Optimal Filtering for Discrete-Time Linear Systems With Multiplicative White Noise Perturbations and Periodic Coefficients

Drăgan, Vasile

doi:10.1109/tac.2012.2215534

Cited by 27 publications

(28 citation statements)

References 13 publications

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“…where I0 ∈ R p 0 ×p 0 and I1 ∈ R p 1 ×p 1 are identity matrices, O0 ∈ R p 1 ×p 0 and O1 ∈ R p 0 ×p 1 are null matrices, t k ∈ [0, t − ] in (8) and t k ∈ (t − , t] in (9). Correspondingly, y(t k ) can also be expressed by Y2(t k ) and Y1(t k ).…”

Section: A Observation Re-organizationmentioning

confidence: 99%

“…Therefore, we describe the active moving feed cabin subsystem as a discrete-time system with timedelay and multi-error measurements, and our aim is to find an optimal estimation approach for it. Optimal state estimation approaches for linear discrete-time systems have been widely studied and have found many practical applications in signal processing, control and communication systems [7], [8], [9]. Optimal state estimation is the minimum mean square error estimation, which is termed as MMSE state estimation [10].…”

Section: Introductionmentioning

confidence: 99%

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MMSE State Estimation Approach for Linear Discrete-Time Systems With Time-Delay and Multi-Error Measurements

Sun

Jing

Liang

et al. 2017

IEEE Trans. Automat. Contr.

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This paper focuses on designing a novel optimal estimation approach for linear discrete-time systems with time-delay and multi-error measurements, inspired by the measurement demands of Five-hundredmeter Aperture Spherical radio Telescope. Measurement errors from different measurement channels, which are considered equal in many previous estimation methods, are usually negatively correlated with timedelays. Measurements with higher time-delays usually have less errors than the ones with lower delays. Our approach improves the estimation accuracy by decreasing the usage rate of measurements with larger errors. To prove the optimality of the approach in the minimum mean square error sense, a derivation procedure is presented. A numerical example and comparison are also given to demonstrate the feasibility and advantage of the proposed approach.Index Terms-explicit time-delay, multi-error measurements, MMSE state estimation approach

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Section: A Observation Re-organizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

MMSE State Estimation Approach for Linear Discrete-Time Systems With Time-Delay and Multi-Error Measurements

Sun

Jing

Liang

et al. 2017

IEEE Trans. Automat. Contr.

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“…From Assumptions 1, 3 and 4, we conclude that in . Then, combining in and (13), we get (14) where is the Kronecker delta function. From (11) and Assumptions 1-4, we see that (15) where (16) (17) Similarly, we can get (18) and (19) Putting (15), (18) and (19) together, we obtain (20) Remark 1: From the above analysis, we conclude that the additive noises in the new measurements are no longer totally correlated.…”

Section: A Measurement Differencingmentioning

confidence: 99%

“…So far, a large number of research results for various types of discrete-time linear systems have been reported. An important part of these results is concerned with discrete time linear systems influenced by multiplicative noises [5]- [14]. In [5]- [9], the state estimation problem for such systems was studied in the sense of linear minimum mean square error (MMSE).…”

Section: Introductionmentioning

confidence: 99%

“…In [12], a robust finite-horizon Kalman filter for discrete-time linear systems with uncertain and multiplicative noises was designed, which guarantees an upper bound on the state estimation error variance for admissible uncertainties. Recently, the filtering problem of discrete-time linear systems with Markov jumps and multiplicative noises has been studied in [13], and the filtering problem of discrete-time linear systems with multiplicative white noise perturbations and periodic coefficients has been investigated in [14]. The state estimation problem for nonlinear systems with multiplicative noises has also been widely studied during the past few years.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

Liu

2015

IEEE Trans. Signal Process.

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In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

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Optimal linear filtering for networked systems with communication constraints, fading measurements, and multiplicative noises

Liu

Zhang

et al. 2016

Adaptive Control & Signal

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SummaryThis paper is concerned with the filtering problem for discrete‐time networked systems with communication constraints, fading measurements, and multiplicative noises. The communication constraint is that, at each sampling instant, at most one of the various transmission nodes in the networked systems is permitted to access a shared communication channel, and then the received data are transmitted to a remote filter to perform the filtering task. The phenomenon of measurement fading appears in a random way when measurements are transmitted via the communication channel that undergoes slow fading. Using the innovation analysis approach and some results developed in this study, an optimal linear filter is proposed. The proposed optimal filter has a recursive structure and does not increase computation and storage load with time. Computer simulations are conducted to examine the performance of the proposed optimal filter. Copyright © 2016 John Wiley & Sons, Ltd.

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Optimal Filtering for Discrete-Time Linear Systems With Multiplicative White Noise Perturbations and Periodic Coefficients

Cited by 27 publications

References 13 publications

MMSE State Estimation Approach for Linear Discrete-Time Systems With Time-Delay and Multi-Error Measurements

MMSE State Estimation Approach for Linear Discrete-Time Systems With Time-Delay and Multi-Error Measurements

Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

Optimal linear filtering for networked systems with communication constraints, fading measurements, and multiplicative noises

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