time (n-1)T.

According to one side, the predicted angle of arrival determiner may calculate the predicted state vector by multiplying the estimated state vector corresponding to the previous time (n-1)T calculated through the initial angle of arrival determiner by a preset dynamic matrix. .

According to one side, the predicted angle of arrival determiner may calculate the predicted state vector corresponding to the next period whenever the period T of the preset value is repeated.

According to one side, the predicted angle of arrival determiner may determine a plurality of predicted angles of arrival corresponding to each of the plurality of signals, and may calculate distances between the plurality of predicted angles of arrival.

According to one side, the angle of arrival recrystallization unit may compare the calculated distances between the plurality of predicted angles of arrival with a preset threshold value, and determine whether the received signal can be decomposed based on the comparison result.

According to one side, the angle of arrival recrystallization unit determines that the decomposition of the received signal is impossible when the distance between the calculated plurality of predicted angles of arrival is less than a preset threshold value, and determines that the received signal cannot be decomposed, and p determined before an arbitrary time nT (where p is n). The estimated state vector may be recalculated through QLS regression (quadratic least square regression) based on the previously estimated angle of arrival of a smaller integer), and the estimated angle of arrival may be re-determined through the recalculated estimated state vector.

According to one side, the angle of arrival recrystallization unit determines that the decomposition of the received signal is possible when the distance between the calculated plurality of predicted angles of arrival is greater than a preset threshold value, and recalculates the estimated state vector through the luenberger observer. , the estimated angle of arrival can be re-determined through the recalculated estimated state vector.

According to one side, the angle of arrival recrystallization unit calculates the root-mean-square-error (RMSE _k ) of the angle of arrival corresponding to the k-th (here, k is a positive integer) receiving antenna, and the calculated RMSE _k It is possible to determine first to third element parameter values that minimize the value of , and optimize an observer gain according to the Luenburger observer through calculation of the determined first to third element parameter values.

In the method of tracking the angle of arrival according to an embodiment, the predicted angle of arrival is determined by the predicted angle of arrival determining unit through a predicted state vector corresponding to a predetermined time nT (where n is an arbitrary integer and T is a period of a preset value) calculating an estimated state vector from the received signal received at an arbitrary time nT in the initial angle of arrival determining unit, determining the estimated angle of arrival through the calculated estimated state vector, and in the angle of arrival recrystallization unit, the determined The method may include determining whether the received signal can be decomposed based on the predicted angle of arrival and recrystallizing the estimated angle of arrival based on the determination result.

According to an embodiment, the angle of arrival may be adaptively estimated based on whether the received signal can be decomposed.

According to an embodiment, very low computational complexity may be implemented by using the Luenburger observer instead of the Kalman filter for estimating and filtering the angle of arrival.

According to an embodiment, the performance may be further improved by optimizing the observer gain in the Luenburger observer.

1 is a diagram for explaining an apparatus for tracking an angle of arrival according to an embodiment.
2A to 2C are diagrams for explaining an example of optimizing an observer gain in an apparatus for tracking an angle of arrival according to an embodiment.
3A to 3D are diagrams for explaining a comparison result of the angle of arrival estimation performance between the apparatus for tracking the angle of arrival according to an exemplary embodiment and a conventional estimation algorithm.
4 is a view for explaining a method of tracking an angle of arrival according to an exemplary embodiment.

Specific structural or functional descriptions of the embodiments according to the concept of the present invention disclosed herein are only exemplified for the purpose of explaining the embodiments according to the concept of the present invention, and the embodiment according to the concept of the present invention These may be embodied in various forms and are not limited to the embodiments described herein.

Since the embodiments according to the concept of the present invention may have various changes and may have various forms, the embodiments will be illustrated in the drawings and described in detail herein. However, this is not intended to limit the embodiments according to the concept of the present invention to specific disclosed forms, and includes changes, equivalents, or substitutes included in the spirit and scope of the present invention.

Terms such as first or second 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 element from another element, for example, without departing from the scope of rights according to the concept of the present invention, a first element may be named as a second element, Similarly, the second component may also be referred to as the first component.

When a component is referred to as being “connected” or “connected” to another component, it is understood that the other component may be directly connected or connected to the other component, but 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 no other element is present in the middle. Expressions describing the relationship between elements, for example, “between” and “between” or “directly adjacent to”, etc. should be interpreted similarly.

The terminology used herein is used only to describe specific embodiments, and is not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly dictates otherwise. In this specification, terms such as "comprise" or "have" are intended to designate that the described feature, number, step, operation, component, part, or combination thereof exists, and includes one or more other features or numbers, It should be understood that the possibility of the presence or addition of steps, operations, components, parts or combinations thereof is not precluded in advance.

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 specification. does not

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. However, the scope of the patent application is not limited or limited by these examples. Like reference numerals in each figure indicate like elements.

1 is a diagram for explaining an apparatus for tracking an angle of arrival according to an embodiment.

으로 표기하고, 행렬 A의 전치행렬(transpose matrix)은

으로 표기하며, 행렬 A의 에르미트 전치행렬(Hermitian transpose matrix 혹은 conjugate transpose matrix)은

로 표기하고, M x N 영행렬(zero matrix)은

으로 표기하며, N x N 항등행렬(identity matrix)은

으로 표기하기로 한다. In the following, the complex conjugation matrix of matrix A is

, and the transpose matrix of matrix A is

and the Hermitian transpose matrix (or conjugate transpose matrix) of matrix A is

denoted as , and the M x N zero matrix is

It is denoted as , and the N x N identity matrix is

to be denoted as

In addition, the angle-of-arrival tracking apparatus according to an embodiment is an equally spaced linear array ( It may be a device applied to a Uniform Linear Array) antenna system to estimate an angle of arrival at each reception antenna.

인 K개(단, K는 양의 정수)의 원거리 신호

가 서로 다른 각도

에서 선형어레이에 도달한다고 가정할 수 있다. 그리고, 선형어레이를 구성하는 N개의 수신 안테나 각각에 수신 신호는

로 표기할 수 있다. Specifically, the wavelength

K distant signals (where K is a positive integer)

are different angles

It can be assumed that a linear array is reached at And, the reception signal to each of the N reception antennas constituting the linear array is

can be denoted as

(단, 여기서

) 를 정의하면 수신 신호는 하기 수학식1과 같이 주어질 수 있다.At this time, the steering vector (steering vector)

(However, here

), the received signal can be given as in Equation 1 below.

[Equation 1]

이고,

이며,

이고,

는 수신 안테나 각각에 대응되는 노이즈(noise)를 성분으로 하는 벡터를 나타낸다. here,

ego,

is,

ego,

denotes a vector having noise corresponding to each reception antenna as a component.

은 선험적으로 알려져 있는 값으로 설정될 수 있고, 수신 안테나 간의 간격 d는

/2로 설정될 수 있다. 또한 충돌 신호의 수(number of impinging signals) K 역시 기존의 방법으로 설정될 수 있다. For example, a preset wavelength in the antenna system

can be set to a value known a priori, and the spacing d between receiving antennas is

It can be set to /2. In addition, the number of impinging signals, K, may also be set by the conventional method.

및

는 하기의 수학식2의 조건을 만족하는 확률벡터(random vector)일 수 있다. 평균적으로 제로(zero, '0')를 만족하며, 하기 수학식2의 조건을 만족하도록 설정될 수 있다. vector

and

may be a random vector satisfying the condition of Equation 2 below. On average, zero (zero, '0') is satisfied, and it may be set to satisfy the condition of Equation 2 below.

[Equation 2]

E [ s (t)] = O _Kx1 , E [ n (t)] = O _Kx1 ,

는 크로네커 델타 함수를 나타내고, P는 대각선 원소의 값으로 음아닌 실수 값

를 갖는 대각 행렬(diagonal matrix)을 나타내며,

는 수신 안테나에 더해지는 노이즈의 세기를 나타내는 값으로 관측을 통해 그 추정값을 얻어낼 수도 있다. here,

denotes the Kronecker delta function, and P is the value of the diagonal element, a nonnegative real value.

Represents a diagonal matrix with

is a value indicating the intensity of noise added to the receiving antenna, and the estimated value may be obtained through observation.

Meanwhile, the angle-of-arrival tracking apparatus according to an embodiment uses signals observed from a plurality of reception antennas for time t = ..., 0, T, 2T, 3T, ..., nT (where n is an integer, T can be traced the path of the signal sources by taking angle estimates in a positive real number.

Referring to FIG. 1 , the apparatus 100 for tracking an angle of arrival according to an embodiment may adaptively estimate an angle of arrival based on whether a signal of a received signal can be resolved.

In addition, very low computational complexity may be implemented by using a luenberger observer instead of a kalman filter for estimating and filtering the angle of arrival.

Also, the apparatus 100 for tracking the angle of arrival may improve performance through motion compensation according to delay.

Also, the angle of arrival tracking apparatus 100 may further improve performance by optimizing an observer gain in the Luenburger observer.

To this end, the angle of arrival tracking apparatus 100 according to an embodiment may include an initial angle of arrival determiner 110 , a predicted angle of arrival determiner 120 , and an angle of arrival recrystallization unit 130 .

에 대한 추정 상태 벡터를

로 표기하고, 추정 상태 벡터

를 통해 결정되는 추정 도래각은

으로 표기하며, 임의의 시간 t = nT에 대응되는 예측 상태 벡터를

로 표기하고, 예측 상태 벡터

를 통해 결정되는 예측 도래각은

으로 표기하기로 한다.Hereinafter, the actual angle of arrival at an arbitrary time t = nT (where n is an arbitrary integer and T is a period of a predetermined value)

the estimated state vector for

denoted as , and the estimated state vector

The estimated angle of arrival determined through

denoted as , and a predicted state vector corresponding to an arbitrary time t = nT

denoted by , and the predicted state vector

The predicted angle of arrival determined through

to be denoted as

)를 산출하고, 산출된 추정 상태 벡터(

)를 통해 추정 도래각(

)을 결정할 수 있다.Specifically, the initial angle of arrival determiner 110 according to an embodiment is configured to obtain an estimated state vector (

), and the calculated estimated state vector (

) through the estimated angle of arrival (

) can be determined.

)의 첫번째 요소(first component)는 도래각을 나타내고, 두번째 요소(second component)는 도래각 속도를 나타내며, 세번째 요소(third component)는 도래각 가속도를 나타낼 수 있다. According to one side, the estimated state vector (

), a first component may indicate an angle of arrival, a second component may indicate a velocity of an angle of arrival, and a third component may indicate an acceleration of the angle of arrival.

)를 산출하여, 산출된 추정 상태 벡터(

)의 첫번째 요소로부터 추정 도래각(

)을 결정할 수 있다.In other words, the initial angle of arrival determiner 110 determines the estimated state vector (

) by calculating the estimated state vector (

Estimated angle of arrival from the first element of ) (

) can be determined.

In addition, the reception signal may be a signal received from at least one signal source at an arbitrary time nT by a plurality of reception antennas disposed at a predetermined interval.

)를 산출할 수 있다.According to one side, the initial angle of arrival calculation unit 110 may include at least one subspace of a multiple signal classification (MUSIC) algorithm, an estimation of signal parameter via rotational invariance techniques (ESPRIT) algorithm, and a direct signal space construction method (DSPCM) algorithm. subspace) based technique or the estimated state vector (

) can be calculated.

)를 산출할 수 있다.In other words, the initial angle of arrival calculation unit 110 estimates based on an angle of arrival estimation technique that is considered most suitable for a given situation, such as a subspace-based technique such as the MUSIC algorithm, the ESPRIT algorithm, the ESPRIT algorithm, and DSPCM, or a beamforming technique. state vector (

) can be calculated.

에 대한 시간 t = -2T, t = -T 및 t = 0에서의 실제 도래각

,

및

의 추정치

,

및

을 획득할 수 있다. More specifically, when the current time t = 0, the initial angle of arrival calculation unit 110 uses an appropriate angle of arrival estimation method to

Actual angle of arrival at time t = -2T, t = -T and t = 0 for

,

and

estimate of

,

and

can be obtained.

를 하기 수학식3을 통해 산출할 수도 있다. As a more specific example, the initial angle of arrival calculation unit 110 calculates the estimated state vector at an arbitrary time t = 0.

can also be calculated through Equation 3 below.

[Equation 3]

의 세번째 요소는 기공지된 알고리즘인 AMEND 및 PASTd Kalman와 같이 '0'으로 설정될 수 있다. Here, the initial estimated state vector

The third element of can be set to '0' as in the well-known algorithms AMEND and PASTd Kalman.

)를 통해 예측 도래각(

)을 결정할 수 있다. The predicted angle of arrival determiner 120 according to an embodiment may include a predicted state vector (

) through the predicted angle of arrival (

) can be determined.

)는 이전 시간 (n-1)T의 시점에서 임의의 시간 nT에 수신될 것으로 예상되는 수신 예측 신호에 기초하여 산출하는 벡터일 수 있다. According to one side, the predicted state vector (

) may be a vector calculated based on a reception prediction signal expected to be received at an arbitrary time nT at the time of the previous time (n-1)T.

)의 첫번째 요소로부터 예측 도래각(

)을 결정할 수 있다. In addition, the angle of arrival determining unit 120 calculates the predicted state vector (

) predicted angle of arrival from the first element of (

) can be determined.

)에 기설정된 동적 행렬(dynamic matrix)이라 불리는 행렬 F를 곱하여 예측 상태 벡터(

)를 산출할 수 있다.According to one side, the predicted angle of arrival determiner 120 determines an estimated state vector (

) is multiplied by a matrix F called a predetermined dynamic matrix, and the predicted state vector (

) can be calculated.

)를 산출할 수 있고, 예측 도래각 결정부(120)는 이전 시간 (n-1)T에 대응되는 추정 상태 벡터(

)를 이용하여 예측 상태 벡터(

)를 산출할 수 있다.In other words, the initial angle of arrival determiner 110 determines the estimated state vector ((n-1)T corresponding to the previous time (n-1)T

), and the predicted angle of arrival determiner 120 calculates the estimated state vector (

) using the predicted state vector (

) can be calculated.

)를 산출할 수 있으며, 이때 동적 행렬 F는 하기 수학식5와 같이 설정될 수 있다.More specifically, the predicted angle of arrival determiner 120 calculates the predicted state vector (

) can be calculated, and in this case, the dynamic matrix F can be set as in Equation 5 below.

[Equation 4]

[Equation 5]

)의 첫번째 요소, 두번째 요소 및 세번째 요소 각각은

,

및

에 대한 예측 값을 의미하고,

는 임의의 시간 nT에서의 실제의 도래각,

는 임의의 시간 nT에서의 실제 도래각의 1차 미분 값,

는 임의의 시간 nT에서의 실제 도래각의 2차 미분 값을 의미할 수 있다. Here, the predicted state vector (

), the first element, the second element, and the third element are each

,

and

means the predicted value for

is the actual angle of arrival at any time nT,

is the first derivative of the actual angle of arrival at any time nT,

may mean a second derivative value of the actual angle of arrival at an arbitrary time nT.

According to one side, the predicted angle of arrival determiner 120 may calculate the predicted state vector corresponding to the next period whenever the period T of the preset value is repeated.

In other words, the predicted angle of arrival determiner 120 determines the next period t+1 = T, 2T, 3T, 4T, ..., ( A predicted state vector corresponding to each of n+1)T may be calculated.

)를 산출할 수 있다.According to one side, the predicted angle of arrival determiner 120 determines a plurality of predicted angles of arrival corresponding to each of the plurality of signals, and a distance (

) can be calculated.

)는 하기 수학식6을 통해 도출될 수 있으며, 여기서,

을 만족하는 실수 값일 수 있다.More specifically, the distance between the plurality of predicted angles of arrival (

) can be derived through Equation 6 below, where

It may be a real value that satisfies .

[Equation 6]

)에 기초하여 수신 신호들의 분해 가능 여부를 판단하고, 판단 결과에 기초하여 추정 도래각(

)을 재결정할 수 있다. 즉, 둘 이상의 도래각 간의 거리(

)가 지나치게 가까워져 관측 분해능 범위 밖으로 벗어날 경우 발생할 수 있는 성능 저하를 방지하기 위하여, 도래각 간의 거리(

)가 특정 수치 미만으로 작아질 경우 도래각 재결정부(130)가 추정 도래각을 재설정함으로써 도래각 추정 성능을 향상시킬 수도 있다.The angle of arrival recrystallization unit 130 according to an embodiment may include the predicted angle of arrival (

) to determine whether the received signals can be resolved, and based on the determination result, the estimated angle of arrival (

) can be re-determined. That is, the distance between two or more angles of arrival (

In order to prevent performance degradation that may occur when ) is too close and out of the observation resolution range, the distance between the angles of arrival (

) becomes smaller than a specific value, the angle of arrival recrystallization unit 130 may reset the estimated angle of arrival, thereby improving the performance of estimating the angle of arrival.

)을 이용하여 추정 도래각을 재결정할 수도 있다.The angle of arrival recrystallization unit 130 according to an embodiment calculates an effective delay time corresponding to a difference value between the times at which the received signal is observed and the time at which the angle of arrival (or position) is to be estimated, and during the calculated effective delay time After estimating the amount of change in the generated angle of arrival, the motion-corrected angle of arrival (

) can also be used to recrystallize the estimated angle of arrival.

In other words, the angle of arrival recrystallization unit 130 estimates the amount of change in the angle of arrival (or position) occurring during the effective delay time, and then corrects the estimated value to the value of the angle of arrival (or position) estimated or predicted from the observed values. By doing so, the estimated angle of arrival can be re-determined.

)과 임의의 시간 nT에 대응되는 예측 상태 벡터(

)에 기초하여 추정 도래각을 재결정할 수 있다.According to one side, the angle of arrival recrystallization unit 130 is a motion-corrected angle of arrival (

) and the predicted state vector (

) based on the estimated angle of arrival can be re-determined.

)를 재산출할 수 있다.According to one side, the angle of arrival recrystallization unit 130 determines whether the received signal can be decomposed, and when it is determined that the received signal can be decomposed, the estimated state vector (

) can be recalculated.

)를 기설정된 임계값과 비교하고, 비교 결과에 기초하여 수신 신호의 분해 가능 여부를 판단할 수 있다. Specifically, the angle of arrival recrystallization unit 130 calculates the distance between the plurality of predicted angles of arrival (

) may be compared with a preset threshold, and it may be determined whether the received signal can be decomposed based on the comparison result.

) 값 중

및

의 조건을 만족하면서 최소 값을 갖는 거리(

) 값을 기설정된 임계값과 비교하여 수신 신호의 분해 가능 여부를 판단할 수 있다. More specifically, the angle of arrival recrystallization unit 130 calculates the distance between the plurality of predicted angles of arrival (

) of the values

and

The distance with the minimum value while satisfying the condition of

) value may be compared with a preset threshold value to determine whether the received signal can be decomposed.

)가 기설정된 임계값 보다 작으면 수신 신호의 분해가 불가능한 것으로 판단하여, 임의의 시간 nT 이전에 결정된 p개(여기서, p는 양의 정수)의 이전 추정 도래각(

, 여기서

)에 기반한 QLS 회귀(quadratic least square regression)를 통해 추정 상태 벡터(

)를 재산출하고, 재산출된 추정 상태 벡터(

)를 통해 추정 도래각(

)을 재결정할 수 있다. According to one side, the angle of arrival recrystallization unit 130 calculates a distance (

) is less than the preset threshold, it is determined that the decomposition of the received signal is impossible, and the previously estimated angles of arrival of p (where p is a positive integer) determined before an arbitrary time nT (

, here

) through QLS regression based on the estimated state vector (

), and the recalculated estimated state vector (

) through the estimated angle of arrival (

) can be re-determined.

,

을 활용하여 하기 수학식8과 같이 상수 a, b, 및 c를 결정할 수 있다.More specifically, if the angle of arrival recrystallization unit 130 determines that it is impossible to decompose the received signal, it is assumed that the previous p actual angles of arrival values satisfy Equation 7 below, and the previous p estimated angles of arrival in the QLS session

,

Constants a, b, and c can be determined by using Equation 8 below.

[Equation 7]

[Equation 8]

)를 하기 수학식9를 통해 재산출할 수 있다. When the constants a , b and c are calculated through Equation 8, the angle of arrival recrystallization unit 130 determines the estimated state vector (

) can be recalculated through Equation 9 below.

[Equation 9]

)의 두번째 성분 및 세번째 성분은 m = n인 조건에서 수학식7의 1차 미분과 2차 미분을 통해 산출될 수 있다. Here, the recalculated estimated state vector (

) and the third component may be calculated through the first and second differentiation of Equation 7 under the condition that m = n.

)를 재산출하고, 재산출된 추정 상태 벡터(

)를 통해 추정 도래각(

)을 재결정할 수 있다. According to one side, the angle of arrival recrystallization unit 130 determines that the received signal can be decomposed if the calculated distances between the plurality of predicted angles of arrival are greater than a preset threshold value, and the estimated state vector through a luenberger observer (

), and the recalculated estimated state vector (

) through the estimated angle of arrival (

) can be re-determined.

)과 움직임 보정된 도래각(

) 및 임의의 시간 nT에 대응되는 예측 상태 벡터(

)를 연산하여 추정 상태 벡터(

)를 재산출할 수 있다. According to one side, the angle of arrival recrystallization unit 130 is an observer gain according to the Luenburger observer.

) and motion-compensated angle of arrival (

) and the predicted state vector corresponding to an arbitrary time nT (

) by calculating the estimated state vector (

) can be recalculated.

)에 기설정된 동적 행렬 F를 곱하는 동작으로만 예측 상태 벡터(

)를 산출하였으나, 도래각 재결정부(130)에서는 (n-1)T 내지 nT의 시간 구간에서 수집된 수신 신호를 고려하여 추정 도래각(

)을 재결정(update)할 수 있다. More specifically, the predicted angle of arrival determiner 120 does not consider the received signal collected in the time interval of (n-1)T to nT, and the estimated state vector (

) is multiplied by a predetermined dynamic matrix F only by the operation of the predicted state vector (

), but the angle of arrival recrystallization unit 130 considers the received signals collected in the time interval of (n-1)T to nT and the estimated angle of arrival (

) can be updated.

)을 재결정할 수 있다.As a more specific example, the angle of arrival recrystallization unit 130 may calculate the estimated angle of arrival (

) can be re-determined.

[Equation 10]

)은 3차원 열벡터(3-dimensional column vector)일 수 있고, 움직임 보정된 도래각(

)은 특정 알고리즘에 의해 얻어지는 임의의 시간 nT에 대응되는 도래각의 추정치일 수 있다. Here, the observer gain (

) may be a 3-dimensional column vector, and the motion-corrected angle of arrival (

) may be an estimate of the angle of arrival corresponding to any time nT obtained by a specific algorithm.

)을 산출하는 알고리즘을 DCDSPCMNE(delay comensated direct signal space construction method newton estimation)이라 명명하기로 한다. In the following, the motion-corrected angle of arrival (

) will be named DCDSPCMNE (delay comensated direct signal space construction method newton estimation).

)은 뉴턴의 방법(Newton's method)을 통해 산출되는 도래각(

)에서 지연 시간에 따른 움직임 보정하여 산출될 수 있다. According to one side, the motion-corrected angle of arrival (

) is the angle of arrival (

) can be calculated by correcting the motion according to the delay time.

)을 산출하고, 뉴턴의 방법을 통해 산출되는 도래각(

)에 대하여 지연 시간에 따른 움직임의 변화를 추적 및 보정함으로써 움직임 보정된 도래각(

)을 산출할 수 있다. In other words, the angle of arrival recrystallization unit 130 uses an algorithm based on Newton's method to determine the angle of arrival (

), and the angle of arrival (

), by tracking and correcting the change in motion according to the delay time,

) can be calculated.

)은 임의의 시간 nT에 대응되는 예측 도래각(

)과 수신 신호에 대응되는 잡음 부공간의 직교정사영 행렬(

)을 연산하여 산출될 수 있다.According to one side, the angle of arrival (

) is the predicted angle of arrival (

) and the orthogonal projection matrix of the noise subspace corresponding to the received signal (

) can be calculated.

Hereinafter, an algorithm based on Newton's method will be referred to as direct signal space construction method newton estimation (DSPCMNE).

)가 최소가 되는 지점을 추정할 수 있다. Specifically, DSPCMNE is a cost function (

) can be estimated at the point at which it is minimized.

[Equation 11]

는 잡음 부공간의 직교정사영 행렬을 의미하고,

는 각도

에 대한 스티어링 벡터를 의미할 수 있다. here,

is the orthogonal projection matrix of the noise subspace,

is the angle

may mean a steering vector for .

)에 대하여 뉴턴 반복 법(Newton's iteration method)에 기반한 제로 서치(zero search)를 수행하여 뉴턴의 방법을 통해 재정의된 각도

를 산출할 수 있다.In addition, DSPCMNE is the cost function (

), the angle redefined through Newton's method by performing a zero search based on Newton's iteration method.

can be calculated.

는 하기 수학식12를 통해 산출될 수 있다. More specifically, the overridden angle

can be calculated through Equation 12 below.

[Equation 12]

는

의 실수부분(real part)을 나타내고, 각도

는 비용 함수의 미분 값(

)에 대한 제로 서치에 따른 대략적인 추정(coarse estimate) 값을 나타낸다. here,

Is

represents the real part of

is the derivative of the cost function (

) represents a coarse estimate value according to the zero search.

으로 인해 무시될 수 있으며, 분모의 첫번째 항이 무시되므로, 뉴턴의 방법을 통해 산출되는 도래각(

)은 하기 수학식13을 통해 산출될 수 있다. Also, in Equation 12, the first term of the denominator is

can be neglected due to , and since the first term in the denominator is ignored, the angle of arrival (

) can be calculated through Equation 13 below.

[Equation 13]

및

는 하기 수학식14를 통해 정의되는 벡터일 수 있다. Also, in Equation 13

and

may be a vector defined through Equation 14 below.

[Equation 14]

는 프로파게이터(propagator)의 추정값으로서 하기 수학식15를 통해 산출될 수 있다. Also, in Equation 13, the matrix

is an estimated value of a propagator and may be calculated through Equation 15 below.

[Equation 15]

은 L×L 크기의 단위행렬(Identity matrix)을 의미하고,

는 LХ1 크기의 정규 직교 벡터들(othonomal vectors)을 의미할 수 있으며, 하기 수학식15-1 및 수학식15-2로부터 얻어지는 신호 벡터에 그람-슈미트 과정(Gram-Schmidt Process)을 적용하여 구할 수도 있다. here,

denotes an identity matrix of L × L size,

may mean orthonormal vectors of LХ1 size, and may be obtained by applying the Gram-Schmidt Process to the signal vector obtained from Equations 15-1 and 15-2 below. have.

[Equation 15-1]

, m=1, 2, 3, ..., M-1

, m=1, 2, 3, ..., M-1

[Equation 15-2]

, m=M, M+1, ..., N

, m=M, M+1, ..., N

는 신호 벡터의 추정치를,

(0 <

< 1)는 forgetting factor를 의미할 수 있다. Here, M is a positive integer of 2 or more that does not exceed N,

is the estimate of the signal vector,

(0 <

< 1) may mean a forgetting factor.

)은 뉴턴의 방법을 통해 산출되는 도래각(

)과, 이전 시간 (n-1)T에 대응되는 추정 상태 벡터(

) 및 기설정된 값의 주기(T) 내에 얻어지는 총 데이터의 수 (Ns)를 연산하여 산출될 수 있다. According to one side, the motion-corrected angle of arrival (

) is the angle of arrival (

) and the estimated state vector corresponding to the previous time (n-1)T(

) and the total number of data (Ns) obtained within the period (T) of the preset value.

)은 (n-1)T와 nT사이의 시간 구간(time interval) 동안 수집된 데이터를 이용하여 획득될 수 있다. 따라서 뉴턴의 방법을 통해 산출되는 도래각(

)은 시간 t = nT에서의 도래각의 추정치라기 보다는 시간 (n-1)T와 nT사이의 어느 순간의 도래각의 추정치라 볼 수 있다.Specifically, the orthogonal projection matrix of the noise subspace (

) may be obtained using data collected during a time interval between (n-1)T and nT. Therefore, the angle of arrival calculated through Newton's method (

) can be viewed as an estimate of the angle of arrival at any instant between time (n-1)T and nT rather than an estimate of the angle of arrival at time t = nT.

를 특정 시간 t = (n-

)T(여기서

는 실효 지연률)에서의 도래각의 추정치로 간주하고, 실효지연시간

T 동안의 움직임을 보정함으로써 움직임 보정된 도래각(

)을 산출할 수 있다. Accordingly, the angle of arrival recrystallization unit 130 according to an embodiment

for a specific time t = (n-

)T(where

is regarded as an estimate of the angle of arrival in the effective delay rate), and the effective delay time

By compensating for motion during T, the motion-compensated angle of arrival (

) can be calculated.

More specifically, assuming that the angular velocity does not change during the interval between time (n-1)T and nT, the angular change in the time interval of time t = (n-1)T and time nT is derived through Equation 16 below can do.

[Equation 16]

)은 수학식16에 기초하는 하기 수학식17을 통해 산출할 수 있다. Also, the motion-corrected angle of arrival (

) can be calculated through Equation 17 below based on Equation 16.

[Equation 17]

라 두고, 시각 (n-1)T에서의 해당 물체의 추정된 위치의 값을

이라 두면, k번째 물체의 움직임이 보정된 시각 nT에서의 위치값

은 하기 수학식18과 같이 산출될 수 있다. Equation 17 is an equation indicating how motion compensation can be performed with respect to an embodiment using the Luenburger estimation technique. However, if properly interpreted, it is not difficult to see that this equation can be applied to the case of estimating the angle of arrival or position using other techniques including the Kalman filter. For this, the position of the k-th object (position information such as angle of arrival) estimated or predicted based on data observed before time nT

Let , the value of the estimated position of the object at time (n-1)T

If , the position value at time nT at which the motion of the k-th object is corrected

can be calculated as in Equation 18 below.

[Equation 18]

는 경우에 따라서는 시각 (n-1)T에서의 보정된 위치 추정값

의 값을 사용할 수도 있고 이외의 다른 위치 추정값을 사용할 수도 있다.in Equation 18

is the corrected position estimate at time (n-1)T in some cases

You can use the value of , or you can use other location estimates.

의 값은 데이터들이 관측되는 시각, 즉, t = T₀, t = T₀ +

, t = T₀ + 2

, ..., t = T₀ + (N_S - 1)

을 forgetting factor

에 따라 가중평균한 값, 즉, 하기 수학식19가 나타내는 값을 (n-

)T라 둠으로써 산출할 수도 있다. 단, 여기서 T₀는 최초 관측 시각,

는 관측 시간 간격을 T로 나눈 값, N_S는 관측하는 총 데이터 수를 의미한다.Next, the effective delay rate

The value of is the time at which the data are observed, that is, t = T ₀ , t = T ₀ +

, t = T ₀ + 2

, ..., t = T ₀ + (N _S - 1)

the forgetting factor

The weighted average value according to (n-

) can also be calculated by setting T. However, where T ₀ is the first observation time,

is the value obtained by dividing the observation time interval by T, and N _S is the total number of data observed.

[Equation 19]

)T라 하면,

의 값은 하기 수학식20에 의해 산출될 수 있다. As described above, the value represented by Equation 19 is (n-

) T, then

The value of can be calculated by Equation 20 below.

[Equation 20]

를 수학식17 또는 수학식18에 적용하면, 움직임 보정된 도래각(

) 또는 위치(

)의 값을 구할 수 있다. Next, the effective delay rate obtained using Equation 20

is applied to Equation 17 or Equation 18, the motion-corrected angle of arrival (

) or location (

) can be found.

)을 결정하며, 결정된 제1 내지 제3 요소 파라미터 값(k₁, k₂,

)의 연산을 통해 루엔버거 옵저버에 따른 옵저버 이득(observer gain)을 최적화할 수 있다. According to one side, the angle of arrival recrystallization unit 130 calculates the root-mean-square-error (RMSE _k ) of the angle of arrival corresponding to the k-th (here, k is a positive integer) receiving antenna. and first to third element parameter values (k ₁ , k ₂ , to minimize the calculated RMSE _{k value)}

), and the determined first to third element parameter values (k ₁ , k ₂ ,

), the observer gain according to the Luenberger observer can be optimized.

In general, the observer gain is a parameter that greatly affects the tracking performance, and the optimal value was determined through an experiment in the well-known AMEND. However, in the experiment in AMEND, the values vary depending on the simulation environment, such as the number of antennas, the number of signal sources, the trajectory of the signal, and the SNRdB, so it is difficult to determine the observer gain every time an experiment is performed.

Accordingly, the angle of arrival recrystallization unit 130 according to an embodiment verifies the performance of the optimal observer gain using the state error and determines the optimal observer gain in a more effective and reliable way based on the verification result. .

)는 하기 수학식21과 같이 정의될 수 있다. Specifically, the state estimation error (

) may be defined as in Equation 21 below.

[Equation 21]

는

로 정의되는 상태 벡터를 의미할 수 있다. here,

Is

It may mean a state vector defined as .

는 하기 수학식22과 같이 정의 될 수 있다. Also, a vector called state evolution mismatch at time t = nT

can be defined as in Equation 22 below.

[Equation 22]

는 제로 벡터와 동일할 수 있다. Here, if the angular acceleration does not change during the time interval between (n-1)T and nT, the vector

may be equal to the zero vector.

)는 하기 수학식20과 같이 정의될 수 있다.Also, the angle measurement error (

) may be defined as in Equation 20 below.

[Equation 23]

In addition, the following Equation 24 can be derived based on Equations 4, 11 and 23.

[Equation 24]

Next, the following Equation 25 can be derived based on Equations 21, 22 and 24.

[Equation 25]

및

이므로 하기 수학식26을 도출할 수 있다. Also, in Equation 25

and

Therefore, the following Equation 26 can be derived.

[Equation 26]

)에 관한 수학식26을 재정렬하면, 하기 수학식27과 같이 표현될 수 있다. state estimation error (

), by rearranging Equation 26, it can be expressed as Equation 27 below.

[Equation 27]

) 및 수신 신호의 총 관측 간격 수(total number of observation intervals, N_T)에 기반하여 하기 수학식 28을 통해 산출될 수 있다. _{On the other hand, the RMSE k} of the angle of arrival corresponding to the k-th signal is the state estimation error (

) and the total number of observation intervals (N _T ) of the received signal may be calculated through Equation 28 below.

[Equation 28]

를

로 대각선화(diagonalize)하면, 옵저버 이득(

)은 하기 수학식29의 우변과 같이 표현될 수 있다.Also, the matrix included in the first term of Equation 27

cast

If we diagonalize to , the observer gain (

) can be expressed as the right side of Equation 29 below.

[Equation 29]

는 대각선 요소가 행렬

의 고유값인 대각 행렬이다.here,

is a matrix with diagonal elements

It is a diagonal matrix that is the eigenvalue of .

)은 고유 값인 대각 행렬

의 대각성분에 의해 결정될 수 있다. That is, the observer gain (

) is the diagonal matrix with eigenvalues

can be determined by the diagonal component of

의 대각성분을

,

및

으로 두면(단, 여기서 제1 요소 파라미터(k₁) 및 제2 요소 파라미터(k₂)는 음이 아닌 실수 값이고 제3 요소 파라미터(

)는 실수), 옵저버 이득(

)의 제1 내지 제3 요소는 하기 수학식30을 통해 산출될 수 있다.More specifically, the diagonal matrix

the diagonal component of

,

and

(provided that the first element parameter (k ₁ ) and the second element parameter (k ₂ ) are non-negative real values and the third element parameter (

) is real), observer gain (

) of the first to third elements can be calculated through the following Equation 30.

[Equation 30]

는 옵저버 이득(

)의 i번째 요소를 의미한다.here,

is the observer gain (

) means the i-th element.

)에 관한 수학식27은 수학식29를 통해 하기 수학식31과 같이 표현될 수 있다. On the other hand, the state estimation error (

Equation 27 for ) can be expressed as Equation 31 below through Equation 29.

[Equation 31]

), 각도 측정 오류(

) 및 state evolution mismatch(

)를 기준으로 상태 추정 오류(

)를 하기 수학식32와 같이 표현할 수 있다.If Equation 31 is repeatedly calculated, the initial value (

), angle measurement error (

) and state evolution mismatch(

) based on the state estimation error (

) can be expressed as Equation 32 below.

[Equation 32]

In Equation 32, the second and third terms are related to the summation from m=1 to m=n, and as N increases, the second and third terms may become large.

의 모든 대각선 요소의 크기를 1 보다 작게 선택하면, n에 가까운 m과의 각도 측정 오류(

)와 state evolution mismatch(

)가 상태 추정 오류(

)의 값에 영향을 미치므로,

는 k가 커짐에 따라 제로 행렬로 수렴할 수 있다.But,

If the size of all diagonal elements of is chosen to be less than 1, then the angle measurement error with m close to n (

) and state evolution mismatch(

) is the state estimation error (

), as it affects the value of

may converge to the zero matrix as k increases.

)의 크기(magnitude)는 각도 측정 오류(

) 보다 작은 크기의 차수로 판단할 수 있다. In addition, unless the period (T) of the preset value is selected to be very large, state evolution mismatch (

) is the magnitude of the angle measurement error (

) can be judged as a smaller order of magnitude.

의 모든 대각선 요소의 크기를 1에 비해 충분히 작게 선택하면, 수학식32의 세번째 항은 일반적인 상황에서 무시할 수 있을 정도로 작은 값으로 설정될 수 있으므로, 상태 추정 오류(

)는 하기 수학식33으로 표현될 수 있다. thus,

If the size of all the diagonal elements of is selected to be sufficiently small compared to 1, the third term of Equation 32 can be set to a value small enough to be neglected in a general situation, so the state estimation error (

) can be expressed by the following Equation 33.

[Equation 33]

이고

라 가정하면 하기 수학식34와 같이 표현될 수 있으며, 수학식34에서 행렬

는 하기 수학식35와 같이 표현될 수 있다.On the other hand, Equation 28 regarding the root mean square error (RMSE _{k ) is}

ego

Assuming that , it can be expressed as Equation 34 below, and in Equation 34

can be expressed as Equation 35 below.

[Equation 34]

[Equation 35]

는 기설정된 값의 주기를 의미한다.Here, the parameter

denotes a period of a preset value.

이 되는 양의 실수

가 존재하면 수학식34 및 수학식35는 하기 수학식36 및 수학식37로 각각 표현될 수 있다. Furthermore, for every n

a positive real number

If is present, Equations 34 and 35 can be expressed by Equations 36 and 37, respectively.

[Equation 36]

[Equation 37]

)의 대각성분 값의 선택에 따른 RMSE_k를 위의 수학식34 내지 37을 이용하여 모니터링함으로써 최적의 옵저버 이득(

)을 결정할 수도 있다. That is, the angle of arrival recrystallization unit 130 according to an embodiment is a diagonal matrix (

) by monitoring the _{RMSE k} according to the selection of the diagonal component value of

) can also be determined.

)을 결정할 수 있다.That is, it is very difficult to obtain the optimum value through observation or simulation of the actual system, whereas the first element parameter (k ₁ ) and the second element parameter (k) are relatively easy using Equations 34 to 37 above. _{2 ), and how the value of RMSE k} changes according to the third element parameter (k ₃ ) may be numerically grasped. Using such numerical data, it is possible to obtain the values of the first, second, and third element parameters giving the _{optimal RMSE k value, and by substituting the three values into Equation 30, the optimal observer gain}

) can be determined.

) 의 값을 수학식30에 대입하여 최적의 옵저버 이득(

)을 구할 수 있다.As a more specific example, the angle of arrival recrystallization unit 130 selects 0.05, 0.10, ..., 0.95 as candidate values of _{the first element parameter k 1} and the second element parameter k _{2 , and the third} After selecting 0, 5, ..., 175 as candidate values of the element parameter (k ₃ ), a combination of these candidate values is substituted into Equations 34 to 37 to calculate the value of _{RMSE k , and then RMSE k} is the minimum A first element parameter (k ₁ ) value, a second element parameter (k ₂ ) value, and a third element parameter (

) by substituting the value of Equation 30 to obtain the optimal observer gain (

) can be obtained.

2A to 2C are diagrams for explaining an example of optimizing an observer gain in an apparatus for tracking an angle of arrival according to an embodiment.

를 단위로 하여 표현되어 있다. 이후 도 2a 내지 도 2c를 통해 설명하는 내용 중 일실시예에 따른 도래각 추적 장치를 통해 설명한 내용과 중복되는 설명은 생략하기로 한다. In other words, FIGS. 2A to 2C are views for explaining an example of the apparatus for tracking the angle of arrival according to the embodiment described with reference to FIG. _{1 . The} numerical value of RMSE k expressed as a contour line is

It is expressed in units of . Hereinafter, descriptions that overlap with those described through the apparatus for tracking the angle of arrival according to an embodiment among the contents described with reference to FIGS. 2A to 2C will be omitted.

)가 35°일 때의 평균 제곱근 오차(RMSE_k) 값이 제1 요소 파라미터(k₁) 및 제2 파라미터(k₂)의 값에 따라 어떻게 변하는지 보여주고 있다. 2A to 2C, reference numeral 210 denotes a third element parameter (

) shows how the value of the root mean square error (RMSE _k ) changes according to the values of the first element parameter (k ₁ ) and the second parameter (k _{2 ) when 35°.}

To obtain the values of the graphs of FIGS. 2A to 2C , 0.05, 0.10, ..., 0.95 as candidate values of _{the first element parameter (k 1} ) and the second element parameter (k _{2 ), the third element parameter (} 0, 5, ..., 175 were selected as candidate values for k _{3 ).}

)가 15°일 때의 RMSE_k 값을 제1 요소 파라미터(k₁) 및 제2 파라미터(k₂)의 함수로 표현하는 그래프를 나타낸다. In addition, reference numeral 220 denotes a third element parameter (

) shows a graph expressing _{the RMSE k} value when 15° is a function of the first element parameter (k ₁ ) and the second parameter (k _{2 ).}

)가 55°일 때의 RMSE_k 값을 제1 요소 파라미터(k₁) 및 제2 파라미터(k₂)의 함수로 표현하는 그래프를 나타낸다.In addition, reference numeral 230 denotes a third element parameter (

) shows a graph expressing the RMSE _k value at 55° as a function of the first element parameter (k ₁ ) and the second parameter (k _{2 ).}

Referring to reference numerals 210 to 230 , it can be seen that _{the RMSE k value increases as the first element parameter k 1} and the second parameter k ₂ move away from (0.7, 0.5) at reference numeral 210 .

)의 값이 35°에서 멀어질수록 RMSE_k 값이 느리게 상승하는 것을 확인할 수 있다. _{In addition, it can be seen that the RMSE k} value significantly increases as the first element parameter (k ₁ ) and the second parameter (k ₂ ) approach 1, and the third element parameter (

), it can be seen that _{the RMSE k} value increases slowly as the value of 35° increases.

)의 값을 더 다양하게 변화시켜가며 참조부호 210 내지 참조부호 230의 그래프와 유사한 그래프를 그려 관찰해 보면 제1 요소 파라미터(k₁)의 값이 0.7, 제2 요소 파라미터(k₂)의 값이 0.5, 제3 요소 파라미터(

)의 값이 35일 때, RMSE_k의 값이 최솟값을 갖는데, 이 값들을 수학식 27에 대입하면 이에 대응되는 최적의 옵저버 이득(

) 값을 구할 수 있다.The third element parameter (

) by drawing and observing a graph similar to the graph of reference numerals 210 to 230 while changing the value of the first element parameter (k ₁ ), the value of the first element parameter (k 1 ) is 0.7, and the value of the second element parameter (k ₂ ) This 0.5, the third element parameter (

) is 35, the value of RMSE _k has a minimum value, and when these values are substituted in Equation 27, the corresponding optimal observer gain (

) can be found.

3A to 3D are diagrams for explaining a comparison result of the angle of arrival estimation performance between the apparatus for tracking the angle of arrival according to an exemplary embodiment and a conventional estimation algorithm.

In other words, FIGS. 3A to 3D are views for explaining an example of the apparatus for tracking an angle of arrival according to an embodiment described with reference to FIGS. 1 to 2C , and an embodiment of the contents described later with reference to FIGS. 3A to 3D . A description that overlaps with the content described through the apparatus for tracking the angle of arrival according to the above will be omitted.

3A to 3D , reference numeral 310 denotes a graph for explaining a trajectory of an angle of arrival for simulation, and reference numeral 320 denotes a device for tracking an angle of arrival according to an embodiment when variables N = 12 and K = 3 ( DSPCLT) and previously known estimation algorithms (AMEND and PASTd Kalman) _{show a graph explaining the change in the root mean square error (RMSE k} ) value with time change.

의 변화에 따른 비용 함수(

)의 변화를 설명하는 그래프를 나타내고, 참조부호 340은 변수 N = 12, K = 5일 때 일실시예에 따른 도래각 추적 장치(DSPCLT)와 기 공지된 추정 알고리즘(AMEND 및 PASTd Kalman)에서 RMSE_k 값의 변화를 설명하는 그래프를 나타낸다.In addition, reference numeral 330 denotes an angle in an angle of arrival tracking device (DSPCLT) and known estimation algorithms (AMEND and PASTd Kalman) according to an embodiment.

The cost function with a change in

), and reference numeral 340 denotes the RMSE in the angle of arrival tracking device (DSPCLT) according to an embodiment and the known estimation algorithms (AMEND and PASTd Kalman) when the variables N = 12 and K = 5 A graph is shown that explains the change in the value of _k.

,

및

으로부터 성능을 비교하기 위해 K = 3인 신호가 반 파장으로 분리된 N = 12개의 수신 안테나로 충돌하는 상황을 고려할 수 있다. According to reference numerals 310 to 340, simulations using AMEND, PASTd Kalman and DSPCLT show the actual angle of arrival in time-varying directions.

,

and

To compare the performance from , consider a situation where a signal with K = 3 collides with N = 12 receive antennas separated by half wavelengths.

Further, the probability of failure is derived from the above-described simulation (failure probability, P _F) and the mean square error (RMSE) may be derived as shown in Table 1 below.

값을 선택해도 실패하지 않기 때문에 가장 안정적인 성능을 나타내는 것을 확인할 수 있으나, RMSE_k 측면에서는 최악의 결과를 나타내는 것을 확인할 수 있다. According to Table 1, AMEND

Since it does not fail even if a value is selected, it can be seen that the most stable performance is shown, but in _{terms of RMSE k} , it can be confirmed that the worst result is shown.

값을 설정하면 제로 오류(zero failures)를 달성할 수 있으며 AMEND보다 더 나은 RMSE_k 값을 보여줌을 확인할 수 있으며, DSPCLT가 가장 우수한 RMSE 성능을 달성할 수 있는 것을 확인할 수 있다. On the other hand, DSPCLT and PASTd Kalman

It can be seen that setting the value achieves zero failures _{and shows a better RMSE k} value than AMEND, confirming that DSPCLT can achieve the best RMSE performance.

The main reason DSPCLT has an overall performance advantage is that it has a relatively large effective aperture size with the same number of receive antennas (sensor elements).

)가 AMEND 및 PASTd Kalman보다 DSPCLT에서 훨씬 더 선명하다는 것을 확인할 수 있다. 이에 DSPCLT는 훨씬 정교한 Kalman 필터 알고리즘을 사용하는 PASTd Kalman 및 PASTd Kalman의 성능을 능가하는 AMEND 대비, RMSE_k 성능 측면에서 보다 향상된 성능을 나타낼 수 있다. Specifically, according to reference numeral 330, the cost function (

) is much sharper in DSPCLT than in AMEND and PASTd Kalman. Therefore, DSPCLT can show better performance in terms of _{RMSE k} performance compared to AMEND, which outperforms PASTd Kalman and PASTd Kalman, which use a much more sophisticated Kalman filter algorithm.

Further, according to reference numeral 330, when the actual signal source is at 70°, 80° and 150°, it can be confirmed that DSPCLT and PASTd Kalman can decompose the signal, but AMEND shows that the graph is distorted and the signal decomposition is impossible.

More specifically, signal decomposition may be affected by SNRdB, the number of antennas, and the like. That is, DSPCLT can show a resolution of about 180/(10×2) = 9° with 10 antennas when snrdB is 5dB, and about 180/(20×2)=4.5° with 20 antennas. resolution can be seen.

In other words, DSPCLT at reference numeral 330 indicates that when the signal source is at 60° and 65°, signal resolution becomes impossible when the number of antennas is 10, and when the number of antennas is 20, signal resolution becomes possible. have.

On the other hand, by increasing the number of objects to the K = 5 when the simulation, the failure probability of the simulation (failure probability, P _F) and the mean square error for the _(k RMSE) can be obtained as shown in Table 2.

According to Table 2, can, even when increasing the number of objects DSPCLT is confirmed that the more excellent characteristics than _k P _F and RMSE PASTd Kalman and AMEND.

On the other hand, DSPCLT has significantly lower computational complexity compared to PASTd Kalman and AMEND. For example, when N=20, M=K=5, Ns=20, the number of real numbers is estimated and compared as shown in Table 3. .

According to Table 3, it can be seen that a significant portion of computational complexity is required for subspace configuration. In particular, it can be seen that AMEND requires a particularly large number of operations in the subspace configuration compared to DSPCLT. In addition, it can be seen that PASTdKalman requires more computation than DSPCLT and AMEND because Kalman filter is applied.

In addition, DSPCLT was found to require a relatively large amount of computation compared to AMEND in the projector configuration and filtering process, but since the amount of computation in the subspace configuration is very small, as a result, it can be confirmed that the total amount of computation is smaller than that of AMEND.

As a result, it can be confirmed that DSPCLT exhibits superior performance compared to the previously known PASTdKalman and AMEND in terms of computational complexity.

4 is a view for explaining a method of tracking an angle of arrival according to an embodiment.

In other words, FIG. 4 is a view of an operating method of the apparatus for tracking an angle of arrival according to an embodiment described with reference to FIGS. 1 to 3D . The apparatus for tracking an angle of arrival according to an embodiment of the contents described later with reference to FIG. 4 is shown. A description that overlaps with the content described above will be omitted.

Referring to FIG. 4 , in step 410 , in the method for tracking the angle of arrival according to an embodiment, the prediction corresponding to the time nT (where n is an arbitrary integer and T is the period of a preset value) is predicted in the predicted angle of arrival determiner. The predicted angle of arrival can be determined through the state vector.

Next, in step 420, the angle of arrival tracking method according to an embodiment calculates an estimated state vector from the received signal received at an arbitrary time nT by the initial angle of arrival determiner, and calculates the estimated angle of arrival through the calculated estimated state vector. can decide

Next, in step 430, the method of tracking the angle of arrival according to an embodiment determines whether the received signal can be decomposed based on the predicted angle of arrival determined by the angle of arrival recrystallization unit, and recrystallizes the estimated angle of arrival based on the determination result. have.

After all, using the present invention, it is possible to adaptively estimate the angle of arrival based on whether the received signal can be decomposed.

In addition, using the present invention, very low computational complexity can be implemented by using a luenberger observer instead of a kalman filter for estimating and filtering the angle of arrival.

In addition, using the present invention, it is possible to improve the performance of estimating the angle of arrival through motion compensation according to the delay.

In addition, by using the present invention, it is possible to further improve the angle of arrival estimation performance by optimizing the observer gain in the Luenburger observer.

As described above, although the embodiments have been described with reference to the limited drawings, various modifications and variations are possible from the above description by those of ordinary skill in the art. For example, the described techniques are performed in a different order than the described method, and/or the described components of the system, structure, apparatus, circuit, etc. are combined or combined in a different form than the described method, or other components Or substituted or substituted by equivalents may achieve an appropriate result.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

100: angle of arrival tracking device 110: initial angle of arrival determination unit
120: predicted angle of arrival determining unit 130: angle of arrival recrystallization unit

Claims (12)

An initial angle of arrival at which an estimated state vector is calculated from a received signal received at an arbitrary time nT (where n is an arbitrary integer and T is a period of a predetermined value), and an estimated angle of arrival is determined through the calculated estimated state vector decision part;
a predicted angle of arrival determiner that determines a plurality of predicted angles of arrival corresponding to each of a plurality of signals through a predicted state vector corresponding to the arbitrary time nT, and calculates a distance between the plurality of predicted angles of arrival;
An angle of arrival recrystallization unit that determines whether the received signal can be decomposed based on the calculated distances between the plurality of predicted angles of arrival and recrystallizes the estimated angle of arrival based on a result of the determination
including,
The distance between the plurality of predicted angles of arrival,
a difference value between any one predicted arrival angle among the plurality of predicted arrival angles and the remaining predicted arrival angles other than the one predicted arrival angle among the plurality of predicted arrival angles;
angle of arrival tracking device. According to claim 1,
The received signal is
A signal received from at least one signal source at the arbitrary time nT by a plurality of receiving antennas arranged at a predetermined interval
angle of arrival tracking device. According to claim 1,
The initial angle of arrival calculation unit,
based on a subspace-based technique or a beamforming technique of at least one of a multiple signal classification (MUSIC) algorithm, an estimation of signal parameter via rotational invariance techniques (ESPRIT) algorithm, and a direct signal space construction method (DSPCM) algorithm. which yields an estimated state vector
angle of arrival tracking device. According to claim 1,
The predicted state vector corresponding to the arbitrary time nT is,
A vector calculated based on a reception prediction signal expected to be received at the arbitrary time nT at the time of the previous time (n-1)T
angle of arrival tracking device. According to claim 1,
The predicted angle of arrival determining unit,
calculating the predicted state vector by multiplying the estimated state vector corresponding to the previous time (n-1)T calculated through the initial angle of arrival determiner by a preset dynamic matrix
angle of arrival tracking device. According to claim 1,
The predicted angle of arrival determining unit,
Each time the period (T) of the preset value is repeated, calculating a predicted state vector corresponding to the next period
angle of arrival tracking device. delete According to claim 1,
The angle of arrival recrystallization unit,
comparing the calculated distances between the plurality of predicted angles of arrival with a preset threshold value, and determining whether the received signal can be decomposed based on the comparison result
angle of arrival tracking device. 9. The method of claim 8,
The angle of arrival recrystallization unit,
If the distance between the calculated plurality of predicted angles of arrival is smaller than a predetermined threshold value, it is determined that the received signal cannot be decomposed, and p (where p is a positive integer) determined before the arbitrary time nT is transferred. recalculating the estimated state vector through quadratic least square regression (QLS) based on the estimated angle of arrival and recrystallizing the estimated angle of arrival through the recalculated estimated state vector;
angle of arrival tracking device. 9. The method of claim 8,
The angle of arrival recrystallization unit,
If the distance between the calculated plurality of predicted arrival angles is greater than a preset threshold, it is determined that the received signal can be decomposed, and the estimated state vector is recalculated through a luenberger observer, and the recalculated Recrystallizing the estimated angle of arrival through the estimated state vector
angle of arrival tracking device. 11. The method of claim 10,
The angle of arrival recrystallization unit,
_{Root-Mean-Square-Error (RMSE k} ) of the angle of arrival corresponding to the k-th (here, k is a positive integer) receiving antenna is calculated, and the value of _{the calculated RMSE k is minimized} determining first to third element parameter values, and optimizing an observer gain according to the Luenburger observer through calculation of the determined first to third element parameter values;
angle of arrival tracking device. In the predicted angle of arrival determining unit, a plurality of predicted angles of arrival corresponding to each of the plurality of signals are determined through a predicted state vector corresponding to an arbitrary time nT (where n is an arbitrary integer, and T is a period of a preset value). and calculating a distance between the plurality of predicted angles of arrival;
calculating an estimated state vector from the received signal received at the arbitrary time nT by the initial angle of arrival determiner, and determining the estimated angle of arrival through the calculated estimated state vector;
determining whether the received signal can be decomposed based on the calculated distances between the plurality of predicted angles of arrival, in the angle of arrival recrystallization unit, and recrystallizing the estimated angle of arrival based on the determination result;
including,
The distance between the plurality of predicted angles of arrival,
a difference value between any one predicted arrival angle among the plurality of predicted arrival angles and the remaining predicted arrival angles excluding the one predicted arrival angle among the plurality of predicted arrival angles;
How to track your angle of arrival.

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