Bounding filter: A simple solution to lack of exact a priori statistics

Nahi, N.; Weiss, I.

doi:10.1109/cdc.1972.269095

Cited by 5 publications

(4 citation statements)

References 10 publications

(1 reference statement)

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“…Some of the methods use the same idea as the discrete counterparts; some of them use different concepts stemming from the state estimation solution for the continuous‐time models. Representative methods can be found in previous works …”

Section: Discussion and Comparison Of Noise CM Estimation Methodsmentioning

confidence: 99%

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Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

117

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This paper deals with the estimation of the noise covariance matrices of systems described by state-space models. Stress is laid on the systematic survey and classification of both the recursive and batch processing methods proposed in the literature with a special focus on the correlation methods. Besides the correlation methods, representatives of other groups are introduced also with respect to their basic idea, estimate properties, assumptions and possible extensions, and user-defined parameters. Common and dual properties of the methods are highlighted, and a simulation comparison using exemplary MATLAB implementations of the methods is provided. KEYWORDSadaptive systems, noise covariance matrix, state estimation, state-space model, system identification INTRODUCTIONKnowledge of a system model is a key prerequisite for many state estimation, signal processing, fault detection, and optimal control problems. The model is often designed to be consistent with random behaviour of the system quantities and properties of the measurements. While the deterministic part of the model often arises from mathematical modelling on the basis of physical, chemical, or biological laws governing the behaviour of the system, the statistics of the stochastic part are often difficult to find by the modelling and have to be identified using the measured data. Incorrect description of the noise statistics may result in significant worsening of estimation, signal processing, detection, or control quality or even in a failure of the underlying algorithms.In the last 5 decades, therefore, a significant research interest has been focused on a design of the methods for the estimation of the properties of the stochastic part of the model. The attention has been devoted to both the input-output models 1-5 and the state-space (SS) models 6-14 and both recursive and batch processing methods. This paper focuses on the methods estimating the properties of the stochastic part of the system described by an SS model discrete in time. In particular, the methods estimating the covariance matrices (CMs) † of noises in the state and measurement equation from a sequence of measured data are of interest. The methods are further denoted as the noise CM estimation methods.

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Section: Discussion and Comparison Of Noise CM Estimation Methodsmentioning

confidence: 99%

“…Another approach to the state estimation under unknown noise CMs is robust estimation, which respects uncertainty of the CMs and other model parameters and provides “conservative estimates” …”

Section: Discussion and Comparison Of Noise CM Estimation Methodsmentioning

confidence: 99%

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

117

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“…In order to improve the robustness and stability against noise, we used a bounding filter [20]. The bounding filter can improve estimation precision through exploiting the prior knowledge that while surgical instruments actively grip objects, the grip force does not exceed a value proportional to the output torque from the motors.…”

Section: B Bounding Filter For Robustness Improvementmentioning

confidence: 99%

Dynamic modeling of cable driven elongated surgical instruments for sensorless grip force estimation

Miyasaka

Haghighipanah

et al. 2016

2016 IEEE International Conference on Robotics and Automation (ICRA)

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Haptic feedback plays a key role in surgeries, but it is still a missing component in robotic Minimally Invasive Surgeries. This paper proposes a dynamic modelbased sensorless grip force estimation method to address the haptic perception problem for commonly used elongated cabledriven surgical instruments. Cable and cable-pulley properties are studied for dynamic modeling; grip forces, along with driven motor and gripper jaw positions and velocities are jointly estimated with Unscented Kalman Filter and only motor encoder readings and motor output torques are assumed to be known. A bounding filter is used to compensate for model inaccuracy and to improve method robustness. The proposed method was validated on a 10mm gripper which is driven by a Raven-II surgical robot. The gripper was equipped with 1dimensional force sensors which served as ground truth data. The experimental results showed that the proposed method provides sufficiently good grip force estimation, while only motor encoder and the motor torques are used as observations.

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“…The Kalman filter is verified to be the optimal estimator against noise with normal distribution by minimizing a wide class of reconstruction error performance index [10], In many practical situations, however, noise covariances may not be accurately known, or else its distribution may not be normal. Numerous reports in regard to this subject have been published [10][11][12][13][14] from the minimax viewpoint by obtaining the saddlepoint solution for the least favorable distribution. The problem of robust Kalman filter synthesis for discrete multiple timedelay stochastic systems with parametric uncertainties and uncertain noise covariances is worthwhile studying since it has not appeared in previous literature.…”

Section: Introductionmentioning

confidence: 99%

Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems

Hsiao

Pan

1996

Journal of Dynamic Systems, Measurement, and Control

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The problem of robust Kalman filter synthesis is considered in this present study for discrete multiple time-delay stochastic systems with parametric and noise uncertainties. A discrete multiple time-delay uncertain stochastic system can be transformed into another uncertain stochastic system with no delay by properly defining state variables. Minimax theory and Bellman-Gronwall lemma are employed on the basis of the upper norm-bounds of parametric uncertainties and noise uncertainties. A robust criterion can consequently be derived which guarantees the asymptotic stability of the uncertain stochastic system. Designed procedures are finally elaborated upon with an illustrative example.

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Bounding filter: A simple solution to lack of exact a priori statistics

Cited by 5 publications

References 10 publications

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Dynamic modeling of cable driven elongated surgical instruments for sensorless grip force estimation

Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems

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