Array algorithm for filtering of discrete-time Markovian jump linear systems

Terra, Marco H.; Ishihara, J.Y.; Júnior, Adalberto Pessoa

doi:10.1109/acc.2006.1655486

Cited by 6 publications

(11 citation statements)

References 24 publications

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“…Derivation of equation (11) Noticing that w k is independent of x k−1 , θ k and v k , and noticing that v k is independent of x k−1 and θ k , we obtain from (1) and (2) that…”

Section: Discussionmentioning

confidence: 99%

A novel suboptimal algorithm for state estimation of Markov jump linear systems

Liu

Zhang

et al. 2011

J. Control Theory Appl.

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This paper is concerned with state estimation problem for Markov jump linear systems where the disturbances involved in the systems equations and measurement equations are assumed to be Gaussian noise sequences. Based on two properties of conditional expectation, orthogonal projective theorem is applied to the state estimation problem of the considered systems so that a novel suboptimal algorithm is obtained. The novelty of the algorithm lies in using orthogonal projective theorem instead of Kalman filters to estimate the state. A numerical comparison of the algorithm with the interacting multiple model algorithm is given to illustrate the effectiveness of the proposed algorithm.

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“…Derivation of equation (11) Noticing that w k is independent of x k−1 , θ k and v k , and noticing that v k is independent of x k−1 and θ k , we obtain from (1) and (2) that…”

Section: Discussionmentioning

confidence: 99%

A novel suboptimal algorithm for state estimation of Markov jump linear systems

Liu

Zhang

et al. 2011

J. Control Theory Appl.

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“…Note that the points j  and the weights j w are obtained from the 3rd-degree cubature rule (14) or the higher 5 th degree cubature rule (15). The corresponding covariance for measurement and cross-covariance are calculated using Eqs.…”

Section: Consensus Based Imm and Cubature Information Filtering Amentioning

confidence: 99%

“…Multiple model system such as Jump Markov Nonlinear System (JMNLS) has been well-studied [15][16][17] to model the maneuvering target and accordingly, the iterative multiple model (IMM) estimator has been shown to be an effective approach for the single sensor system. In [17], a distributed multiple model UKF was proposed for the estimation of JMNLS and shown to achieve the same performance as the centralized filter.…”

Section: Introductionmentioning

confidence: 99%

Multiple UAV Target Tracking Using Consensus-Based Distributed High Degree Cubature Information Filter

Sun

Xin

2015

AIAA Guidance, Navigation, and Control Conference

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In this paper, a distributed nonlinear estimation scheme is proposed for target tracking with a team of UAVs. The maneuvering target is modeled as a jump Markov nonlinear system and the interacting multiple model approach is employed based on the integration of a new high degree cubature information filter with the consensus algorithm. Each UAV only communicates with its neighbors and the fusion of the estimates is achieved by the distributed information filtering and the consensus process. In addition to the advantages of the distributed tracking, the proposed scheme is able to achieve higher estimation accuracy than the unscented information filter.

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“…However, when Kalman filters are computed via Riccati equations, some fundamental properties to guarantee their stability, as for example, Hermitian solutions, are no longer guaranteed (see for instance, [17] for more details). Although the computational and numerical issues have been studied for standard state-space systems for a long time, for MJLSs, only [15,18] have dealt with this kind of problem. These two works proposed array algorithms to compute the linear minimum mean square error estimator (LMMSE) for MJLSs, which provide more accuracy and numerical stability if compared with solutions on the basis of Riccati equations.…”

Section: Introductionmentioning

confidence: 99%

“…The first part solves a Lyapunov equation whose result is used in the second part, which solves a simplified Riccati equation. The better performance of this algorithm, if compared with the array algorithms of [15,18], is because the algorithm exploits the properties that all parameters of the estimator developed in [19] can be frozen. Its solution converges with the assumptions that the system is mean square stable and the Markov chain is ergodic.…”

Section: Introductionmentioning

confidence: 99%

Fast array algorithm for filtering of Markovian jump linear systems

Terra

Ishihara

Jesus

2011

Adaptive Control & Signal

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This paper deals with numerical performance of linear minimum mean square error estimator for discretetime Markovian jump linear systems. We propose a fast array algorithm to compute this estimator in virtue of the reduction of the computational effort that it provides, if compared with the standard array algorithms. It is particularly useful for this case because the dimension of the linear minimum mean square error estimator increases proportionally to the number of Markovian states. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

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Array algorithm for filtering of discrete-time Markovian jump linear systems

Cited by 6 publications

References 24 publications

A novel suboptimal algorithm for state estimation of Markov jump linear systems

A novel suboptimal algorithm for state estimation of Markov jump linear systems

Multiple UAV Target Tracking Using Consensus-Based Distributed High Degree Cubature Information Filter

Fast array algorithm for filtering of Markovian jump linear systems

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