• 한국항공우주학회지
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• 제40권2호
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• pp.108-117
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• 2012

본 논문은 비선형 필터 기법에 따른 지형참조항법 성능 분석에 관한 연구를 수행하였다. 지형참조항법에 사용되는 기본 필터에는 확장 칼만 필터(EKF)가 있다. 본 연구는 EKF 원형외에 반복형 EKF(IEKF), stochastic linearization(SL) 조건이 추가된 EKF-SL과 unscented Kalman Filter(UKF) 알고리듬을 소개한다. 또한, 연속적(sequential) 필터 외에 일괄적(batch)필터 기법인 칼만 필터 무리(bank of Kalman filters)를 이용한 항법 기술도 비교군으로 추가하고 필터 간 항법 성능을 분석한다. 가상 궤적을 가진 항공기 시뮬레이션을 통해 초기위치 오차가 클 때도 강건한(robust) 필터로 stochastic linearization EKF가 선정되었으며, 다만 빠른 항법 해의 수렴이 요구될 때에는 칼만 필터 무리를 이용한 일괄적 필터가 효과적인 것으로 분석되었다.

• Journal of Electrical Engineering and Technology
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• 제9권6호
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• pp.2107-2113
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• 2014

Particle filtering (PF) has shown its outperforming results compared to that of classical Kalman filtering (KF), particularly for highly nonlinear problems. However, PF may not be universally superior to the extended KF (EKF) although the case (i.e. an example that the EKF outperforms PF) is seldom reported in the literature. Particularly, PF approaches show degraded performance for problems where the state noise is very small or zero. This is because particles become identical within a few iterations, which is so called particle impoverishment (PI) phenomenon; consequently, no matter how many particles are employed, we do not have particle diversity regardless of if the impoverished particle is close to the true state value or not. In this paper, we investigate this PI phenomenon, and show an example problem where a classical KF approach outperforms PF approaches in terms of mean squared error (MSE) criterion. Furthermore, we compare the processing speed of the EKF and PF approaches, and show the better speed performance of classical EKF approaches. Therefore, PF approaches may not be always better option than the classical EKF for nonlinear problems. Specifically, we show the outperforming result of unscented Kalman filter compared to that of PF approaches (which are shown in Fig. 7(c) for processing speed performance, and Fig. 6 for MSE performance in the paper).

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2013년도 춘계학술대회 논문집
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• pp.311-312
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• 2013

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2013년도 춘계학술대회 논문집
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• pp.313-314
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• 2013

• 제어로봇시스템학회논문지
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• 제12권2호
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• pp.93-100
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• 2006

In this paper, a new-type Extended Kalman Filter (EKF) is proposed as a robust nonlinear filter for a stochastic nonlinear system. The original EKF is widely used for various nonlinear system applications. But it is fragile to its estimation errors because they give rise to linearization errors that affect the system mode1 as the modeling errors. The linearization errors are nonlinear functions of the estimation errors therefore it is very difficult to obtain the accurate error covariance of the EKF using the linear form. The inaccurately estimated error covariance hinders the EKF from being a sub-optimal estimator. The proposed filter tries to obtain the upper bound of the error covariance tolerating the uncertainty of the error covariance instead of trying to obtain the accurate one. It treats the linearization errors as uncertain modeling errors that can be handled by the robust linear filtering. In order to be more robust to the estimation errors than the original EKF, the proposed filter minimizes the upper bound like the robust linear filter that is applied to the linear model with uncertainty. The in-flight alignment problem of the inertial navigation system with GPS position measurements is a good example that the proposed robust filter is applicable to. The simulation results show the efficiency of the proposed filter in the robustness to initial estimation errors of the filter.

• 전자공학회논문지
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• 제50권1호
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• pp.232-238
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• 2013

본 논문은 노이즈가 비 정규 분포를 따르는 수중 환경에서 비 선형 필터 기법에 따른 Mass-Damper-Spring (MBK) 시스템 위치추정에 관한 연구 내용이다. 최근 위치 추정에 사용되는 필터는 확장 칼만 필터 (EKF: Extended Kalman Filter) 와 파티클 필터(Particle Filter)가 주목 받고 있다. EKF는 가우시안 잡음 (Gaussian Noise) 이 존재하는 비선형 시스템에서 정확도가 높은 알고리즘으로 널리 사용되고 있지만, 수중 환경과 같이 비 가우시안 잡음이 존재하는 경우 사용에 많은 제약이 따른다. 이에 본 논문에서는 상태예측을 기반으로 둔 EKF와 비교하여, 통계적 발생 가능성 인자 (Maximum Likelihood) 에 기반한 분포 재해석 기법을 이용한 개선된 ODPF (One-Dimension Particle Filter)를 제안한다. 모의 실험을 통하여 non-Gaussian noise가 존재하는 수중 환경에서 EKF와 제안한 Particle filter를 사용한 위치 추정 결과를 비교 분석하였으며, 계산 용량 및 통계 샘플이 충분한 경우 ODPF가 EKF 대비 정확한 위치 추정 결과를 제공하는 것을 확인하였다.

• Journal of Astronomy and Space Sciences
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• 제25권3호
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• pp.283-290
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• 2008

이 논문에서는 간섭계 구성의 기본이 되는 위성 간 상대위치 추정에 관한 알고리즘을 개발하고 검증하였다. 편대위성 간 상대위치 추정을 실시간으로 수행하기 위해 확장칼만필터 (EKF, Extended Kalman Filter)와 Unscented 칼만필터 (UKF, Unscented Kalman Filter) 를 사용하였다. 칼만 필터를 이용한 상태벡터 (state-vector)의 갱신(update)을 위한 관측 데이터는 시뮬레이션을 통해 얻어진 GPS 위성 신호의 단일차분 (Single Difference)에 대한 값을 사용하였다. 이 연구에서 개발한 알고리즘으로 추정된 편대위성 간 상대위치는 확장칼만필터와 Unscented 칼만필터 모두 참 값으로 가정한 STK(Satellite Tool Kit) 의 시뮬레이션된 관측 값에 대해 ${\pm}1m$ 이내의 오차로 수렴함을 확인하였다. 또한 두 종류의 칼만필터를 이용하여 상대위치 결정을 수행함으로써 비선 형성을 가지는 경우 Unscented 칼만필터의 성능이 상대적으로 우수함을 확인할 수 있었다.

• Journal of Positioning, Navigation, and Timing
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• 제6권3호
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• pp.105-116
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• 2017

Several wireless localization algorithms are evaluated for the IR-UWB-based indoor location with the assumption that the ranging measurements contain the channelwise Non-Calibration Error (NCE). The localization algorithms can be divided into the Model-free Localization (MfL) methods and Model-based Kalman Filtering (MbKF). The algorithms covered in this paper include Iterative Least Squares (ILS), Direct Solution (DS), Difference of Squared Ranging Measurements (DSRM), and ILS-Common (ILS-C) methods for the MfL methods, and Extended Kalman Filter (EKF), EKF-Each Channel (EKF-EC), EKF-C, Cubature Kalman Filter (CKF), and CKF-C for the MbKF. Experimental results show that the DSRM method has better accuracy than the other MfL methods. Also, it demands smallest computation time. On the other hand, the EKF-C and CKF-C require some more computation time than the DSRM method. The accuracy of the EKF-C and CKF-C is, however, best among the 9 methods. When comparing the EKF-C and CKF-C, the CKF-C can be easily used. Finally, it is concluded that the CKF-C can be widely used because of its ease of use as well as it accuracy.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.188-188
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• 2000

The most important problem in target tracking can be said to be modeling the tracking system correctly. Although the simple linear dynamic equation for this model has used until now, the satisfactory performance could not be obtained owing to uncertainties of the real systems in the case of designing the filters baged on the dynamic equations. In this paper, we propose the extended robust Kalman filter (ERKF) which can be applied to the real target tracking system with the parameter uncertainties. A nonlinear dynamic equation with parameter uncertainties is used to express the uncertain system model mathematically, and a measurement equation is represented by a nonlinear equation to show data from the radar in a Cartesian coordinate frame. To solve the robust nonlinear filtering problem, we derive the extended robust Kalman filter equation using the Krein space approach and sum quadratic constraint. We show the proposed filter has better performance than the existing extended Kalman filter (EKF) via 3-dimensional target tracking example.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2006년도 춘계학술발표회 논문집(I)
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• pp.506-509
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• 2006

Extended Kalman Filter iterate the prediction and the filtering based on Initial state for the next time step. EKF method for the estimation of nonlinear parameters of a structural dynamic system is necessary that initial of state vector and error covariance matrix. Because those are unknown exactly, generally selected random values. That occasion observability problem appear because of unknown initial values. In this study, for the estimation of the nonlinear parameters, a simple one degree of Freedom example is carried out by Extended Kalman Filter. And initial value assumption for Parameter Estimation of Dynamic System are developed. The result of analysis is compared with calculated standard values.