Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

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Parameter Estimation of Dynamic System Based on UKF

UKF 기반한 동역학 시스템 파라미터의 추정

  • Seung, Ji-Hoon (Electronics and Information Department, Chonbuk National University) ;
  • Chong, Kil-To (Electronics and Information Department, Chonbuk National University)
  • Received : 2011.11.16
  • Accepted : 2012.02.10
  • Published : 2012.02.29
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Abstract

In this paper, the states and the parameters in the dynamic system are simultaneously estimated by applying the UKF(Unscented Kalman Filter), which is widely used for estimating the state of non-linear systems. Estimating the parameter is very important in various fields, such as system control, modeling, analysis of performance, and prediction. Most of the dynamic systems which are dealt with in engineering have non-linearity as well as some noise. Therefore, the parameter estimation is difficult. This paper estimates the states and the parameters applying to the UKF, which is a non-linear filter and has strong noise. The augmented equation is used by including the addition of the parameter factors to the original state equation of the system. Moreover, it is simulated by applying to a 2-DOF(Degree of Freedom) dynamic system composed of the pendulum and the slide. The measurement noise of the dynamic equation is assumed to be a Gaussian distribution. As the simulation results show, the proposed parameter estimation performs better than the LSM(Least Square Method). Furthermore, the estimation errors and convergence time are within three percent and 0.1 second, respectively. Consequentially, the UKF is able to estimate the system states and the parameters for the system, despite having measurement data with noise.

본 논문은 비선형 시스템의 상태 추정에 널리 사용 되는 Unscented Kalman Filter(UKF)를 활용하여 동역학 시스템의 상태를 추정함과 동시에 파라미터를 추정하였다. 파라미터의 추정은 시스템 제어, 모델링, 성능분석 및 예측 등 다양한 분야에서 매우 중요하다. 공학에서 다루는 대부분의 시스템은 비선형성과 잡음이 존재하므로 파라미터 추정이 매우 어렵다. 이러한 경우에 대하여 본 논문에서는 비선형 필터로서 잡음에 강한 UKF를 이용하여 상태와 파라미터를 추정하였다. 본 논문에서 제안한 파라미터 추정은 기존의 상태방정식에 파라미터 항을 추가하여 확장된 비선형 방정식을 사용하였으며, 진자와 슬라이드로 구성된 2-자유도 동역학 시스템에 적용하였으며, 시스템 운동방정식의 측정 잡음으로 가우시안 잡음을 추가하여 컴퓨터 시뮬레이션을 실시하였다. 시뮬레이션 결과 제안한 방법이 LSM보다 좋은 성능을 보였다. 추정 오차는 3%이내이며, 0.1sec 이내의 수렴하는 것을 확인하였다. 결과적으로 UKF는 상태나 측정 데이터에 잡음이 존재하더라도 시스템의 상태 및 파라미터 추정이 가능하다.

Keywords

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