• 한국항행학회논문지
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• 제20권1호
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• pp.53-58
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• 2016

우리는 본 논문에서 이차 칼만 필터를 이용한 영상 기반 객체 추적분야의 새로운 알고리즘을 제안한다. 최근에 발표된 이차 칼만 필터는 영상 기반의 객체의 실제 3차원 공간의 위치를 추적하는 것에는 아직 적용되지 않았다. 2차원 영상 내의 위치를 3차원 공간상의 위치로 환원시키는 것은 비선형적 변환을 수반하기 때문에 그에 맞는 추적 알고리즘을 사용해야만 한다. 이러한 상황에서, 비선형 수식을 이차식으로 근사화하는 이차 칼만 필터가 선형으로 근사화하는 확장 칼만 필터보다 더 정확한 성능을 낼 수 있다. 우리는 동일한 상황을 가정하여 확장 칼만 필터, 무향 칼만 필터, 파티클 필터, 그리고 우리가 제안한 이차 칼만 필터를 이용하여 객체를 추적하고, 그 결과를 비교해 본다. 결론적으로 이차 칼만 필터가 발산율이 확장 칼만 필터에 비해 거의 절반가량 감소하며, 추적 정확도 측면에서 무향 칼만 필터에 비해 1% 가량 우수한 성능을 나타낸다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.45.2-45
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• 2002

$\textbullet$ Uncertainties are described by sum quadratic constraint(SQC) $\textbullet$ SQC is converted into an indefinite quadratic cost function $\textbullet$ A Kalman filter developed in indefinite inner product space is Krein space Kalman filter $\textbullet$ To minimize the SQC, the Krein space Kalman filter is used $\textbullet$ The proposed robust filter outperforms the standard Kalman filter and existing robust Kalman filter $\textbullet$ The proposed filter has the same recursive, simple structure as the standard Kalman filter $\textbullet$ Easy to design, adequate for on-line implementation

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 합동 추계학술대회 논문집 정보 및 제어부문
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• pp.104-109
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• 2002

A new robust Kalman filter is designed for the linear discrete-time system with norm-bounded parametric uncertainties. Sum quadratic constraint, which describes the uncertainties of the system, is converted into an indefinite quadratic form to be minimized in indefinite inner product space. This minimization problem is solved by the new robust Kalman filter. Since the new filter is obtained by simply modifying the conventional Kalman filter, robust filtering scheme can be more readily designed using the proposed method in comparison with the existing robust Kalman filters. A numerical example demonstrates the robustness and the improvement of the proposed filter compared with the existing filters.

• 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.

• 한국항행학회논문지
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• 제25권6호
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• pp.543-549
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• 2021

본 논문에서는 불확실성의 크기가 유한한 파라미터를 갖는 스트랩다운 관성항법시스템에 대한 강인한 전달정렬 기법을 제안하였다. 크레인 공간을 이용하면 에너지가 유한한 불확실성을 갖는 강인한 필터는 일반적인 칼만필터와 동일한 구조를 갖게 된다. 단지 측정 행렬과 측정 잡음의 공분산값을 수정하면 된다. 본 논문에서 제안한 강인한 전달정렬 기법의 성능을 분석하기 위해서 항체가 고기동 운항을 하면서 측정치에 시간 지연이 발생하는 경우를 가정하여 시뮬레이션을 수행하였고 제안한 기법의 강인성을 검증하였다.

• 대한전기학회논문지:전력기술부문A
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• 제48권5호
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Transactions on Control, Automation and Systems Engineering
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• 제1권2호
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• pp.134-140
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• 1999

The robust generalized H2 filtering problem for a class of discrete time uncertain linear systems satisfying the sum quadratic constraints(SQCs) is considered. The objective of this paper is to develop robust stability condition using SQCs and design a robust generalized Ha filter to take place of the existing robust Kalman filter. The robust generalized H2 filter is designed based on newly derived robust stability condition. The robust generalized Ha filter bounds the energy to peak gain from the energy bounded exogenous disturbances to the estimation errors under the given positive scalar ${\gamma}$. Unlike the robust Lalman filter, it does not require any spectral assumptions about the exogenous disturbances . Therefore the robust generalized H2 filter can be considered as a deterministic formulation of the robust Kalman filter. Moreover, the variance of the estimation error obtained by the proposed filter is lower than that by the existing robust Kalman filter. The robustness of the robust generalized H2 filter against the uncertainty and the exogenous signal is illustrated by a simple numerical example.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 B
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• pp.433-436
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• 2003

The estimation of the position and the orientation for the mobile robot constitutes an important problem in mobile robot navigation. Although the odometry can be used to describe the motions of the mobile robots, there inherently exist the gaps between the real robots and the mathematical model, which may be caused by a number of error sources contaminating the encoder outputs. Hence, applying the standard extended Kalman filter for the nominal model is not supposed to give the satisfactory performance. As a solution to this problem, a new robust extended Kalman filter is proposed based on the Krein space approach. We consider the uncertain discrete time nonlinear model of the mobile robot that contains the uncertainties represented as sum quadratic constraints. The proposed robust filter has the merit of being constructed by the same recursive structure as the standard extended Kalman filter and can, therefore, be easily designed to effectively account for the uncertainties. The simulations will be given to verify the robustness against the parameter variation as veil as the reliable performance of the proposed robust filter.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.246-248
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• 2004

In this paper, we propose an optimal power control algorithm for CDMA cellular systems. The proposed power control algorithm is based on linear quadratic control theory. As the cellular system includes the changeability of system environment or various noise, Kalman filter is adapted to estimate the time-varying interference. This is the well-known linear quadratic Gaussian (LQG) theory. Through this algorithm, power transmission of each mobile with optimal one is more realistic. Simulation results show a fast convergence rate to optimal power value, and a rapid decreasing outage probability.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.305-307
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• 1992

This paper presents a technique, which identifies both process noise covariance and sensor noise covariance by using innovation correlation test. A correlation test, which checks whether the square root Kalman filter is workingly optimal or not, is given. The system is stochastic autoregressive moving-average model with auxiliary white noise Input. The linear quadratic Gaussian control is used for minimizing stochastic cost function. This paper indentifies Q, R, and estimates parametric matrics $A(q^{-1}),B(q^{-1}),C(q^{-1})$ by means of extended recursive least squares and model reference control. And The proposed technique has been validated in simulation results on the fourth order system.