Extended Kalman Filter Modifications Based on an Optimization View Point (original) (raw)
Related papers
A Review on Tuning of Extended Kalman Filter using Optimization Techniques for State Estimation
International journal of computer applications, 2016
State estimation is the common problem in every area of engineering. There are different filters used to overcome the problem of state estimation like Kalman filter, Particle filters etc. Kalman Filter is popular when the system is linear but when the system is highly non-linear then the different derivatives of Kalman Filter are used like Extended Kalman Filter (EKF), Unscented Kalman filter. But these estimation techniques require tuning of process and noise covariance matrices. The different optimization techniques are used to tune the filter parameters of EKF. In this paper, various optimization techniques have been studied for non-linear state estimation based on EKF.
A modified extended kalman filter as a parameter estimator for linear discrete-time systems
1988
Title of Thesis: A Modified Extended Kalman Filter As A Parameter Estimator For Linear Discrete-Time Systems Bruno J. Schnekenburger Master of Science, 1988 Thesis directed by: Prof. Dr. Andrew U. Meyer Asst. Prof. Dr. B. Tank Oranc This thesis presents the derivation and implementation of a modified Extended Kalman Filter used for joint state and parameter estimation of linear discrete-time systems operating in a stochastic Gaussian environment. A novel derivation for the discrete-time Extended Kalman Filter is also presented. In order to eliminate the main deficiencies of the Extended Kalman Filter, which are divergence and biasedness of its estimates, the filter algorithm has been modified. The primary modifications are due to Ujung, who stated global convergence properties for the modified Extended Kalman Filter, when used as a parameter estimator for linear systems. Implementation of this filter is further complicated by the need to initialize the parameter estimate error covar...
Tuning of Extended Kalman Filter for nonlinear State Estimation
IOSR Journal of Computer Engineering, 2016
Kalman Filter is the most popular method for state estimation when the system is linear. State estimation is the typical issue in every part of engineering and science. But, for non linear systems, different extensions of Kalman Filter are used. Extended Kalman Filter is famous to discard the non linearity which uses First order Taylor series expansion. But for these estimation techniques, the tuning of process noise covariance and measurement noise covariance matrices is required. There are different optimization techniques used to tune the parameters of Extended Kalman Filter. In this paper, Particle Swarm Optimization has been proposed to tune the EKF parameters and then the simulations are implemented for permanent magnet synchronous motor.
Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, 2007
The paper addresses the problem of errors-in-variables filtering, i.e. the optimal estimation of inputs and outputs from noisy observations. While the optimal solution is known for linear time-varying systems of known parameterisation, this paper considers a suboptimal approach where only an approximated set of parameters is available. The proposed filter is derived by the means of joint state and parameter estimation using the extended Kalman filter approach which, in turn, leads to a coupled state-parameter estimation procedure. However, the resulting parameter estimates appear to be biased in the presence of input noise. The novel filter is compared with a previously proposed suboptimal filter.
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003
A generalized performance evaluation method is presented for Extended Kalman Filter based state estimation of first order nonlinear dynamic systems. The first order nonlinear dynamic systems are placed in three categorizes in terms of the upper bound of the absolute values of the derivatives of the nonlinear functions. According to the proposed theoretical analysis, it is shown that different state estimation performances are achieved by applying the Extended Kalman Filter to the first order nonlinear systems in these three categorizes. The steady state mean square error performance of the filter is presented explicitly in terms of the bounds on the nonlinearity and noise variance. The advantage of this performance evaluation method is that the convergence property of estimation error variance can be easily concluded from the system nonlinearity before its implementation. This provides insight into what is going to happen in applications, e.g. for dynamic systems used in chaotic synchronization. The simulation of several different nonlinear dynamic systems shows the effectiveness of the proposed performance evaluation criteria.
Methods for Improving the Linearization Problem of Extended Kalman Filter
Journal of Intelligent & Robotic Systems, 2014
In this paper, in order to reduce the linearization error of Kalman filters family, three new methods are proposed and their effectiveness and feasibility are evaluated by means of Simultaneous Localization and Mapping (SLAM) problem. In derivative based methods of Kalman filters family, linearization error is brought into estimation unavoidably because of using Taylor expansion to linearize nonlinear motion model and observation model. These three methods lessen the linearization error by replacing the Jacobian matrix of observation function with new formulas. Simulation results done with 'Car Park Dataset' indicate that all proposed methods have less linearization error than other mentioned methods and the method named Improved Weighted Mean Extended Kalman Filter (IWMEKF) performs much better than other mentioned Kalman filters in this paper on linearization error. In addition, simulation results confirm that our proposed approaches are computationally efficient. From estimation accuracy and computational complexity point of view, IWMEKF is the best solution for solving nonlinear SLAM problem among all Kalman filters mentioned in this paper.
Robust extended Kalman filtering
IEEE Transactions on Signal Processing, 1999
Linearization errors inherent in the specification of an extended Kalman filter (EKF) can severely degrade its performance. This correspondence presents a new approach to the robust design of a discrete-time EKF by application of the robust linear design methods based on the H 1 norm minimization criterion. The results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications.
Simplified extended Kalman filter for automotive state estimation
International Journal of Modelling, Identification and Control, 2008
This paper demonstrates the implementation of an Extended Kalman Filter (EKF) technique as a model-based vehicle state estimator. In this approach, the KF is simplified such that the Kalman gain matrix is not calculated online via the Jacobian and covariance matrices, but using a table of velocity dependent approximating functions, thus reducing the computational effort. Results to date indicate that this is an effective approach, which is of significant potential benefit to the automotive industry.
Criteria for When the Extended Kalman Filter Works and Issues with Sigma Point Kalman Filters
The extended Kalman filter (EKF) is frequently tried for solving nonlinear estimation problems, but often fails. There have been no published objective criteria that can be used to determine whether the EKF will work. The EKF is the most basic nonlinear Gaussian filter approximation (NGFA), where the estimate is correct to first order and the covariance correct to second order. For a filter observation with a nonlinear measurement function an NGFA uses a Taylor series expansion about the mean to compute the mean and covariance of the measurement. We show that a requirement for the EKF to work is that the part of the fourth order covariance term of the measurement covariance that involves the products of the second order derivatives of the measurement function must be negligible in comparison to the covariance of the observation error. We also show that when this condition is not met we can implement an NGFA using the standard Kalman filter update equations where instead of the observation error covariance we use the sum of the observation error covariance and the above fourth order covariance term. We also discuss the limitations of the various sigma point filters because they do not implement this fourth order term correctly.