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Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

100%
Biçer C., Özbek L., Erbay H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
934-945
EN
In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable. The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.
2
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Straight-lines modelling using planar information for monocular SLAM

100%
Santana A., Medeiros A.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
|
nr 2
409-421
EN
This work proposes a SLAM (Simultaneous Localization And Mapping) solution based on an Extended Kalman Filter (EKF) in order to enable a robot to navigate along the environment using information from odometry and pre-existing lines on the floor. These lines are recognized by a Hough transform and are mapped into world measurements using a homography matrix. The prediction phase of the EKF is developed using an odometry model of the robot, and the updating makes use of the line parameters in Kalman equations without any intermediate stage for calculating the distance or the position. We show two experiments (indoor and outdoor) dealing with a real robot in order to validate the project.
3
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Simultaneous state and parameter estimation based actuator fault detection and diagnosis for an unmanned helicopter

88%
Wu C., Qi J., Song D., Qi X., Han J.
International Journal of Applied Mathematics and Computer Science
|
2015
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tom 25
|
nr 1
175-187
EN
Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD) for single-rotor unmanned helicopters (UHs) is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs), which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed into a general nonlinear estimation one: given control inputs and the measured flight state contaminated by measurement noises, estimate both the flight state and AHCs recursively in each time-step, which is also known as the simultaneous state and parameter estimation problem. The estimated AHCs can further be used for fault tolerant control (FTC). Based on the existing widely used nonlinear estimation methods such as the unscented Kalman filter (UKF) and the extended set-membership filter (ESMF), three kinds of adaptive schemes (KF-UKF, MIT-UKF and MIT-ESMF) are proposed by our team to improve the actuator FDD performance. A comprehensive comparative study on these different estimation methods is given in detail to illustrate their advantages and disadvantages when applied to unmanned helicopter actuator FDD.
4
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Disturbance modeling and state estimation for offset-free predictive control with state-space process models

88%
Tatjewski P.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
|
nr 2
313-323
EN
Disturbance modeling and design of state estimators for offset-free Model Predictive Control (MPC) with linear state-space process models is considered in the paper for deterministic constant-type external and internal disturbances (modeling errors). The application and importance of constant state disturbance prediction in the state-space MPC controller design is presented. In the case with a measured state, this leads to the control structure without disturbance state observers. In the case with an unmeasured state, a new, simpler MPC controller-observer structure is proposed, with observation of a pure process state only. The structure is not only simpler, but also with less restrictive applicability conditions than the conventional approach with extended process-and-disturbances state estimation. Theoretical analysis of the proposed structure is provided. The design approach is also applied to the case with an augmented state-space model in complete velocity form. The results are illustrated on a 2×2 example process problem.
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