Minimum variance state estimators with disturbance decoupling property for optimal filtering problems with unknown inputs

Tanikawa, Akio; Sawada, Yuichi

doi:10.5687/sss.2004.96

Cited by 9 publications

(24 citation statements)

References 7 publications

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“…In this system, the control accuracy for the flexible arms goes down when the collision occurs. In this paper, to improve the control accuracy after the collision is detected, the robust optimal filter with unknown input proposed by one of the authors is employed for obtaining the state estimate [15]. The collision force acting at the tip of the arm is supposed as an unknown input.…”

Section: Such Flexible Arms Have Useful Applications Inmentioning

confidence: 99%

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Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

Sawada

Fujimoto

Moritani

et al. 2012

Stochastic Systems Theory and its Applications (SSS)

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This paper describes a method of collision detection and control of a single-link flexible arm using a couple of state estimators. In order to improve the control performance of the flexible arm with the innovation based collision detection system when unlooked-for obstacles collide with the side of the arm, we introduce a robust optimal filter, which decouples undesirable effect of the collision force from the estimation error. The controller generates a control torque based on the state estimate using the robust optimal filter. Collision detection is then realized by using the innovation of a Kalman filter. The proposed system enables to avoid that the control performance is deteriorated when collisions occur.

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Section: Such Flexible Arms Have Useful Applications Inmentioning

confidence: 99%

“…The robust optimal filter presented in the literature [15] can isolate the undesirable effect of the unknown collision input for the flexible arm. Such robust filter [15] designed for the system given by (9) and (10) are described as follows: …”

Section: Robust Optimal Filtermentioning

confidence: 99%

Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

Sawada

Fujimoto

Moritani

et al. 2012

Stochastic Systems Theory and its Applications (SSS)

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“…In Section 4, we construct the fixed-interval smoother given in Tanikawa (2008) from the fixed-point smoother obtained in Section 3. In Section 5, we construct the fixed-lag smoother given in Tanikawa (2008) from the optimal filter in Tanikawa & Sawada (2003). Finally, the new feature and advantages of the obtained results are summarized here.…”

mentioning

confidence: 99%

“…We assume in this paper that random variables e 0 , {η t }, {ζ t } are independent. As in , Chen & Patton (1999) and Tanikawa & Sawada (2003), we consider state estimate (3)-(4) with the matrices F t+1 , T t+1 , H t+1 and K t+1 of the forms:The next lemma on equality (6) was obtained and used by and Chen & Patton (1999)). Before stating it, we assume that E k is a full column rank matrix.…”

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confidence: 99%

“…In this chapter, all three problems are discussed in a comrehensive and self-contained manner as much as possible. Namely, after some preliminary results in Section 2, we derive the fixed-point smoothing algorithm given in Tanikawa (2006) in Section 3 for the system with unknown inputs explicitly by applying the optimal filter with disturbance decoupling property obtained in Tanikawa & Sawada (2003). In Section 4, we construct the fixed-interval smoother given in Tanikawa (2008) from the fixed-point smoother obtained in Section 3.…”

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confidence: 99%

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New Smoothers for Discrete-time Linear Stochastic Systems with Unknown Disturbances

Tanikawa¹

2011

Discrete Time Systems

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4www.intechopen.com x k/t of the state x k for a fixed k based on the observations {Y t , t = k + 1, k + 2, ···}. Algorithms for computingx k/t , t = k + 1, k + 2, ··· , recursively are called fixed-point smoothers. For the second problem, the fixed-interval smoothing, we investigate the optimal estimatex t/N of the state x t at all times t = 0, 1, ··· , N based on the observation Y N of all the outputs {y 0 , y 1 , ··· , y N }. Fixed-interval smoothers are algorithms for computingx t/N , t = 0, 1, ··· , N recursively. The third problem, the fixed-lag smoothing, is to investigate the optimal estimatê x t−L/t of the state x t−L based on the observation Y t for a given L ≥ 1. Fixed-lag smoothers are algorithms for computingx t−L/t , t = L + 1, L + 2, ··· , recursively. See the references such as Anderson & Moore (1979), Bryson & Ho (1969), Kailath (1975) and Meditch (1973) for early research works on smoothers. More recent papers have been published based on different approaches such as stochastic realization theory (e.g., Badawi;Lindquist & Pavon (1979) and Faurre; Clerget & Germain (1979)), the complementary models (e.g., Ackner & Kailath (1989a), Ackner & Kailath (1989b), Bello;Willsky & Levy (1989), Bello; Willsky; Levy & Castanon (1986) Desai; Weinert & Yasypchuk (1983) and Weinert & Desai (1981)) and others. Nice surveys can be found in Kailath; Sayed & Hassibi (2000) and Katayama (2000). When stochastic systems contain unknown inputs explicitly, Tanikawa (Tanikawa (2006)) obtained a fixed-point smoother for the first problem. The second and the third problems were discussed in Tanikawa (2008). In this chapter, all three problems are discussed in a comrehensive and self-contained manner as much as possible. Namely, after some preliminary results in Section 2, we derive the fixed-point smoothing algorithm given in Tanikawa (2006) in Section 3 for the system with unknown inputs explicitly by applying the optimal filter with disturbance decoupling property obtained in Tanikawa & Sawada (2003). In Section 4, we construct the fixed-interval smoother given in Tanikawa (2008) from the fixed-point smoother obtained in Section 3. In Section 5, we construct the fixed-lag smoother given in Tanikawa (2008) from the optimal filter in Tanikawa & Sawada (2003). Finally, the new feature and advantages of the obtained results are summarized here. To the best of our knowledge, no attempt has been made to investigate optimal fixed-interval and fixed-lag smoothers for systems with unknown inputs explicitly (see the stochastic system given by (1)-(2)) before Tanikawa (2006) and Tanikawa (2008). Our smoothing algorithms have similar recursive forms to the standard optimal filter (i.e., the Kalman filter) and smoothers. Moreover, our algorithms reduce to those known smoothers derived from the Kalman filter (see e.g., Katayama (2000)) when the unknown inputs disappear. Thus, our algorithms are consistent with the known smoothing algorithms for systems without unknown inputs. PreliminariesConsider the following discrete-time linear...

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Transfer Case Clutch Torque Estimation Using an Extended Kalman Filter With Unknown Input

Wei

Dourra

Zhu

2022

IEEE/ASME Trans. Mechatron.

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Minimum variance state estimators with disturbance decoupling property for optimal filtering problems with unknown inputs

Cited by 9 publications

References 7 publications

Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

Robust Filter Based Control of A Single-link Flexible Arm and Its Collision Detection Using Innovation Process

New Smoothers for Discrete-time Linear Stochastic Systems with Unknown Disturbances

Transfer Case Clutch Torque Estimation Using an Extended Kalman Filter With Unknown Input

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