H∞-Property of the Continuous-Time Extended Kalman Filter

2016 ◽  
Author(s):  
Jennifer L. Bonniwell ◽  
Susan C. Schneider ◽  
Edwin E. Yaz
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Continuous Time ◽  
Estimation Error ◽  
Finite Energy ◽  
Minimum Variance ◽  
Nonlinear Observer ◽  
Minimum Variance Estimator ◽  
Error Energy ◽  
Special Case

This work elucidates another theoretical property of the ubiquitous extended Kalman filter by analyzing the energy gain of the continuous-time extended Kalman filter used as a nonlinear observer in the presence of finite-energy disturbances. The analysis provides a bound on the ratio of estimation error energy to disturbance energy, which shows that the extended Kalman filter inherently has the H∞-property along with being the locally optimal minimum variance estimator. A special case of this result is also shown to be the H2-property of the extended Kalman filter.

Gas pipeline leakage detection in the presence of parameter uncertainty using robust extended Kalman filter

2021 ◽  
pp. 014233122198911
Author(s):  
Mohadese Jahanian ◽  
Amin Ramezani ◽  
Ali Moarefianpour ◽  
Mahdi Aliari Shouredeli
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Parameter Uncertainty ◽  
Oil And Gas ◽  
Estimation Error ◽  
Real Data ◽  
Gas Pipeline ◽  
Pipeline System ◽  
Parameter Uncertainties ◽  
Simulation Results

One of the most significant systems that can be expressed by partial differential equations (PDEs) is the transmission pipeline system. To avoid the accidents that originated from oil and gas pipeline leakage, the exact location and quantity of leakage are required to be recognized. The designed goal is a leakage diagnosis based on the system model and the use of real data provided by transmission line systems. Nonlinear equations of the system have been extracted employing continuity and momentum equations. In this paper, the extended Kalman filter (EKF) is used to detect and locate the leakage and to attenuate the negative effects of measurement and process noises. Besides, a robust extended Kalman filter (REKF) is applied to compensate for the effect of parameter uncertainty. The quantity and the location of the occurred leakage are estimated along the pipeline. Simulation results show that REKF has better estimations of the leak and its location as compared with that of EKF. This filter is robust against process noise, measurement noise, parameter uncertainties, and guarantees a higher limit for the covariance of state estimation error as well. It is remarkable that simulation results are evaluated by OLGA software.

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.

Dynamic Sliding Mode Control of Air-to-Fuel Ratio in Internal Combustion Engines Using the Hybrid Extended Kalman Filter

2012 ◽  
Vol 433-440 ◽  
pp. 2092-2098 ◽  
Author(s):  
Majid Zohari ◽  
Mohamadreza Ahmadi ◽  
Hamed Mojallali
Keyword(s):  
Kalman Filter ◽  
Sliding Mode Control ◽  
Extended Kalman Filter ◽  
Sliding Mode ◽  
Nonlinear Observer ◽  
Superior Performance ◽  
Fuel Ratio ◽  
Mode Control ◽  
Dynamic Sliding Mode Control ◽  
Dynamic Sliding Mode

The large modeling uncertainties and the nonlinearities associated with air manifold and fuel injection in spark ignition (SI) engines has given rise to difficulties in the task of designing an adequate controller for air-to-fuel ratio (AFR) control. Although sliding mode control approaches has been suggested, the inescapable time-delay between control action and measurement update results in chattering. This paper proposes the implementation of a nonlinear observer based control scheme incorporating the hybrid extended Kalman filter (HEKF) and the dynamic sliding mode control (DSMC). The results established upon the proposed methodology are given which demonstrate superior performance in terms of reducing the chattering magnitude.

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

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn 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.

NONLINEAR OBSERVER VIA EXTENDED KALMAN FILTER ALGORITHM FOR EULER ANGLES ESTIMATION WITHOUT ATTITUDE SENSOR MEASUREMENTS

2015 ◽  
Vol 77 (28) ◽  
Author(s):  
Nor Hazadura Hamzah ◽  
Sazali Yaacob ◽  
Hariharan Muthusamy ◽  
Norhizam Hamzah ◽  
Teoh Vil Cherd ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Moment Equation ◽  
Nonlinear Observer ◽  
Euler Angles ◽  
Satellite Attitude ◽  
Observer Model ◽  
Kalman Filter Algorithm ◽  
Sensor Measurement ◽  
Attitude Sensor

This paper designs and investigates an observer system via Extended Kalman Filter algorithm to estimate the satellite’s Euler angles attitude during the absence of the attitude sensor measurement. This work contributes as a backup or an alternative system during unavailable attitude sensor measurement due to malfunction sensor or for cost reduction by reducing the number of sensors. In this work, the observer model for satellite attitude is presented in their non-simplified nonlinear form by combining the Euler’s Moment Equation and kinematics Euler angles parameter. The performance of the designed observer via Extended Kalman Filter algorithm is analyzed and verified using real flight data of Malaysian satellite.

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