KR20200033571A - Method and apparatus for estimating the number of signals, by considering SML cost function and hypothesis test - Google Patents

Abstract

The present invention relates to a method for estimating the number of signals in consideration of an SML cost function and hypothesis verification preceding the arrival angle (DoA) estimation in a radar system for a vehicle, and to an apparatus thereof. According to the method of the present invention, following processes are executed. First, an initial DOA estimate is determined by using an SML cost function in a covariance matrix of a received signal. The initial number of signals is set to one. By using the determined initial DOA estimate, the number of signals is estimated by applying a GLRT method to the SML cost function. When the estimated value is greater than a certain threshold, one signal is added to the number of signals, and then the DOA estimation is continuously performed using an alternating projection technique. When the estimated value is not greater than a threshold value, the estimation of the number of signals is terminated.

Description

Method and apparatus for estimating the number of signals, by considering SML cost function and hypothesis test}

The present invention relates to a method and apparatus for estimating the number of signals in consideration of a stochastic maximum likelihood (SML) cost function and hypothesis verification prior to the arrival angle (DoA) estimation in a vehicle radar system.

In order to detect a target, a vehicle radar system detects the distance, speed, and angle of the target by processing the received signal after transmitting the transmission waveform. In particular, one of methods for detecting the angle of a target, a method using a subspace of a signal (MUSIC, Root-MUSIC, ESPRIT, etc.) requires information on the number of targets (signals).

Existing methods for estimating the number of signals include an AIC method, an MDL method, and an intuitive method that uses a eigenvalue of a covariance matrix generated by Hermitian product by sampling a received signal. The signal count estimation algorithm of the AIC and MDL methods estimates the signal count using the ratio of the sum of the eigenvalues and the product. However, these methods do not estimate the number of signals well when both direct and reflected waves are present. The intuitive method is a method of estimating the maximum index through the ratio of eigenvalues as the number of signals. However, this method is very efficient in terms of computational complexity, but when the eigenvalue of the covariance matrix is too small, the number of signals may be estimated incorrectly.

The intuitive method, which is a known algorithm for estimating the number of signals, cannot estimate the number of signals well if the eigenvalues are too small or the information on the ratio of eigenvalues is not accurately known. The AIC and MDL methods estimate the number of signals of the direct wave well, but the signal number of both the direct wave and the reflected wave does not estimate the number of signals.

Accordingly, in order to compensate for the problem of low reliability of the existing algorithms due to the eigenvalues of the covariance matrix, it is intended to increase reliability using an SML cost function and a signal number estimation method using hypothesis verification.

A more efficient method in terms of accuracy than the above-described conventional algorithm is a signal count estimation algorithm considering SML (Stochastic Maximum Likelihood) cost function and hypothesis test. Like the existing methods, the present invention also uses the covariance matrix of the received signal, but in addition, it takes into account the SML cost function and precedes the process of estimating the angle of arrival (DoA) of the signal and applies the GLRT method from the estimated angle of arrival. To estimate. In the present invention, a process of updating the number of signals using the SML cost function is disclosed.

The process of the present invention is summarized as follows. First, an initial arrival angle estimate is determined by using the SML cost function in the covariance matrix of the received signal. The initial number of signals is set to one. Using the determined initial arrival angle estimate, the number of signals is estimated by applying the GLRT method to the SML cost function. If the estimate is greater than a certain threshold, the number of signals is added, and then the angle of arrival is continuously performed using an alternating projection technique. If it is not greater than the threshold, the number of signals is estimated.

When introducing the process of the present invention in more detail as follows.

FFT is executed from the received signal to generate a covariance matrix. Looking at the process of generating the covariance matrix, first, a zero signal is padded to a received signal that is time data, that is, a beat signal, and then a fast Fourier transform (FFT) is performed and a positive frequency domain is generated. Take and extract the peak bin and select the number of bins. Through this process, a frequency covariance matrix is generated.

Next, the arrival angle is estimated by applying the covariance matrix of the received signal generated as above to the SML cost function. When a ULA antenna is used, received signals incident on a plane wave have the same arrival angle (DoA) information for each component antenna, and an array vector is used to define the SML cost function for estimating the arrival angle. Should be defined. However, since the distance from the signal to each sensor is different, time-delay occurs. This should be considered.

Next, the ML algorithm is initialized and optimized using an alternating projection technique. This step may include the following detailed steps.

1) Obtain the SML cost function by changing the arrival angle of the first incident signal at regular search intervals

2) Fixing the first arrival angle as the initial estimate of the first incident signal

3) Obtaining the SML cost function by changing the arrival angle of the second incident signal at a constant search interval

Finally, the SML cost function is calculated using the arrival angle estimate, and the number of signals is finally estimated by applying the Generalized Likelihood Ratio Test (GLRT). To estimate the number of signals, the null hypothesis verification method can be used. To verify the null hypothesis, a threshold value is set based on a chi-square distribution, and if the estimate is larger than a certain threshold, add a signal number and then use an alternate projection technique to arrive. Each estimation is continuously performed, and if it is not greater than a threshold, estimation of the number of signals is terminated.

The above disclosure of the present invention will be further clarified by describing specific embodiments with drawings in the future.

In the case of the present invention, unlike the conventional algorithm, the reliability of estimating the number of signals is very high. After the received signal was N-point FFT, a covariance matrix was generated with bins where peaks occur and side bins of the peak bins. Considering the target range, after generating the covariance matrix by the number of targets, the number of signals is estimated, and the number of signal estimates for each covariance matrix is added to obtain the final number of signals.

Table 1 below shows the result of estimating the number of signals for 5 bins. A covariance matrix was generated using one peak bin, four side bins, and a total of five bins. Considering the SML cost function and hypothesis verification, each signal number estimation result was obtained for SNR (signal-to-noise ratio) of -10dB, 0dB, and 10dB. Scenario with one incident signal with a distance of 6 m and an incident angle of -10 deg, Scenario with two incident signals with a distance of 6 m, 15 m with an incident angle of -10 deg, 20 deg, and a distance of 6 m, 15 m, 24 m with an incident angle of -10 deg, 0 deg , Table 1 shows the result of estimating the number of signals for each scenario with three incident signals of 20 deg.

Table 2 shows the result of estimating the number of signals for 7 bins. The number of signals was estimated with 6 peak bins and 6 side bins. In the rest, the signal count estimation results were obtained in the same scenario as in Table 1.

1 is a block diagram of the present invention
FIG. 2 is a block diagram showing the construction of the covariance matrix of FIG. 1 (100).
3 is a structural diagram of the ULA antenna
FIG. 4 is an execution process diagram of the signal number estimation steps 400 and 500 of FIG. 1.

Advantages and features of the present invention, and a method of achieving them will be made clear by referring to embodiments described in detail with reference to the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but will be implemented in various different forms, and only the present embodiments make the disclosure of the present invention complete, and have ordinary knowledge in the technical field to which the present invention pertains. It is provided to fully inform the person of the scope of the invention, and the invention is defined by the description of the claims.

On the other hand, the terms used in this specification are for describing the embodiments and are not intended to limit the present invention. In this specification, the singular form also includes the plural form unless otherwise specified in the phrase. As used herein, the terms "comprises" or "comprising" do not exclude the presence or addition of one or more other components, steps, or actions other than the stated component, step, or action. Meaning.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. First, in adding reference numerals to the components of each drawing, the same components are assigned the same reference numerals as much as possible even though they are displayed on different drawings, and in describing the present invention, specifics of related well-known components or functions are described. When the description may obscure the subject matter of the present invention, the detailed description is omitted.

1 is a configuration block diagram of the present invention, and is a block diagram of a signal number estimation algorithm considering SML cost function and hypothesis verification according to the present invention. Each step is explained in order.

100: FFT is executed from the received signal to generate a covariance matrix

2 shows a step 100 of generating the covariance matrix, and Equation 1 shows a covariance matrix using a time average of a received signal. Referring to the process of generating the covariance matrix in FIG. 2, first, a received signal that is time data, that is, a beat signal 110 is zero padded (120). Zero padding is the process of filling a pixel with a value of 0 around the input map to increase the output size and scan more pixels of the input map. Thereafter, a fast Fourier transform (FFT) is performed (130), a positive frequency domain is taken (140), a peak bin is extracted, and the number of bins is selected (150). Through this process, a frequency covariance matrix (see Equation 1) is generated (160).

200: The arrival angle is estimated by applying the covariance matrix of the received signal generated in step 100 to the SML cost function.

3 shows a ULA (Uniform Linear Array) antenna. The ULA antenna excites all antennas constituting the array with a current of the same size and maintains an equal distance between sensors. In the case of ULA antennas, signals S1, S2, and S3 incident as plane waves have the same angle of arrival (DoA) information θ for each antenna. To define the SML cost function for estimating the arrival angle, an array vector must be defined. However, since the distance from the signal to each sensor is different, time-delay occurs. Reflecting this, the array vector in the ULA antenna can be expressed as Equation 2.

Equation 3 shows the antenna sensor response for deriving the SML cost function.

When the sampled antenna sensor response value is transformed by a fast Fourier, the antenna sensor response can be expressed as in Equation 4.

는 신호를 나타내고

는 잡음을 나타낸다. 그리고 N은 선택된 FFT bin의 개수를 나타낸다. 평균을 0으로 가지고, 복소수값으로 구성되었으며, 가우시안 random process로 표현된다. here

Indicates a signal

Indicates noise. And N represents the number of selected FFT bins. It has an average of 0, consists of complex values, and is represented by a Gaussian random process.

The covariance matrix at the first angle of arrival is shown in Equation 5.

에 대한 Likelihood 함수를 구하면 다음 수학식 6과 같다. One observation using covariance matrix

When the Likelihood function for is obtained, Equation 6 below is obtained.

가 독립적이고 동일하게 분포한다(iid: independent and identically distributed)고 가정하면 전체 관측에 대한 Likelihood 함수는 수학식 7과 같다. 수학식 7에서 M은 안테나 센서의 개수이다.

Assuming that is independent and identically distributed (iid), the Likelihood function for the whole observation is as shown in Equation 7. In Equation 7, M is the number of antenna sensors.

에 대한 SML 방법에 의한 추정치 (1)은 수학식 8로부터 구해진다.

The estimated value (1) by the SML method for is obtained from Equation (8).

는 다음 수학식 9와 같이 주어진다.In Equation 8

Is given by the following equation (9).

에 대한 SML 방법에 의한 추정치 (2)는 수학식 10으로 주어진다.In addition, the equation (7)

The estimate (2) by the SML method for is given by Equation (10).

는 추정된 신호 공분산행렬,

는 추정된 잡음파워를 나타내는데 각각 수학식 11, 12와 같다.In Equation 10

Is the estimated signal covariance matrix,

Denotes the estimated noise power, as shown in Equations 11 and 12, respectively.

는

의 Pseudo Inverse를 의미한다. 수학식 12에서

는

의 영공간(null space)으로의 직교 투영행렬이다. 최종적으로 본 단계 200에서 SML 적용시의 도래각의 최종 추정치는 수학식 13과 같다.Meanwhile, in Equation 11

The

Means Pseudo Inverse. In Equation 12

The

Is an orthogonal projection matrix to the null space. Finally, in step 200, the final estimated value of the arrival angle when SML is applied is as shown in Equation 13.

300: Initialization and optimization of ML algorithm using alternating projection technique

This step includes the following detailed steps.

1) Obtain the SML cost function by changing the arrival angle of the first incident signal at regular search intervals

2) Fixing the first arrival angle as the initial estimate of the first incident signal

3) Obtaining the SML cost function by changing the arrival angle of the second incident signal at a constant search interval

Equation 14 shows the arrival angle estimate of the first signal and the arrival angle estimate of the second signal.

400: SML cost function is calculated using the estimated angle of arrival, and GLRT (Generalized Likelihood Ratio Test) is applied.

500: Estimate the number of signals.

4 shows an execution process of steps 400 and 500 for estimating the number of signals using the arrival angle estimate. The variable notation used below is as follows.

=0으로 설정한다.410:

Set to 0.

라는 귀무가설(Null hypothesis) H₀을 세운다. 즉, H₀:

420:

The null hypothesis H ₀ . In other words, H ₀ :

의 자유도(degree of freedom)를 갖는 카이제곱분포(chi-square distribution)의 꼬리부분(tail area)에 기반하여 문턱값

를 설정한다. 430: To verify the null hypothesis

Threshold based on the tail area of the chi-square distribution with the degree of freedom of

To set.

를 계산한다. 440: Equation 13 under the H ₀

To calculate.

이 문턱값

보다 크면, 추정 신호개수를

로 설정하여 다시 귀무가설 H₀:

로 돌아간다.450: What if

This threshold

If greater than, the estimated number of signals

Set it back to the null hypothesis H ₀ :

Return to.

이 문턱값

보다 크지 않으면, 귀무가설 H₀을 수용하고 절차를 종료한다. 460: In the above step

This threshold

Otherwise, accept the null hypothesis H ₀ and end the procedure.

The components described in the method embodiments of the present invention are at least one of a digital signal processor (DSP), a processor, a controller, an application-specific IC (ASIC), a programmable logic device (FPGA, etc.), and other electronic devices, and It is feasible as a hardware element that includes a combination. Also, the functions or processes described in the method embodiments of the present invention can be realized by software, which can be stored in a recording medium. And the components, functions, and processes described in the method embodiment of the present invention can be realized by combining hardware and software.

The configuration of the present invention has been described in detail through preferred embodiments of the present invention, but those skilled in the art to which the present invention pertains are disclosed herein without changing the technical spirit or essential features of the present invention. It will be understood that the lesson may be implemented in other specific forms. It should be understood that the embodiments described above are illustrative in all respects and not restrictive. The protection scope of the present invention is defined by the claims below, rather than by the detailed description, and all changes or modifications derived from the claims and equivalent concepts should be interpreted to be included in the technical scope of the present invention. .

Claims (1)

Determining an initial arrival angle estimate using the SML cost function in the covariance matrix of the received signal,
Using the determined initial arrival angle estimate, the number of signals is estimated by applying the GLRT method to the SML cost function, but if the estimate is larger than the threshold value, the number of signals is added and then the shift angle estimation is continuously performed using the alternate projection technique. Performing, and if not greater than the threshold value, including the step of ending the signal count estimation, SML cost function and the signal number estimation method considering the hypothesis verification.

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