• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.33.4-33
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• 2001

This paper considers a stochastic discrete algebraic Riccati equation, which is a generalized version of the well-known standard discrete algebraic Riccati equation, and has additional linear terms. Under controllability, observability and the assumption that the additional terms are not too large, the existence of a positive definite solution is guaranteed. It is shown that it arises in optimal control of a linear discrete-time system with multiplicative White noise and quadratic cost. A numerical example is given.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.432-435
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• 1995

In this paper a new approach to obtain the solution of the linear-quadratic Gaussian control problem for singularly perturbed discrete-time stochastic systems is proposed. The alogorithm proposed is based on exploring the previous results that the exact solution of the global discrete algebraic Riccati equations is found in terms of the reduced-order pure-slow and pure-fast nonsymmetric continuous-time algebraic Riccati equations and, in addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.7
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• pp.637-648
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• 2007

This paper presents a sensor fusion method based on indirect Kalman filter(IKF) for error compensation of low-cost inertial sensors and its application to the determination of attitude and position of small flying robots. First, the analysis of the measurement error characteristics to zero input is performed, focusing on the bias due to the temperature variation, to derive a simple nonlinear bias model of low-cost inertial sensors. Moreover, from the experimental results that the coefficients of this bias model possess non-deterministic (stochastic) uncertainties, the bias of low-cost inertial sensors is characterized as consisting of both deterministic and stochastic bias terms. Then, IKF is derived to improve long term stability dominated by the stochastic bias error, fusing low-cost inertial sensor measurements compensated by the deterministic bias model with non-inertial sensor measurement. In addition, in case of using intermittent non-inertial sensor measurements due to the unreliable data link, the upper and lower bounds of the state estimation error covariance matrix of discrete-time IKF are analyzed by solving stochastic algebraic Riccati equation and it is shown that they are dependant on the throughput of the data link and sampling period. To evaluate the performance of proposed method, experimental results of IKF for the attitude determination of a small flying robot are presented in comparison with that of extended Kaman filter which compensates only deterministic bias error model.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.477-491
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• 2021

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2311-2313
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• 2000

In this paper, we consider $H^{\infty}$ optimal Kalman filter problems for linear weakly coupled stochastic systems. We introduce a decomposition for the systems of the Hamiltonian form, which plays an important role of exclusion of ill-condition by ${\varepsilon}$-effect and the parallel computation possibility. It is shown that the algebraic Riccati equation of the weakly coupled $H^{\infty}$ optimal Kalman filter problem is decoupled into completely independent reduced-order, well-defined, two suboptimal Kalman filters.