KR20210153918A - Method and apparatus for estimating robust range using hyper-tangent loss function - Google Patents

Abstract

Disclosed are a method and an apparatus for robust distance estimation using a hyper-tangent loss function. The method for robust distance estimation using a hyper-tangent loss function implemented in a computer according to an embodiment comprises the steps of: calculating an error using a difference between an i-th distance observation value and a distance estimate value; calculating a weight for the distance observation value using a hyper-tangent loss function; and calculating a distance estimation value using the predicted weight and the distance observation value.

Description

Robust distance estimation method and apparatus using hypertangent loss function

The following embodiments relate to a robust distance estimation algorithm based on a hyper-tangent loss function. This invention is a research conducted with the support of the Information and Communication Planning and Evaluation Institute with funding from the government (Ministry of Science and ICT) in 2019 (No.2017-0-00474, development of intelligent voice signal processing technology for AI speaker voice assistant).

Distance estimation is a technique for determining the distance between an emitter and a receiver using a received signal strength (RSS) or time-of-arrival (TOA) measurement. Distance information is very important in distance-based localization using TOA and RSS measurement, and the higher the accuracy of the distance measurement, the better the localization accuracy. Distance estimation is used in source localization in a multi-path environment, autonomous driving, location-based service (LBS), sensor networks in multipath situations, intrusion or event detection, and the like. In previous studies, the problem of distance estimation in line-of-sight (LOS) environments was studied. As an example, an optimal unbiased and linear least squares distance estimator is provided based on RSS measurement (Non-Patent Document 1). However, it is a non-robust distance estimation and the performance deteriorates rapidly in a multipath environment.

As such, existing studies have some open problems, and an important task among them is to estimate the distance between the emitter and the receiver in a line-of-sight (LOS)/non-line of sight (NLOS) mixed situation. For example, the LOS path between emitter and receiver can be obstructed indoors or in complex urban situations. The M estimator has received attention because it mitigates the side effects of outliers. M estimators have been widely used for robust signal processing, but M estimators require statistical tests to identify normal and outliers. Huber and bi-square loss functions are widely used in M estimation. A statistical test is necessary because other loss functions must be used for the error magnitude. The flat loss function increases rapidly as the error size increases. This large error severely degrades the estimation performance. To solve this problem, we use a linear or flat loss function when the error magnitude exceeds a certain threshold. Therefore, a statistical test is needed to determine whether the error magnitude exceeds a predefined threshold. This has a high computational burden on the algorithm because the test has to be performed on a sample-by-sample basis. In addition, an optimal threshold value should be determined for normal and outlier identification. This is difficult when the environment or channel changes rapidly because the threshold value must be determined according to the changed environment.

Chitte, S. D., Dasgupta, S., Ding, Z.: 'Distance estimation from received signal strength under log-normal shadowing: bias and variance', IEEE Signal Process. Lett., vol. 16, no. 3, pp. 216-218, Jun. 2009.

The embodiments describe a robust distance estimation method and apparatus using a hyper-tangent loss function, and more specifically, a robust distance estimation algorithm based on a hyper-tangent loss function that does not require a statistical test to estimate distance information. provides

Embodiments estimate distance information using an M estimator algorithm based on a hyper-tangent loss function, so that statistical testing and determination of an optimal threshold are not required, so that the implementation of the algorithm is simpler and more efficient. To provide a robust distance estimation method and apparatus using

According to an embodiment, a robust distance estimation method using a hyper-tangent loss function implemented by a computer includes: calculating an error using a difference between an i-th distance observation value and a distance estimation value; calculating a weight for the distance observation value using a hypertangent loss function; and calculating a distance estimation value using the predicted weight and the distance observation value.

setting an initial distance value and initial parameters; after calculating the error, calculating a standard deviation for the distance observation value; and calculating a parameter for the distance observation value.

Calculating the weights for the distance observation values using the hypertangent loss function includes statistical verification and predefined thresholds by automatically utilizing the hypertangent loss function by providing an M estimator to which weights are assigned. A robust distance estimation algorithm that does not require a value can be provided.

In the step of calculating the weight for the distance observation value using the hypertangent loss function, when the hypertangent loss function is used for the M estimator, a small weight is given to the outlier without statistical testing, and a large weight is given to the normal value. can

Calculating a distance estimate value using the weight and the distance observation value may include calculating the error, calculating the standard deviation, calculating the parameter, and calculating the weight for the distance observation value until the distance estimate value converges. The process of calculating and calculating the distance estimation value may be repeated.

A robust distance estimator using a hyper-tangent loss function according to another embodiment includes an error estimator configured to calculate an error using a difference between an i-th distance observed value and a distance estimate value; a weight calculator for calculating a weight for the distance observation value using a hypertangent loss function; and a distance estimation value calculator configured to calculate a distance estimation value using the predicted weight and the distance observation value.

an initial value setting unit for setting an initial distance value and initial parameters; a standard deviation calculator for calculating the standard deviation for the distance observation value after calculating the error; and a parameter calculator configured to calculate a parameter for the distance observation value.

The weight estimator provides an M estimator to which weights are assigned to automatically utilize a hypertangent loss function to provide a robust distance estimation algorithm that does not require statistical verification and a predefined threshold value. can

When the hypertangent loss function is used for the M estimator, the weight calculator may give a small weight to an outlier without statistical testing and a large weight to a normal value.

The process of calculating the error, calculating the standard deviation, calculating the parameter, calculating the weight, and calculating the distance estimate value may be repeated until the distance estimate value converges.

According to embodiments, by estimating distance information using an M estimator algorithm based on a hyper-tangent loss function, statistical testing and determination of an optimal threshold are not required, so that the implementation of the algorithm is simpler and more efficient. It is possible to provide a robust distance estimation method and apparatus using a loss function.

1 is a flowchart illustrating a robust distance estimation method using a hypertangent loss function according to an embodiment.
2 is a block diagram illustrating a robust distance estimation apparatus using a hypertangent loss function according to an embodiment.
3 is a graph illustrating an MSE according to a distance according to an embodiment.
4 is a graph illustrating MSE according to variance of normal values according to an embodiment.
5 is a graph illustrating MSE as a function of standard deviation of outlier noise according to an exemplary embodiment.
6 is a graph illustrating an MSE according to a bias according to an embodiment.

Hereinafter, embodiments will be described with reference to the accompanying drawings. However, the described embodiments may be modified in various other forms, and the scope of the present invention is not limited by the embodiments described below. In addition, various embodiments are provided in order to more completely explain the present invention to those of ordinary skill in the art. The shapes and sizes of elements in the drawings may be exaggerated for clearer description.

The following embodiments propose a robust distance estimation algorithm based on a hyper-tangent loss function to estimate distance information. In a real noise environment, it is known that impulse noise exists in addition to Gaussian noise. In order to prevent the estimation performance from being degraded by the impact noise, M estimator is used. The environment in which the impact noise is present is modeled as a mixed Gaussian distribution. Here, we present a robust distance estimator for impact noise using only the magnitude of the received signal. M estimators have been widely used for robust signal processing. Existing M estimators require statistical tests to distinguish between inliers and outliers. However, the existing M estimator is algorithmically challenging and computationally burdensome because it requires a statistical test that includes a threshold with time-varying optimality. In this case, the threshold used for statistical testing is a very important parameter, and it is generally difficult to determine this value. These statistical tests have a high computational burden on the algorithm because tests must be performed on each observation. To solve the above problem, we propose an M estimator algorithm based on a hypertangent loss function that does not require statistical testing.

Through the simulation results, it was shown that the estimation performance of the proposed method is similar to that of the existing skipped filter method even without a statistical test procedure. Hereinafter, a robust distance estimation method and apparatus using a hypertangent loss function will be described in more detail.

To solve the above problem, we propose an M estimator that does not require statistical test threshold adjustment. That is, we can automatically utilize the hypertangent loss function by providing an M estimator to which weights are assigned. When using this loss function for the M estimator, it is possible to weight the outliers with small weights while the normals receive large weights and without statistical testing. In addition, a robust Bayesian M estimator is provided using prior information obtained using prior M distance estimates.

Although the proposed method does not require statistical testing and optimal threshold determination in the simulation results, it shows that the mean square error (MSE) performance of the proposed method is similar to that of the skipped filter and is superior to other existing algorithms. The MSE performance of the robust Bayesian M estimator is significantly better than other deterministic methods in the low signal-to-noise ratio (SNR) regime. In fact, the tanh loss function was used as the loss function for robust adaptive filtering. However, the tanh loss function was not utilized as a loss function for the M estimator. Although the information theory learning (ITL) method does not require statistical testing, its estimation performance is inferior to the proposed method. Since the estimation performance is highly dependent on the loss function, the choice of the loss function is important. Therefore, the proposed method is valid because the tanh loss function-based algorithm leads to the improvement of the estimation performance. It should be noted that the proposed distance estimation vulnerability is only a single sensor, but the estimation accuracy can be satisfactory if the sample set size is large enough.

The points according to the embodiments may be summarized as follows.

1) The tanh loss function is used as the loss function of the M estimator.

2) In the existing M estimator utilizing Huber, Hampel, or bi-square loss functions, different loss functions must be used for the error size, so statistical testing is required. However, statistical tests increase the computational complexity of the algorithm because tests must be performed per observation. We also need to find an optimal threshold to identify LOS and NLOS noise. This is difficult when the environment or channel changes rapidly because the threshold value must be determined according to the changed environment. To circumvent this problem, the embodiments provide a robust algorithm that does not require statistical tests and optimal thresholds.

3) Perform MSE analysis of the proposed algorithm according to the embodiments.

4) The MSE performance of the proposed algorithm according to the embodiments is similar to that of the skipped filter and outperforms other existing algorithms. Moreover, it does not require statistical testing and selection of optimal threshold values.

Below, we first deal with the LOS/NLOS mixed distance estimation problem. Next, the conventional distance estimation method will be briefly described. Then, the proposed robust M estimation algorithm based on the tanh loss function is described. Next, after evaluating the MSE performance through the simulation results, a conclusion is presented.

LOS/NLOS Mixed Distance Estimation Problem

The purpose of distance estimation methods utilizing RSS measurements is to accurately estimate the range between the source and receiver to minimize error criteria (eg MSE or sum of squared errors). In the context of mixed LOS/NLOS distance estimation, the RSS measurement equation can be defined as

[Equation 1]

는 경로 손실 지수이고, n_i는 수신기의 총 샘플 수를 나타내는 N과 함께

분포를 따르는 랜덤 변수이다.

는 각각 평균

이고, 분산이

인 가우시안 확률 밀도 함수(PDF)이다. LOS/NLOS 상황의 혼합된 손실 함수, LOS 환경과의 다른 손실 함수가 활용된다. 이상치는 MSE를 훨씬 크게 렌더링하므로 오류가 클 경우 추정 성능이 심각하게 저하될 수 있다. 따라서 손실 함수는 일반적으로 상수로 제한되거나 이상치의 부작용을 줄이기 위해 오류의 크기가 클 때 선형 함수로 설계된다. Here, P _i is the i-th RSS for the receiver in decibels (dB), P _o is the signal strength at the reference distance (d _{o ), d o} is 1m for convenience, and d is the actual distance.

is the path loss exponent, n _i with N representing the total number of samples in the receiver

It is a random variable that follows a distribution.

is the average of each

, and the variance is

is a Gaussian probability density function (PDF). A mixed loss function of the LOS/NLOS situation, and a different loss function with the LOS environment are utilized. Outliers render the MSE much larger, so large errors can severely degrade estimation performance. Therefore, the loss function is usually limited to a constant or designed as a linear function when the magnitude of the error is large in order to reduce the side effects of outliers.

와 P_o가 priori로 알려져 있다고 가정한다. 일관성을 갖기 위한 조건은 다음과 같다. 첫째, 소규모 페이딩은 시간 평균에 의해 무시되어야 한다. 둘째, 추정된 매개변수 P_o와

는 참 값에 상당히 근접해야 한다. 셋째, 간섭에서 발생하는 배경 잡음의 영향은 무시할 수 있어야 하며 신호는 성공적으로 복조되어야 한다. 기존 LOS 환경에서 측정 오류 n_i는 N(0,

)의 가우시안 분포를 따른다. 그러나 잡음 분포는 실내 및 도시 지역의 heavy-tailed 잡음에 의한 다중 경로 효과로 인해 종래의 가우시안 분포를 따르는 경우는 드물다. 따라서 잡음 분포는 LOS 잡음 성분이 N(0,

)을 따르고 NLOS 잡음이 N(

)에 의해 분포되는 2-모드 가우시안 혼합 분포로 모델링해야 한다. LOS 잡음은 1-

의 확률이 있고 NLOS 잡음은 ε의 확률이 있다. LOS/NLOS 혼합 상황에 대한 이전 연구와 유사한 반면, 이상치 분포의 평균과 분산을 얻을 수 없다. 잡음 분포는 두 가지 모드 가우시안 혼합 분포로 알려져 있지만, 이 분포의 매개변수는 정상치 가우시안 분포의 분산을 제외하고 알려져 있지 않다는 점에 유의해야 한다. 여기서

(0≤

≤1)은 오염 척도로, 보통 0.1보다 작다.In this embodiment, the tanh loss function in which the loss function is truncated to a constant when the magnitude of the error is large may be used. Here, through the calibration campaign

Assume that and P _o are known as priori. The conditions for consistency are as follows. First, small fading should be ignored by time averaging. Second, the estimated parameters P _o and

should be fairly close to the true value. Third, the influence of background noise from interference must be negligible and the signal must be successfully demodulated. In the traditional LOS environment, the measurement error n _i is N(0,

) follows a Gaussian distribution of However, the noise distribution rarely follows the conventional Gaussian distribution due to the multi-path effect caused by heavy-tailed noise in indoor and urban areas. Therefore, the noise distribution is N(0,

) and the NLOS noise is N(

) should be modeled as a two-mode Gaussian mixture distribution distributed by LOS noise is 1-

, and the NLOS noise has a probability of ε. While similar to previous studies of the LOS/NLOS mixed situation, the mean and variance of the outlier distribution could not be obtained. It should be noted that the noise distribution is known as a two-mode Gaussian mixed distribution, but the parameters of this distribution are unknown except for the variance of the stationary Gaussian distribution. here

(0≤

≤1) is a measure of pollution, usually less than 0.1.

Conventional Distance Estimation Method

The conventional median-based range estimator is determined as follows.

And, when a sample is determined as an outlier in the skipped filter, the corresponding sample is removed from the sample set of the receiver. Since the contamination ratio (the proportion of outliers in the sample set) is usually less than 10%, the probability that the filtered sample will be exhausted is small.

)를 사용한다. M 추정량에는 Huber, Tukey, Hampel과 같은 여러 손실 함수를 사용할 수 있지만, 본 실시예에서 기존의 M 추정량에 대해서는 ITL 기반 손실 함수를 채택한다. ITL에 기반한 강인한 솔루션을 달성하기 위해 다음과 같은 비용 함수를 활용할 수 있다.The M estimate for the positional parameter can be viewed as a weighted average of the observations. In this example, the boundary cost function (

) is used. Although several loss functions such as Huber, Tukey, and Hampel can be used for the M estimator, an ITL-based loss function is adopted for the existing M estimator in this embodiment. The following cost functions can be utilized to achieve a robust solution based on ITL.

[Equation 2]

이고,

는 스케일 매개변수이고

이다. 목표는 다음과 같이 추정 매개변수(d)와 관련하여 비용 함수(

)를 최소화하는 것이다.here,

ego,

is the scale parameter

to be. The goal is the cost function (

) is to be minimized.

[Equation 3]

가 구별 가능한 경우, d 산출량과 관련하여 [수학식 3]을 구별한다.

[Equation 3] is distinguished in relation to the amount of output d when .

[Equation 4]

이다. 그러면 [수학식 4]는 다음과 같이 표현할 수 있다.here,

to be. Then, [Equation 4] can be expressed as follows.

[Equation 5]

Or equivalently, it can be expressed as

[Equation 6]

이다. 즉, M 알고리즘은 추정치를 가중 평균으로 나타낸다. 위치 추정치

는 [수학식 6]의 양쪽에

가 존재하기 때문에 반복적으로 얻는다. 스케일 매개변수 (

)는

로 추정된다. 여기서,

이고, d는

^T를 나타내며, 1_N은 NХ1의 크기를 가진 모든 것으로 구성된 벡터이다. 대안으로, 스케일은 다음과 같이 반복적으로 계산할 수 있다.here,

to be. That is, the M algorithm represents the estimate as a weighted average. location estimate

is on both sides of [Equation 6]

is iteratively obtained because scale parameter (

)Is

is estimated to be here,

and d is

^{Representing T} , 1 _N is a vector consisting of all of the size NХ1. Alternatively, the scale can be iteratively computed as

[Equation 7]

Proposed robust distance estimation method (robust M estimation algorithm)

Classical M estimators using Huber or bi-square loss functions require statistical validation because different loss functions must be used for error magnitudes. Statistical validation increases the computational complexity of the algorithm because validation must be performed per sample. In addition, an appropriate threshold should be determined to discriminate between outliers and outliers. This is a difficult task when the environment or channel changes rapidly because the threshold value must be determined according to the changed environment. Due to these problems, here we propose a robust distance estimation algorithm that does not require statistical verification and predefined thresholds.

1 is a flowchart illustrating a robust distance estimation method using a hypertangent loss function according to an embodiment.

Referring to FIG. 1 , a robust distance estimation method using a hyper-tangent loss function implemented by a computer according to an embodiment includes calculating an error using a difference between an i-th distance observation value and a distance estimation value. Including step 120, calculating a weight for the distance observation value using a hypertangent loss function (150), and calculating a distance estimate value using the predicted weight and distance observation value (160) can be done

In addition, the steps of setting the initial distance value and the initial parameters (110), calculating the error, and then calculating the standard deviation for the distance observation value (130), and calculating the parameters for the distance observation value (140) may be further included.

Hereinafter, each step of the robust distance estimation method using the hypertangent loss function according to an embodiment will be described.

The robust distance estimation method using the hypertangent loss function according to the embodiment may be described in more detail by using the robust distance estimation apparatus using the hypertangent loss function according to the embodiment.

2 is a block diagram illustrating a robust distance estimation apparatus using a hypertangent loss function according to an embodiment.

Referring to FIG. 2 , a robust distance estimation apparatus 200 using a hypertangent loss function according to an embodiment includes an initial value setting unit 210 , an error calculating unit 220 , a standard deviation calculating unit 230 , and parameters The calculation unit 240 , the weight calculation unit 250 , and the distance estimation value calculation unit 260 may be included.

In step 110 , the initial value setting unit 210 may set an initial distance value and initial parameters.

In operation 120 , the error calculating unit 220 may calculate an error using the difference between the i-th distance observation value and the distance estimate value.

In step 130 , the standard deviation calculating unit 230 may calculate the standard deviation for the distance observation value after calculating the error.

In step 140 , the parameter calculating unit 240 may calculate a parameter for the distance observation value.

In step 150 , the weight calculating unit 250 may calculate a weight for the distance observation value using the hypertangent loss function. The weight estimator 250 automatically utilizes the hypertangent loss function by providing an M estimator to which weights are assigned. A robust distance estimation algorithm that does not require statistical verification and a predefined threshold is implemented. can provide In this case, when the hypertangent loss function is used for the M estimator, the weight estimator 250 may give a small weight to the outlier and a large weight to the normal value without statistical testing.

In operation 160 , the distance estimate value calculator 260 may calculate a distance estimate value using the predicted weight and the distance observation value. The process of calculating the error, calculating the standard deviation, calculating the parameter, calculating the weight, and calculating the distance estimate value for the distance observation value may be repeated until the distance estimate value converges.

A robust distance estimation method and apparatus using a hypertangent loss function as an example will be described below.

First, we can provide an M estimator based on the tanh loss function.

The M estimator is a kind of robust estimator considered for NLOS mitigation purposes. M estimators have been widely used for robust signal processing. Huber, Tukey, and Hampel loss functions are used as loss functions for the M estimator. However, the tanh loss function was not adopted for the M estimator. Here, we propose an M estimator using the tanh loss function because the magnitude is limited to a constant when the magnitude of the error is large. First, the tanh loss function can be defined as

[Equation 8]

The weight of the tanh loss function can be obtained as follows.

[Equation 9]

는 최소 평균 제곱(LMS) 알고리즘을 사용하여 구하며, 1.4826 Х MAD로 추정한다. 거리 추정치는 [수학식 9]에 의해 가중치를 구하는 M 추정량을 사용하여 계산한다. tanh 손실 함수를 사용하는 M 추정량은 [표 1]의 알고리즘 1에 요약되어 있다.parameter

is obtained using the least mean squares (LMS) algorithm, and is estimated to be 1.4826 Х MAD. The distance estimate is calculated using the M estimator for which the weight is obtained by [Equation 9]. The M estimator using the tanh loss function is summarized in Algorithm 1 in Table 1.

[Table 1]

), 오차를 계산

하며, 표준편차를 계산

할 수 있다. 그리고, 매개변수

를 계산(Least mean squares 알고리즘)하고, 가중치를 계산

하고, 거리 추정 값을 계산

하며,

이 수렴할 때까지 반복할 수 있다. Referring to Table 1, first determine the initial value (

), calculate the error

and calculate the standard deviation

can do. and the parameter

(Least mean squares algorithm) and compute the weights

and calculate the distance estimate

and

This can be repeated until convergence.

In addition, it is possible to provide a robust Bayesian M-based distance estimation algorithm.

The motivation of the robust Bayesian M-based distance estimation algorithm is that it can improve the accuracy of the robust estimation method using previous information and measurements simultaneously when compared with the existing deterministic robust estimator under low SNR conditions. We can provide a distance estimation method using the mean and variance of the previously obtained distributions of the previous M distance estimates. The distribution of the M estimator is asymptotically Gaussian. In addition, the previously obtained distance follows a Gaussian distribution because it is a statistic obtained from the M distance estimation. Then, the posterior function of the distance estimation using the observed value and the previous value can be expressed as a product of the Gaussian distribution as follows.

[Equation 10]

는 측정을 사용하는 거리에 대해 [수학식 6]에서 정의한 M 추정치, dP는 선행 평균,

은 M 추정치의 표준 편차,

는 선행 표준 편차이다. 그런 다음 베이지안 M 기반 거리 추정치를 다음과 같이 계산할 수 있다.here,

is the M estimate defined in [Equation 6] for the distance using the measurement, dP is the leading average,

is the standard deviation of the M estimate,

is the leading standard deviation. Then we can compute the Bayesian M-based distance estimate as

[Equation 11]

을 대략적으로 산출할 수 있다.However, the variance of the distance estimate using the M estimator is unknown because the NLOS noise variance is not available. So as

can be roughly calculated.

[Equation 12]

는 i번째 정상치 관련 가중치이고, N_l은 정상치의 총 수이고,

는 i번째 이상치 관련 가중치이다. 이 근사치는 e_i가 증가하고

가 작을 때 가중치가 0에 빠르게 접근하기 때문에 유효하다. 따라서 이상치는 M 추정치의 분산에 영향을 미칠 수 없다. 또한, 이전 평균과 분산을 이전에 얻은 M 거리 추정치에 대한 표본 평균 및 표본 분산으로 계산할 수 있다.here,

is the weight associated with the i-th stationary, N _l is the total number of stationary,

is the i-th outlier-related weight. This approximation is that e _i increases and

It is valid because the weight approaches 0 quickly when is small. Therefore, outliers cannot affect the variance of the M estimate. In addition, the previous mean and variance can be calculated as the sample mean and sample variance for the previously obtained M distance estimates.

We compared the performance of the proposed LOS/NLOS mixed distance estimation method with the performance of the MED distance estimator, the existing robust distance estimator, that is, the skipped filter and M estimator using ITL. Simulation settings can be shown in [Table 2].

[Table 2]

Table 3 summarizes the abbreviations used in one example.

[Table 3]

MSE may be defined as follows.

[Equation 13]

는 k번째 거리집합의 에미터에서 센서까지의 추정 거리이고, d는 추정되는 실제 거리를 나타낸다.here,

is the estimated distance from the emitter to the sensor of the k-th distance set, and d is the estimated actual distance.

3 is a graph illustrating an MSE according to a distance according to an embodiment.

Referring to FIG. 3 , as the distance increases, the MSE increases because ^{Var[di] is proportional to d 2 .} It can be seen that the MSE performance of the proposed MSE estimator based on the tanh loss function is similar to that of the existing skipped filter. It should be noted that the proposed method showed similar performance to the skipped filter without statistical validation and optimal threshold selection. In particular, the MSE for the median-based method was higher than other robust methods. A threshold of 3 was chosen for all simulations.

4 is a graph illustrating MSE according to variance of normal values according to an embodiment.

Referring to FIG. 4 , the analysis of tanh loss shows error variance and square bias. Again, the MSE of the proposed method was similar to the skipped filter and was superior to other existing methods. The performance of all robust methods deteriorated as the variance of the stationary noise increased. The MSE analysis of the proposed method was almost identical to the MSE of the proposed algorithm obtained through Monte Carlo simulation.

5 is a graph illustrating MSE as a function of standard deviation of outlier noise according to an exemplary embodiment.

Referring to FIG. 5 , the MSE for the proposed robust distance estimation method is similar to the skipped filter and outperforms other methods. The MSE of the robust algorithm is not affected by outlier noise because outliers are given small weights. Again, the MSE analysis was almost identical to the Monte Carlo simulation-based MSE of the proposed algorithm.

6 is a graph illustrating an MSE according to a bias according to an embodiment.

Referring to Figure 6, in the mixed LOS/NLOS environment, since the signal propagates a longer distance than the direct LOS path, the bias must be considered and modeled as a negative constant or random variable (RSS of the NLOS path is the distance of the direct LOS path) less than). The MSE of all methods was almost constant with different bias, and the MSE of the proposed method was similar to the skipped filter and outperformed other existing algorithms. The estimation performance of the proposed distance estimation algorithm was not affected by the bias because the negative influence of outliers was weakened by the robust estimation method.

As such, the existing M estimator employing information theory learning (ITL) also does not require statistical testing, but the mean square error (MSE) performance for distance estimation is inferior to that of the proposed method. In addition, MSE analysis can be performed on the proposed algorithm. Monte Carlo simulation not only verifies the theoretical analysis of the proposed method, but can also demonstrate that the MSE performance of the proposed method is almost identical to that of the existing elicitation filter, although it does not require statistical tests and optimal threshold selection.

As described above, according to embodiments, by estimating distance information using an M estimator algorithm based on a hyper-tangent loss function, statistical testing and determination of an optimal threshold are not required, so that the implementation of the algorithm is simpler and efficient

The device described above may be implemented as a hardware component, a software component, and/or a combination of the hardware component and the software component. For example, devices and components described in the embodiments may include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable array (FPA), It may be implemented using one or more general purpose or special purpose computers, such as a programmable logic unit (PLU), microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. A processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For convenience of understanding, although one processing device is sometimes described as being used, one of ordinary skill in the art will recognize that the processing device includes a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that can include For example, the processing device may include a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as parallel processors.

Software may comprise a computer program, code, instructions, or a combination of one or more thereof, which configures a processing device to operate as desired or is independently or collectively processed You can command the device. The software and/or data may be any kind of machine, component, physical device, virtual equipment, computer storage medium or apparatus, to be interpreted by or to provide instructions or data to the processing device. may be embodied in The software may be distributed over networked computer systems and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through 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 medium may be specially designed and configured for the embodiment, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute 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.

As described above, although the embodiments have been described with reference to the limited embodiments and drawings, various modifications and variations are possible from the above description by those skilled in the art. For example, the described techniques are performed in an order different from 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.

Claims (10)

In a robust distance estimation method using a computer-implemented hyper-tangent loss function,
calculating an error using a difference between the i-th distance observation value and the distance estimate value;
calculating a weight for the distance observation value using a hypertangent loss function; and
calculating a distance estimation value using the predicted weight and the distance observation value;
Including, a distance estimation method. According to claim 1,
setting an initial distance value and initial parameters;
after calculating the error, calculating a standard deviation for the distance observation value; and
calculating parameters for the distance observations;
Further comprising, a distance estimation method. According to claim 1,
Calculating a weight for the distance observation value using the hypertangent loss function comprises:
To provide a robust distance estimation algorithm that does not require statistical validation and predefined thresholds as it automatically utilizes a hypertangent loss function by providing a weighted M estimator.
characterized in that, a distance estimation method. According to claim 1,
Calculating a weight for the distance observation value using the hypertangent loss function comprises:
Giving small weights to outliers and large weights to normal values without statistical testing when using the hypertangent loss function for the M estimator
characterized in that, a distance estimation method. According to claim 1,
Calculating a distance estimation value using the weight and the distance observation value includes:
repeating the process of calculating the error, calculating the standard deviation, calculating the parameter, calculating the weight, and calculating the distance estimate value for the distance observation value until the distance estimate value converges
characterized in that, a distance estimation method. In a robust distance estimation apparatus using a hyper-tangent loss function,
an error estimator for calculating an error by using the difference between the i-th distance observation value and the distance estimate value;
a weight calculator for calculating a weight for the distance observation value using a hypertangent loss function; and
A distance estimation value calculator for calculating a distance estimation value using the predicted weight and the distance observation value
Including, distance estimation device. 7. The method of claim 6,
an initial value setting unit for setting an initial distance value and initial parameters;
a standard deviation calculator for calculating the standard deviation for the distance observation value after calculating the error; and
A parameter estimator that calculates parameters for the distance observation value.
Further comprising, a distance estimation method. According to claim 1,
The weight calculation unit,
To provide a robust distance estimation algorithm that does not require statistical validation and predefined thresholds as it automatically utilizes a hypertangent loss function by providing a weighted M estimator.
characterized in that, the distance estimation device. 7. The method of claim 6,
The weight calculation unit,
Giving small weights to outliers and large weights to normal values without statistical testing when using the hypertangent loss function for the M estimator
characterized in that, the distance estimation device. 7. The method of claim 6,
repeating the process of calculating the error, calculating the standard deviation, calculating the parameter, calculating the weight, and calculating the distance estimate value for the distance observation value until the distance estimate value converges
characterized in that, the distance estimation device.

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