Enhanced Polynomial Chaos-Based Extended Kalman Filter Technique for Parameter Estimation

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Jeremy Kolansky ◽  
Corina Sandu
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Parameter Uncertainty ◽  
Polynomial Chaos ◽  
Recursive Least Squares ◽  
Mathematical Technique ◽  
Generalized Polynomial ◽  
State Tracking ◽  
Parameter Distributions

The generalized polynomial chaos (gPC) mathematical technique, when integrated with the extended Kalman filter (EKF) method, provides a parameter estimation and state tracking method. The truncation of the series expansions degrades the link between parameter convergence and parameter uncertainty which the filter uses to perform the estimations. An empirically derived correction for this problem is implemented, which maintains the original parameter distributions. A comparison is performed to illustrate the improvements of the proposed approach. The method is demonstrated for parameter estimation on a regression system, where it is compared to the recursive least squares (RLS) method.

Generalized Polynomial Chaos-Based Extended Kalman Filter: Improvement and Expansion

2013 ◽  
Author(s):  
Jeremy Kolansky ◽  
Corina Sandu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
Polynomial Chaos ◽  
Computationally Efficient ◽  
Generalized Polynomial Chaos ◽  
Parameter Estimations ◽  
Generalized Polynomial ◽  
State Estimations ◽  
Polynomial Chaos Expansions

The generalized polynomial chaos (gPC) method for propagating uncertain parameters through dynamical systems (previously developed at Virginia Tech) has been shown to be very computationally efficient. This method seems also to be ideal for real-time parameter estimation when merged with the Extended Kalman Filter (EKF). The resulting technique is shown in the present paper for systems in state-space representations, and then expanded to systems in regressions formulations. Due to the way the filter interacts with the polynomial chaos expansions, the covariance matrix is forced to zero in finite time. This problem shows itself as an inability to perform state estimations and causes the parameters to converge to incorrect values for state space systems. In order to address this issue, improvements to the method are implemented and the updated method is applied to both state space and regression systems. The resultant technique shows high accuracy of both state and parameter estimations.

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.

Parameter estimation of an SMA actuator model using an extended Kalman filter

Mechatronics ◽  
2018 ◽  
Vol 50 ◽  
pp. 148-159 ◽  
Author(s):  
M. Soltani ◽  
M. Bozorg ◽  
M.R. Zakerzadeh
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Sma Actuator
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