KR102121274B1 - Method for estimating analytic weight least squrares based on robust filter, unsupervised clustering - Google Patents

Abstract

An analytical weight least squares location estimation technique based on robust filters and unsupervised clusters is disclosed. A location estimation method performed by a location estimation apparatus according to an embodiment includes: performing unsupervised learning on an observation value obtained by estimating location information using a Gaussian mixture model; Deriving the weight as the unsupervised learning is performed; And estimating a positional parameter using a least-squares method based on the weight.

Description

METHOD FOR ESTIMATING ANALYTIC WEIGHT LEAST SQURARES BASED ON ROBUST FILTER, UNSUPERVISED CLUSTERING}

The description below relates to a technique for estimating a least squares weighted position.

This field is used to estimate the location of an object when GPS cannot be used in a mobile phone terminal location estimation or in an environment where indoor outliers exist. Since the existing method does not use weights, the accuracy of observations cannot be taken into account, so the estimation performance is inevitably lower than when using weights.

Non-Patent Document 1 "Robust time-of-arrival source localization employing error covariance of sample mean and sample median in line-of-sight/non-line-of-sight mixture environments, Eurasip Journal on Advances in Signal Processing, 2016:89 According to ", since the weight is constant, if the contamination rate exceeds 50%, the position estimation performance rapidly decreases.

According to the non-patent document 2 "Generalized Hampel filters, Eurasip Journal on Advances in Signal Processing, 2016:87", since the weight is not used, the estimation performance is inevitably lowered than the weight-based method.

It is possible to provide a data-driven based analytical method for calculating weights in position estimation using a Skipped filter and a Hampel filter. In addition, it is possible to provide a method of distinguishing an inlier from an outlier using a Gaussian mixture model (GMM), and estimating the weight for the normal to perform weight-based position estimation.

The location estimation method performed by the location estimation apparatus includes: performing unsupervised learning on an observation value obtained by estimating location information using a Gaussian mixture model; Deriving the weight as the unsupervised learning is performed; And estimating a positional parameter using a least-squares method based on the weight.

The step of performing unsupervised learning on the obtained observation value by estimating location information using the Gaussian mixture model may include the obtained observation value as a normal value and an outlier using the Gaussian mixture model. Classifying may include.

The step of deriving the weight as the unsupervised learning is performed is classified into normal values and outliers with respect to the obtained observation values, and then based on the normal values obtained by calculating by statistical tests. And deriving a weight.

The step of deriving the weight by performing the unsupervised learning may include calculating an weight by removing an outlier from a measured value for the location information or replacing it with another value using a robust filter. have.

In the step of deriving the weight as the unsupervised learning is performed, an observed value excluding an abnormal value for location information is obtained using a skipped filter and a Hampel filter, and the abnormality for location information is obtained. The method may include deriving a weight for estimation of location information by replacing the value with a median value and using the observed value excluding the outlier value and a normal value including the median value.

The step of estimating a positional parameter using the least squares method based on the weight may include calculating a position estimate based on the derived weights of the normal values classified as the unsupervised learning is performed.

The apparatus for estimating a location includes: an unsupervised learning unit configured to perform unsupervised learning on an observation value obtained by estimating location information using a Gaussian mixture model; A weight derivation unit deriving the weight as the unsupervised learning is performed; And a location estimator for estimating location parameters using the least squares method based on the weights.

The unsupervised learning unit may classify the obtained observation values into normal values and outliers using the Gaussian mixture model.

The weight derivation unit may classify the obtained observation values into normal values and outliers, and then derive weights based on the normal values obtained by calculating by a statistical test.

The weight derivation unit may calculate a weight by removing an outlier from a measured value for the location information or replacing it with another value using a robust filter.

The weight derivation unit acquires an observation value excluding an outlier value for location information by using a skipped filter and a Hampel filter, replaces the outlier value for location information with an intermediate value, and the outlier value Weights for estimation of location information may be derived by using observation values excluding and normal values including the median values.

The position estimator may calculate a position estimate based on the derived weights of normal values classified as the unsupervised learning is performed.

The apparatus for estimating a location according to an embodiment may improve the performance of location estimation by estimating the location using a weighted least squares method based on a robust filter and an unsupervised learning cluster.

The position estimation apparatus according to an embodiment may reduce the influence of outliers by calculating weights using a data driven method.

1 is a block diagram illustrating a configuration of a location estimation apparatus according to an embodiment.
2 is a flowchart illustrating a method for estimating a position of a position estimation apparatus according to an embodiment.
3 is an example showing a sensor disposed in a position estimation apparatus according to an embodiment.
4 is an example showing a standard deviation of a noise versus an average squared error for an abnormal value in a position estimation apparatus according to an embodiment.
5 is an example showing a standard deviation of a standard deviation of an NLOS noise versus an average square error in the case of an NLOS sensor and an LOS sensor in a position estimation apparatus according to an embodiment.
6 is an example of a standard deviation versus an average squared error of LOS noise in a position estimation apparatus according to an embodiment.
7 is a result of the pollution degree versus the mean square error of the position estimation apparatus according to an embodiment.
8 shows a result of applying a Gaussian mixture model to the classification of normal and outlier values in a position estimation apparatus according to an embodiment.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings.

1 is a block diagram illustrating a configuration of a location estimation apparatus according to an embodiment, and FIG. 2 is a flowchart illustrating a location estimation method of a location estimation apparatus according to an embodiment.

The location estimation apparatus 100 is for improving the performance of location estimation, and may include an unsupervised learning unit 110, a weight derivation unit 120, and a location estimation unit 130. These components may be representations of different functions performed by the processor according to a control command provided by the program code stored in the position estimation apparatus 100. The components may control the position estimation apparatus 100 to perform steps 210 to 230 included in the position estimation method of FIG. 2. At this time, the components may be implemented to execute instructions according to the code of the operating system included in the memory and the code of at least one program.

The processor of the location estimation apparatus 100 may load the program code stored in the file of the program for the location estimation method into the memory. For example, when the program is executed in the location estimation apparatus 100, the processor may control the location estimation apparatus 100 to load the program code from the file of the program into the memory under the control of the operating system. In this case, each of the processor and the unsupervised learning unit 110, the weight derivation unit 120, and the position estimation unit 130 included in the processor execute instructions of corresponding portions of the program codes loaded in the memory, and then perform the subsequent steps ( 210 to 230) may be different functional expressions of the processor for executing.

In step 210, the unsupervised learning unit 110 may perform unsupervised learning by using a Gaussian mixture model on the observations obtained by estimating location information. The unsupervised learning unit 110 may classify observations obtained using a Gaussian mixture model into normal values and outliers. For example, in classifying normal values and outliers, when an observation value is included in a preset reference range, it is determined to be in a normal range and classified as a normal value, and when not included in a preset reference range, an abnormal range It can be judged as being in and classified as an outlier.

In step 220, the weight deriving unit 120 may derive the weight as the unsupervised learning is performed. The weight derivation unit 120 may classify the obtained observation values into normal values and outliers, and then derive weights based on the obtained normal values as calculated by a statistical test. The weight derivation unit 120 may calculate the estimated value by removing the outlier from the observed value measured for the location information using a robust filter or substituting it for another value. Specifically, the weight deriving unit 120 obtains observation values excluding outliers for location information by using a skipped filter and a Hampel filter, and replaces the outliers for location information with an intermediate value. Then, a weight for estimating location information may be derived using normal values including observation values and median values excluding outliers. For example, the weight can be derived using only the normal value excluding the outlier for the location information using the skipped filter, and the outlier for the location information is replaced with the intermediate value using the hampel filter, and replaced Weights can be derived using median and normal values.

In step 230, the location estimator 130 may estimate the location parameter using a least squares method based on weights. The location estimator 130 may calculate the location estimate based on the derived weights of the normal values classified as the unsupervised learning is performed.

3 is an example showing a sensor disposed in a position estimation apparatus according to an embodiment.

The position estimation apparatus according to the embodiment may estimate the positional parameter using a weighted least squares method based on a robust filter and an unsupervised learning cluster to improve the performance of the conventional position estimation using a robust filter. At this time, the position estimation technique using weights can be estimated by observation values excluding outliers or by replacing the outliers with an intermediate value, and then by an intermediate value and an observation value. In addition, by performing clustering based on unsupervised learning using a Gaussian mixture model, it is classified into a normal value (inlier) and an outlier value, and the weight is obtained by taking only a normal value by a statistical test (e.g., average). Can be derived. Accordingly, the position estimation apparatus can exhibit superior position estimation performance than the conventional method.

The weight can be calculated as follows using a Hampel filter.

,

,

는 정상치로 판정된 샘플의 수,

는 이상치로 판정된 샘플의 수,

는 중간값(median),

는 정상치로 판정된 센서의 인덱스(index),

는 이상치로 판정된 센서의 인덱스를 의미한다. here,

,

,

Is the number of samples determined to be normal,

Is the number of samples judged to be outliers,

Is the median,

Is the index of the sensor determined to be normal,

Denotes the index of the sensor determined as an outlier.

The position estimation is estimated by a weighted least squares error algorithm and can be expressed as follows.

이다.here,

to be.

In general, the position estimate in the first step may be improved by a well-known two-step position estimation algorithm.

The weight by the skipped filter can be calculated as follows.

Likewise, the position estimation is estimated by a weight-based least squares error method and can be expressed as follows.

이다.here,

to be.

Also, the final position can be determined by the well-known two-step least-squares error technique.

The Gaussian mixture model can be divided into E-step and M-step as follows.

은 잠재변수(latent variable),

은 n번째 관측값,

는 j번째 가우시안 성분의 평균,

는 j번째 가우시안 성분의 분산,

는 혼합 가중치,

는 owner 가중치이다. n번째 관측값은

가 가장 클 때 j번째 가우시안 혼합 성분에 속한다고 판정된다.here,

Is the latent variable,

Is the nth observation,

Is the mean of the jth Gaussian component,

Is the variance of the jth Gaussian component,

Is mixed weight,

Is the owner weight. The nth observation

When is the largest, it is determined to belong to the jth Gaussian mixture component.

Referring to Figure 3, it is an example showing that the sensor is arranged. Source localization may be performed using the sensor arrangement as shown in FIG. 3. ○ indicates the sensor position. For example, 200 Monte Carlo simulations can be performed on 10 signal source locations extracted from a uniform distribution within a square of 20 m wide and 20 m long.

): 20%, the bias of NLOS noise (

): 4m, standard deviation of LOS noise (

): 0.1m이고, 도 4(b)는

: 30%,

: 0.1m,

: 4 이다. 도 4에서 센서 5, 6, 7이 NLOS(non-line-of-sight) 센서이고, 센서 5, 6, 7 이외의 나머지 센서는 LOS(line-of-sight) 센서이다. 실시예에서 제안된 weighted skipped 필터와 weighted Hampel 필터와 비지도 학습을 이용한 가중치 최소 자승법을 통하여 위치 추정을 수행하기 때문에 기존의 방법인 <C. Park and J. Chang, "Robust time-of-arrival source localization employing error covariance of sample mean and sample median in line-of-sight/non-line-of-sight mixture environments," Eurasip Journal on Advances in Signal Processing, 2016:89>, <J. Riba and A, Urruela, "A non-line-of-sight mitigation technique based on ML-detection," in Proc. of the ICASSP Montreal, QC, Canada, 1721 May 2004.> 보다 우수한 성능을 보이는 것을 확인할 수 있다. 이때, 각각의 종래의 기술을 도 4 내지 도 8의 그래프에서는 [28], [30]으로 기입하였다. 4 is an example showing the standard deviation of the standard deviation of the noise against the abnormal value of the position estimation apparatus according to an embodiment. Figure 4 (a) is the contamination ratio (

): 20%, the bias of NLOS noise (

): 4m, standard deviation of LOS noise (

): 0.1m, Fig. 4(b)

: 30%,

: 0.1m,

: 4 In FIG. 4, sensors 5, 6, and 7 are non-line-of-sight (NLOS) sensors, and the remaining sensors other than sensors 5, 6, and 7 are line-of-sight (LOS) sensors. Since the location estimation is performed through the weighted least square method using the weighted skipped filter, the weighted Hampel filter, and the unsupervised learning proposed in the embodiment, the <C. Park and J. Chang, "Robust time-of-arrival source localization employing error covariance of sample mean and sample median in line-of-sight/non-line-of-sight mixture environments," Eurasip Journal on Advances in Signal Processing, 2016:89>, <J. Riba and A, Urruela, "A non-line-of-sight mitigation technique based on ML-detection," in Proc. of the ICASSP Montreal, QC, Canada, 1721 May 2004.> You can see that it shows better performance. At this time, each conventional technique is written as [28] and [30] in the graphs of FIGS. 4 to 8.

): 20%, the bias of NLOS noise (

): 4m, standard deviation of LOS noise (

): 0.1m이고, 도 5(b)는

: 30%,

: 0.1m,

: 4m이다. 도 5를 참고하면, 센서 4, 5, 6, 7이 NLOS 센서이고, 센서 4, 5, 6, 7이외의 나머지 센서가 LOS 센서일 때, NLOS 잡음의 표준 편차 대 평균자승오차를 나타낸 것이다. 5 is an example showing a standard deviation of a standard deviation of an NLOS noise versus an average square error in the case of an NLOS sensor and an LOS sensor in a position estimation apparatus according to an embodiment. 5(a) shows contamination ratio (

): 20%, the bias of NLOS noise (

): 4m, standard deviation of LOS noise (

): 0.1m, Fig. 5(b)

: 30%,

: 0.1m,

: It is 4m. Referring to FIG. 5, when the sensors 4, 5, 6, and 7 are NLOS sensors, and the remaining sensors other than sensors 4, 5, 6, and 7 are LOS sensors, the standard deviation of the NLOS noise versus the mean square error is shown.

): 4m, contamination ratio: 30%, standard deviation of NLOS noise (

) :10m이다. 실시예에서 제안된 기법의 평균자승오차가 기존의 방법보다 작은 것을 확인할 수 있다. 또한, LOS 잡음이 증가함에 따라 모든 알고리즘의 평균 자승 오차는 증가하는 것을 확인할 수 있다. 6 is an example of a standard deviation versus an average squared error of LOS noise in a position estimation apparatus according to an embodiment. In Figure 6 bias of NLOS noise (

): 4m, contamination ratio: 30%, standard deviation of NLOS noise (

): 10m. It can be seen that the mean square error of the proposed method in the embodiment is smaller than the existing method. In addition, it can be seen that as the LOS noise increases, the mean square error of all algorithms increases.

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.1m, standard deviation of NLOS noise (

) :10m이다. 도 7을 참고하면, 오염율이 50%를 초과하는 경우 기존 방법에서는 추정 성능이 급격히 저하되지만 제안된 방법의 성능은 크게 변화가 없는 것을 확인할 수 있다. 7 is a result of an average squared error versus a contamination ratio of a position estimation apparatus according to an embodiment. In Figure 7 bias of NLOS noise (

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.1m, standard deviation of NLOS noise (

): 10m. Referring to FIG. 7, when the contamination rate exceeds 50%, it can be confirmed that in the existing method, the estimated performance is rapidly reduced, but the performance of the proposed method is not significantly changed.

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.1m, standard deviation of NLOS noise (

) :10m이고, 도 8(b)에서 bias of NLOS noise (

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.25m, standard deviation of NLOS noise (

) :10m이다. 도 8을 참고하면, 관측 잡음의 분산이 작은 경우 가우시안 혼합 모델은 정상치와 이상치를 양호하게 분류할 수 있음을 확인할 수 있다. 그러나, 관측 잡음의 크기가 큰 경우 가우시안 혼합모델의 분류 성능이 저하됨으로써 이상값과 정상값을 바르게 분류할 수 없음을 볼 수 있다. 따라서, 관측 잡음의 표준 편차가 작은 경우에는 가우시안 혼합 모델과 같은 비지도 학습 기반의 분류 방법을 이용 가능하지만 표준편차가 큰 경우에는 이의 사용이 바람직하지 않고 강인 필터를 사용하는 것이 더 바람직하다. 이는 도 6의 결과와 양립함을 볼 수 있다.8 shows a result of applying a Gaussian mixture model to the classification of normal and outlier values in a position estimation apparatus according to an embodiment. In Figure 8 (a) bias of NLOS noise (

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.1m, standard deviation of NLOS noise (

): 10m, bias of NLOS noise in FIG. 8(b) (

): 4m, contamination ratio: 30%, standard deviation of LOS noise (

): 0.25m, standard deviation of NLOS noise (

): 10m. Referring to FIG. 8, when the variance of the observed noise is small, it can be confirmed that the Gaussian mixture model can classify the normal and outliers satisfactorily. However, it can be seen that when the magnitude of the observed noise is large, the classification performance of the Gaussian mixture model deteriorates, so that the outliers and the normal values cannot be properly classified. Therefore, when the standard deviation of the observed noise is small, an unsupervised learning-based classification method such as a Gaussian mixture model can be used, but when the standard deviation is large, its use is not preferable, and a robust filter is more preferable. This can be seen to be compatible with the results of FIG. 6.

The position estimation apparatus according to an embodiment may reduce the influence of outliers because the weight is reduced using the data driven method even when the contamination rate exceeds 50% by estimating the weight calculation method using the data driven method. In addition, it is possible to improve estimation performance by calculating weights using analytical methods and unsupervised learning.

The device described above may be implemented with hardware components, software components, and/or combinations of hardware components and software components. For example, the devices and components described in the embodiments include, for example, processors, controllers, arithmetic logic units (ALUs), digital signal processors (micro signal processors), microcomputers, field programmable gate arrays (FPGAs). , A programmable logic unit (PLU), microprocessor, or any other device capable of executing and responding to instructions, may be implemented using one or more general purpose computers or special purpose computers. The processing device may run an operating system (OS) and one or more software applications running on the operating system. In addition, the processing device may access, store, manipulate, process, and generate data in response to the execution of the software. For convenience of understanding, a processing device may be described as one being used, but a person having ordinary skill in the art, the processing device may include a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that may include. For example, the processing device may include a plurality of processors or a processor and a controller. In addition, other processing configurations, such as parallel processors, are possible.

The software may include a computer program, code, instruction, or a combination of one or more of these, and configure the processing device to operate as desired, or process independently or collectively You can command the device. Software and/or data may be interpreted by a processing device, or to provide instructions or data to a processing device, of any type of machine, component, physical device, virtual equipment, computer storage medium or device. Can 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 on a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, or the like alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiments or may be known and usable by those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs, DVDs, and magnetic media such as floptical disks. Includes hardware devices specifically configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include high-level language code that can be executed by a computer using an interpreter, etc., as well as machine language codes produced by a compiler.

As described above, although the embodiments have been described by a limited embodiment and drawings, those skilled in the art can make various modifications and variations from the above description. For example, the described techniques are performed in a different order than the described method, and/or the components of the described system, structure, device, circuit, etc. are combined or combined in a different form from the described method, or other components Alternatively, even if substituted or substituted by equivalents, appropriate results can be achieved.

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

Claims (12)

In the position estimation method performed by the position estimation apparatus,
Performing unsupervised learning on the observations obtained by estimating location information using a Gaussian mixture model;
Deriving weights as the unsupervised learning is performed; And
Estimating a positional parameter using a least-squares method based on the weight
Including,
The step of deriving the weight as performing the unsupervised learning,
Classifying the obtained observation values into normal values and outliers, and then deriving weights based on the obtained normal values as calculated by statistical tests.
Location estimation method comprising a. According to claim 1,
The step of performing unsupervised learning on the obtained observation value by estimating location information using the Gaussian mixture model is:
Classifying the obtained observation values into normal values and outliers using the Gaussian mixture model.
Location estimation method comprising a. delete In the position estimation method performed by the position estimation apparatus,
Performing unsupervised learning on the observations obtained by estimating location information using a Gaussian mixture model;
Deriving weights as the unsupervised learning is performed; And
Estimating a positional parameter using a least-squares method based on the weight
Including,
The step of deriving the weight as performing the unsupervised learning,
Calculating weights by removing outliers or replacing them with other values from observations measured for the location information using a robust filter
Location estimation method comprising a. The method of claim 4,
The step of deriving the weight as performing the unsupervised learning,
Obtained observation values excluding the outliers for the location information are obtained by using the skipped filter and the Hampel filter, and the outliers for the location information are replaced with an intermediate value, and the observed values excluding the outliers Deriving a weight for estimation of location information using a normal value including the median value
Location estimation method comprising a. In the position estimation method performed by the position estimation apparatus,
Performing unsupervised learning on the observations obtained by estimating location information using a Gaussian mixture model;
Deriving weights as the unsupervised learning is performed; And
Estimating a positional parameter using a least-squares method based on the weight
Including,
The step of estimating the positional parameter using the least-squares method based on the weight may include:
Calculating a position estimate based on the derived weights of the normal values classified as the unsupervised learning is performed
Location estimation method comprising a. In the position estimation device,
An unsupervised learning unit that performs unsupervised learning on a Gaussian mixture model based on the obtained observations by estimating location information;
A weight derivation unit deriving a weight as the unsupervised learning is performed; And
Position estimator for estimating positional parameters using least square method based on the weight
Including,
The weight derivation unit,
After classifying the obtained observation values into normal values and outliers, the weights are derived based on the obtained normal values as calculated by statistical tests.
Position estimation device. The method of claim 7,
The unsupervised learning unit,
Using the Gaussian mixture model, the obtained observations are classified into normal values and outliers.
Position estimation device characterized in that. delete In the position estimation device,
An unsupervised learning unit configured to perform unsupervised learning on the observation value obtained by estimating location information using a Gaussian mixture model;
A weight derivation unit deriving a weight as the unsupervised learning is performed; And
Position estimator for estimating positional parameters using least square method based on the weight
Including,
The weight derivation unit,
Calculate the weight by removing the outlier from the observed value measured for the location information or replacing it with another value using a robust filter
Position estimation device characterized in that. The method of claim 10,
The weight derivation unit,
Obtained observation values excluding the outliers for the location information are obtained by using the skipped filter and the Hampel filter, and the outliers for the location information are replaced with an intermediate value, and the observed values excluding the outliers Deriving a weight for estimation of location information using a normal value including the median
Position estimation device characterized in that. In the position estimation device,
An unsupervised learning unit that performs unsupervised learning on a Gaussian mixture model based on the obtained observations by estimating location information;
A weight derivation unit deriving a weight as the unsupervised learning is performed; And
Position estimator for estimating positional parameters using least square method based on the weight
Including,
The position estimation unit,
As the non-supervised learning is performed, a normalized value is calculated based on the derived weight to calculate a position estimate.
Position estimation device characterized in that.

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