• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 B
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• pp.750-753
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• 1998

This paper gives a simple parameterization of all stable unbiased filters to solve the suboptimal mixed $H_2/H_{\infty}$ filtering problem. Using the central filter, mixed $H_2/H_{\infty}$ filter is designed which minimizes the upper bound for the $H_2$ norm of the transfer matrix from a white noise to the estimation error subject to an $H_{\infty}$ norm constraint on the transfer matrix from an energy-bounded noise to the estimation error. The problem of finding suitable estimator gain can be converted into a convex optimization problem involving linear matrix inequalities.

• 제어로봇시스템학회논문지
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• 제14권8호
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• pp.727-732
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• 2008

In this paper, the state-space representation of generalized complimentary filter is proposed. Complementary filter has the suitable structure to merge information from sensors whose frequency regions are complementary. First, the basic concept and structure of complementary filter is introduced. And then the structure of the generalized filter and its state-space representation are proposed. The state-space representation of complementary filter is able to design the complementary filter by applying modern filtering techniques like Kalman filter and $H_{\infty}$ filter. To show the usability of the proposed state-space representation, the design of Inertial Navigation System(INS) vertical channel damping loop using Global Positioning System(GPS) is described. The proposed GPS/INS damping loop lends the structure of Baro/INS(Barometer/INS) vertical channel damping loop that is an application of complementary filter. GPS altitude error has the non-stationary statistics although GPS offers navigation information which is insensitive to time and place. Therefore, $H_{\infty}$ filtering technique is selected for adding robustness to the loop. First, the state-space representation of GPS/INS damping loop is acquired. And next the weighted $H_{\infty}$ norm proposed in order to suitably consider characteristics of sensor errors is used for getting filter gains. Simulation results show that the proposed filter provides better performance than the conventional vertical channel loop design schemes even when error statistics are unknown.

• 전자공학회논문지
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• 제49권10호
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• pp.181-186
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• 2012

본 논문에서는 변수 불확실성과 필터이득 섭동을 가지는 시스템에 대한 견실비약성 $H_{\infty}$ 칼만형필터 설계기법을 제안한다. 필터가 존재할 충분조건과 견실비약성 $H_{\infty}$ 필터 설계기법을 선형행렬부등식 (LMI: Linear Matrix Inequality 접근법으로 제안하고 시스템과 필터의 불확실성을 매개변수화 선형행렬부등식(PLMI: Parameterized Linear Matrix Inequality)으로 구조화된 불확실성의 형태로 표현한 후 Lyapunov 함수를 통해 시스템의 불확실성과 더불어 필터이득섭동을 고려한 칼만형 $H_{\infty}$ 필터가 존재할 충분조건과 필터설계기법을 PLMI 형태로 보인다. PLMI는 무한개의 LMI의 형태로 나타나므로 완화기법(relaxation technique)을 적용하여 유한개의 LMI의 형태로 변환한 후 견실하고 최적화된 필터이득과 필터섭동범위를 계산하고, 예제와 모의실험을 통해 제시된 필터의 타당성을 검증한다.

• 한국컴퓨터정보학회논문지
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• 제18권6호
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• pp.9-19
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• 2013

본 논문에서는 상태 및 출력변수에 시간지연을 가지는 이산 비선형 마코비안 점프시스템의 퍼지 $H_{\infty}$ 필터 설계 방법을 다룬다. 리아프노프(Lyapunov) 함수를 이용하여 상태추정 오차시스템이 확률적 안정하며 외부외란 및 초기값 불확실성에 대하여 $H_{\infty}$ 성능을 만족하는 조건식을 유도하고 필터 존재 조건을 선형행렬부등식으로 나타낸다. 완화된 필터 존재 조건식을 유도하기 위하여 리아프노프 함수 선택 시에 시스템 모드에 종속적일뿐만 아니라 퍼지 멤버십 함수를 포함하는 확률-퍼지 리아프노프 함수를 선택한다. 또한 $H_{\infty}$ 성능 조건식 유도 시에 외부외란 뿐만 아니라 최기값 불확실성을 고려한다. 수치적 예제 및 컴퓨터 시뮬레이션을 통하여 제안된 방법의 타당성을 보인다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.344-347
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• 1995

The standard estimation and filtering theory are well known and has recently been incorporated with the H$_{\infty}$ optimization techniques where the parametrizations of all estimators and filters are utilized. The issue of reducing its order is always of interest. This paper presents a method for synthesizing low-order stable state estimators. The method presented in this paper is based on the utilization of a free parameter function contained in the parametrization of all state estimators. The results obtained in the paper are compared with standard results on low-order estimators. Both results are shown to be the same in a sense of its orders, but the approaches taken are largely different. It is also shown in the paper that the method can easily and directly be extended to the Kalman filters and the H$_{\infty}$ (sub)optimal filters. Consequently, the orders of all state estimators, Kalman filters, and H$_{\infty}$ filters are shown to be reduced down to the number of states minus the number of outputs, respectively.ly.

• Transactions on Control, Automation and Systems Engineering
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• 제3권2호
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• pp.83-88
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• 2001

The robust linear H(sub)$\infty$ FIR filter, which guarantees a prescribed H(sub)$\infty$ performance, is designed for continuous time-varying systems with unknown cone-bounded nonlinearity. The infinite horizon filtering for time-varying systems is systems is investigated in therms of two Riccati equations by the finite moving horizon.

• 제어로봇시스템학회논문지
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• 제7권8호
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• pp.703-710
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• 2001

The nonlinear observers are proposed for a nonlinear system. To improve the characteristics such as stability, convergence, and $H^{\infty}$ filter performance criterion, we utilize an $H^{\infty}$ filter Riccati equation or a modified $H^{\infty}$ filter Riccati equation with a freedom parameter. Using the Lyapunov function method, the characteristics of the observers are analyzed. Then the in-flight alignment for a strapdown inertial navigation system(SDINS) is designed using the proposed observer. And the additive quaternion error model is especially used to reduce the uncertainty of the SDINS error model. Simulation results show that the observer with the modified $H^{\infty}$ filter Riccati equation effectively improves the performance of the in-flight alignment.

• International Journal of Naval Architecture and Ocean Engineering
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• 제6권3호
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• pp.626-637
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• 2014

On ship, especially on large ship, the flexure deformation between Master (M)/Slave (S) Inertial Navigation System (INS) is a key factor which determines the accuracy of the integrated system of M/S INS. In engineering this flexure deformation will be increased with the added ship size. In the M/S INS integrated system, the attitude error between MINS and SINS cannot really reflect the misalignment angle change of SINS due to the flexure deformation. At the same time, the flexure deformation will bring the change of the lever arm size, which further induces the uncertainty of lever arm velocity, resulting in the velocity matching error. To solve this problem, a $H_{\infty}$ algorithm is proposed, in which the attitude and velocity matching error caused by deformation is considered as measurement noise with limited energy, and measurement noise will be restrained by the robustness of $H_{\infty}$ filter. Based on the classical "attitude plus velocity" matching method, the progress of M/S INS information fusion is simulated and compared by using three kinds of schemes, which are known and unknown flexure deformation with standard Kalman filter, and unknown flexure deformation with $H_{\infty}$ filter, respectively. Simulation results indicate that $H_{\infty}$ filter can effectively improve the accuracy of information fusion when flexure deformation is unknown but non-ignorable.

• 대한전기학회논문지:전력기술부문A
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• 제48권3호
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• pp.270-277
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• 1999

This paper deals with the maneuver detection and target tracking problem in uncertain parameter systems using a robust{{{{ { H}_{ } }}}} FIR filter to improve the unacceptable tracking performance due to the parametr uncertainty. The tracking filter used in the current paper is based on the robust{{{{ { H}_{ } }}}} FIR filter proposed by Kwon et al. [1,2] to estimate the state signal in uncertain systems with parameter uncertainty, and the basic scheme of the proposed method is the input estimation approach. Tracking performance of the maneuver detection and target tracking method proposed is compared with other techniques, Bogler allgorithm [4] and FIR tracking filter [2], via some simulations to examplify the good tracking performance of the proposed method over other techniques.