Stochastic stability of the continuous-time unscented Kalman filter

2008 ◽  
Author(s):  
Jiahe Xu ◽  
Shi Wang ◽  
Georgi M. Dimirovski ◽  
Yuanwei Jing
Keyword(s):  
Kalman Filter ◽  
Stochastic Stability ◽  
Continuous Time ◽  
Unscented Kalman Filter

Stochastic stability of the derivative unscented Kalman filter

2015 ◽  
Vol 24 (7) ◽  
pp. 070202 ◽  
Author(s):  
Gao-Ge Hu ◽  
She-Sheng Gao ◽  
Yong-Min Zhong ◽  
Bing-Bing Gao
Keyword(s):  
Kalman Filter ◽  
Stochastic Stability ◽  
Unscented Kalman Filter

scholarly journals Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Seyed Fakoorian ◽  
Vahid Azimi ◽  
Mahmoud Moosavi ◽  
Hanz Richter ◽  
Dan Simon
Keyword(s):  
Kalman Filter ◽  
Continuous Time ◽  
Lyapunov Functions ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Reaction Force ◽  
Force Estimation ◽  
Joint Angles ◽  
Estimation Errors ◽  
Reaction Forces

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.

Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises

2020 ◽  
Vol 42 (9) ◽  
pp. 1618-1631
Author(s):  
Xiaojiao Chen ◽  
Zhe Gao ◽  
Ruicheng Ma ◽  
Xiaomin Huang
Keyword(s):  
Kalman Filter ◽  
Fractional Order ◽  
Continuous Time ◽  
Kalman Filters ◽  
Unscented Kalman Filter ◽  
Nonlinear Function ◽  
Fractional Order Systems ◽  
Error Matrix ◽  
Current Time ◽  
Measurement Noises

Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Grünwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time. Meanwhile, the unscented transformation used in the UKF is also concerned for the nonlinear function at the previous time. By using the HEUKF designed in this paper, the third-order approximations for the nonlinear function can be achieved to enhance the accuracy of state estimation and estimation error matrix. Finally, numerical examples are provided to illustrate the effectiveness of the proposed HEUKF for nonlinear fractional-order systems.

Stochastic stability of the continuous-time extended Kalman filter

2000 ◽  
Vol 147 (1) ◽  
pp. 45-52 ◽  
Author(s):  
K. Reif ◽  
R. Unbehauen ◽  
E. Yaz ◽  
S. Günther
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Stochastic Stability ◽  
Continuous Time
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