Minimization of the estimation error of the Kalman filter with an H/sub ∞/ error bound by Secant method

2002 ◽  
Author(s):  
Bing-Fei Wu ◽  
Hung-Hseng Hsu
Keyword(s):  
Kalman Filter ◽  
Error Bound ◽  
Estimation Error ◽  
Secant Method

scholarly journals Optimal Tuner Selection for Kalman Filter-Based Aircraft Engine Performance Estimation

2009 ◽  
Vol 132 (3) ◽  
Author(s):  
Donald L. Simon ◽  
Sanjay Garg
Keyword(s):  
Kalman Filter ◽  
Estimation Error ◽  
Engine Performance ◽  
Aircraft Engine ◽  
Operating Conditions ◽  
Performance Estimation ◽  
Experimental Simulation ◽  
Tuning Parameter ◽  
Estimation Accuracy ◽  
On Line

A linear point design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multivariable iterative search routine that seeks to minimize the theoretical mean-squared estimation error. This paper derives theoretical Kalman filter estimation error bias and variance values at steady-state operating conditions, and presents the tuner selection routine applied to minimize these values. Results from the application of the technique to an aircraft engine simulation are presented and compared with the conventional approach of tuner selection. Experimental simulation results are found to be in agreement with theoretical predictions. The new methodology is shown to yield a significant improvement in on-line engine performance estimation accuracy.

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 Application of Federal Kalman Filter with Neural Networks in the Velocity and Attitude Matching of Transfer Alignment

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Lijun Song ◽  
Zhongxing Duan ◽  
Bo He ◽  
Zhe Li
Keyword(s):  
Neural Networks ◽  
Kalman Filter ◽  
Navigation System ◽  
Inertial Navigation System ◽  
Estimation Error ◽  
Inertial Navigation ◽  
Transfer Alignment ◽  
The Neural Networks ◽  
Initial Attitude ◽  
Noise Statistics

The centralized Kalman filter is always applied in the velocity and attitude matching of Transfer Alignment (TA). But the centralized Kalman has many disadvantages, such as large amount of calculation, poor real-time performance, and low reliability. In the paper, the federal Kalman filter (FKF) based on neural networks is used in the velocity and attitude matching of TA, the Kalman filter is adjusted by the neural networks in the two subfilters, the federal filter is used to fuse the information of the two subfilters, and the global suboptimal state estimation is obtained. The result of simulation shows that the federal Kalman filter based on neural networks is better in estimating the initial attitude misalignment angle of inertial navigation system (INS) when the system dynamic model and noise statistics characteristics of inertial navigation system are unclear, and the estimation error is smaller and the accuracy is higher.

scholarly journals End-Effector Pose Estimation in Complex Environments Using Complementary Enhancement and Adaptive Fusion of Multisensor

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Mingrui Luo ◽  
En Li ◽  
Rui Guo ◽  
Jiaxin Liu ◽  
Zize Liang
Keyword(s):  
Kalman Filter ◽  
Pose Estimation ◽  
Unscented Kalman Filter ◽  
Rbf Neural Network ◽  
Estimation Error ◽  
Estimation Method ◽  
Original Data ◽  
Measurement Unit ◽  
Complex Environments ◽  
End Effector

Redundant manipulators are suitable for working in narrow and complex environments due to their flexibility. However, a large number of joints and long slender links make it hard to obtain the accurate end-effector pose of the redundant manipulator directly through the encoders. In this paper, a pose estimation method is proposed with the fusion of vision sensors, inertial sensors, and encoders. Firstly, according to the complementary characteristics of each measurement unit in the sensors, the original data is corrected and enhanced. Furthermore, an improved Kalman filter (KF) algorithm is adopted for data fusion by establishing the nonlinear motion prediction of the end-effector and the synchronization update model of the multirate sensors. Finally, the radial basis function (RBF) neural network is used to adaptively adjust the fusion parameters. It is verified in experiments that the proposed method achieves better performances on estimation error and update frequency than the original extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithm, especially in complex environments.

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.

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.

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