• International Journal of Control, Automation, and Systems
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• 제4권4호
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• pp.456-465
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• 2006

The problem of recursive filtering far linear discrete-time systems with uncertainties is considered. A new suboptimal filtering algorithm is herein proposed. It is based on the fusion formula, which represents an optimal mean-square linear combination of local Kalman estimates with weights depending on cross-covariances between local filtering errors. In contrast to the optimal weights, the suboptimal weights do not depend on current measurements, and thus the proposed algorithm can easily be implemented in real-time. High accuracy and efficiency of the suboptimal filtering algorithm are demonstrated on the following examples: damper harmonic oscillator motion and vehicle motion constrained to a plane.

• 대한전기학회논문지
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• 제45권2호
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• pp.256-264
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• 1996

In this paper, the decentralized suboptimal H$_{2}$ filtering problem is considered. An additional term is added to the centralized optimal H$_{2}$ filter so that the whole filter is decentralized. We derive a necessary and sufficient condition for existence of proposed decentralized filters By employing the solution procedure for the exact model matching problem, we obtain a set of decentralized H$_{2}$ filters, and choose a suboptimal filter from this set of decentralized H$_{2}$ filters.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.2045-2050
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• 2004

An optimal combination of arbitrary number correlated estimates is derived. In particular, for two estimates this combination represents the well-known Millman and Bar-Shalom-Campo formulae for uncorrelated and correlated estimation errors, respectively. This new result is applied to the various estimation problems as least-squares estimation, Kalman filtering, and adaptive filtering. The new approximate adaptive filter with a parallel structure is proposed. It is shown that this filter is very effective for multisensor systems containing different types of sensors. Examples demonstrating the accuracy of the proposed filter are given.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1993년도 정기총회 및 추계학술대회 논문집 학회본부
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• pp.323-325
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• 1993

In this paper, the decentralized suboptimal $H_2$ filtering problem is considered. An additional term is added to the centralized optimal $H_2$ filter so that the whole filter is decentralized. We derive a sufficient condition for existence of such decentralized filters. By employing the solution procedure for the exact model matching problem, we obtain a set of decentralized $H_2$ filters, and choose a suboptimal filter from this set of decentralized $H_2$ filters. Naturally the resulting filter is guaranteed to be stable.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.16-21
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• 2005

This paper considers the problem of state estimation in linear continuous-time systems with multi-sensor environment and observation uncertainties. We propose two suboptimal filtering algorithms for these types of systems. The filtering algorithms consist of two steps: The local optimal Kalman estimates are computed at the first step. And, these local estimates are lineally fused at the second step. The implementation of the two-step filtering algorithms needs a lower memory demand than the optimal Kalman and adaptive Lainiotis-Kalman filters. In consequence of parallel structure of the proposed filters, the parallel computers can be used for their design. The examples exhibit the effect of common noise on the performance of fusion of the local Kalman estimates based on observations from different sensors and in the presence of uncertainties.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1477-1480
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• 1997

This paper is concerned with the design of a suboptimal robust Kalman filter using LMI approach for system models in the state space, which are subjected to parameter uncertainties in both the state and measurement atrices. Under the assumption that augmented system composed of the uncertain system and the state estimation error dynamics should be stable, a Lyapunov inequality is obtained. And from this inequaltiy, the filter design problem can be transformed to the gneric LMI problems i.e., linear objective minimization problem and generalized eigenvalue minimization problem. When applied to uncertain linear system modles, the proposed filter can provide the minimum upper bound of the estimation error variance for all admissible parameter uncertainties.

• 대한전기학회논문지:전력기술부문A
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• 제48권6호
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• pp.735-746
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• 1999

We design the robust and inherently fault tolerant decetralized$$H^infty$$ filter for the multisensor state estimation problem when there are insufficient priori informations on the statistical properties of external disturbances. For developing the proposed algorithm, an alternative form of suboptimal$$H^infty$$ filter equations are formulated by applying an alternative form of Kalman filter equations to the indefinite inner product space state model of suboptimal$$H^infty$$ filtering problems. The decentralized$$H^infty$$ filter that consists of local and central fusion filters can be designed effciently using the proposed alternative$$H^infty$$ filiter gain equations. The proposed decentralized$$H^infty$$ filter is robust against un-known external disturbances since it bounds the maximum energy gain from the external disturbances to the estimation errors under the prescribed level$$r^2$$ in both local and central fusion filters and is also fault tolerant due to its inherent redundancy. In addition, the central fusion equations between the global and local data can reduce the unnecessary calculation burden effectively. Computer simulations are made to ceritfy the robustness and fault tolerance of the proposed algorithm.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.45-60
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• 2017

This paper focuses on estimation of an non-integral quadratic function (NIQF) and integral quadratic function (IQF) of a random signal in dynamic system described by a linear stochastic differential equation. The quadratic form of an unobservable signal indicates useful information of a signal for control. The optimal (in mean square sense) and suboptimal estimates of NIQF and IQF represent a function of the Kalman estimate and its error covariance. The proposed estimation algorithms have a closed-form estimation procedure. The obtained estimates are studied in detail, including derivation of the exact formulas and differential equations for mean square errors. The results we demonstrate on practical example of a power of signal, and comparison analysis between optimal and suboptimal estimators is presented.

• 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.