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Train Navigation Control and Information Management System
Published in Tanuja Patgar, Devi CS Kavitha, On-Board Design Models and Algorithm for Communication Based Train Control and Tracking System, 2022
Tanuja Patgar, Devi CS Kavitha
The trade-off between accurate and fast localization and tracking algorithms has very high computation and memory requirements. Constrained devices such as wireless sensors usually require algorithms with low computational and memory requirements. The Kalman Filter (KF) has initially been proposed for linear systems. It comparatively requires low computation power compared to other Bayesian algorithms and has been extensively studied in the past few years for its usability in wireless sensors. The main limitation of KF is requirement of linear state information and estimation equations. The EKF algorithm is most widely used for nonlinear systems in linearization of the observation model. The EKF has been extensively used in many areas including probabilistic robotics, neural networks, image processing or depth recovery and Global Navigation Satellite Systems. The EKF is an extended version of KF to better handle non-linearity. EKF core basically remains the same; however, its computation complexity may vary depending on how state information is described or presented and updated. The conventional EKF and IEKF algorithms do not take into account the linearization errors and lead toward inconsistent state estimates.
Conventional Nonlinear Filters
Published in Bin Jia, Ming Xin, Grid-based Nonlinear Estimation and Its Applications, 2019
In this chapter, some conventional nonlinear filters that have been well recognized and extensively applied are presented. The first nonlinear filter is a natural extension of the Kalman filter derived from the linearization of nonlinear dynamic and measurement equations, which is called the extended Kalman filter (EKF) and its variants. The EKF, in spite of not being optimum, has been successfully applied to many nonlinear systems over the past decades. It is based on the notion that the true state is sufficiently close to the estimated state. Thus, the error dynamics can be represented fairly accurately by the first-order Taylor series expansion. The second class of nonlinear filters is the PDF approximation based method including the point-mass filter and the particle filter, which use an analytically designed deterministic grid and a large number of random Monte Carlo samples to approximate PDF, respectively. Another sampling point based nonlinear filter, the ensemble Kalman filter, is reviewed as a simple extension of the classical Kalman filter to solve large-scale nonlinear estimation problems. Two continuous-time nonlinear filtering methods based on the Zakai equation and Fokker Planck equation are presented at the end.
Real-Time Implementation of a Novel Fault Detection and Accommodation Algorithm for an Air-Breathing Combustion System
Published in Jitendra R. Raol, Ajith K. Gopal, Mobile Intelligent Autonomous Systems, 2016
Rahee Walambe, Nitin K. Gupta, Niteen Bhange, N. Ananthkrishnan, Ik Soo Park, Jong Ho Choi, Hyun Gull Yoon
For estimating correct system states and filtering the noise and disturbances present in the P4 measurements, the EKF [16] is applied. To estimate the states, EKF needs two independent measurements. In this case, one measurement is obtained by the actual P4 sensor and the second independent measurement is obtained from the modelled T07 (discussed in Section 31.4). These two measurements are fed to the KF. Thus, there are three KF in all, one for each of the three backpressure sensors. The continuous time version of KF is used. Since the system is non-linear, the EKF which uses the (linearized) Jacobian matrices at specific operating conditions along the trajectory is implemented. The Jacobian matrices are obtained by the small perturbation theory.
Deep Learning Based Object Attitude Estimation for a Laser Beam Control Research Testbed
Published in Applied Artificial Intelligence, 2023
Leonardo Herrera, Kim Jae Jun, Jeffrey Baker, Brij N. Agrawal
The EKF is a recursive algorithm that estimates the state vector of a nonlinear system; it is a generalization of the well-known Kalman Filter (KF) (Kalman 1960) but is dedicated to nonlinear systems. It is due to Stanley F. Schmidt and his staff (McGee et al. 1985). It keeps, although locally, the optimality property of the KF, which is the minimization of the trace of the estimation error covariance () during the estimation process. To estimate the state vector, the EKF employs the knowledge of the nonlinear system model (10) and the measurement (11). This algorithm can be found in many works of literature, see (Grewal & Andrews, 2014; Kim 2011; Simon 2006) to name a few, and is given by the following relations
An estimation scheme of road friction coefficient based on novel tyre model and improved SCKF
Published in Vehicle System Dynamics, 2022
Zhida Zhang, Ling Zheng, Hang Wu, Ziwei Zhang, Yinong Li, Yixiao Liang
In engineering practice, the Kalman filter (KF), the EKF, the UKF and the particle filter (PF) are often used to estimate the state and parameters of dynamic systems. The KF can be used for linear estimation, but it is not suitable for nonlinear systems. The EKF linearises the system equation by solving Jacobian matrix, which can be used for nonlinear estimation. However, when the system has strong nonlinearity, the linearisation calculation will cause large truncation error and seriously affect the estimation accuracy [42]. The UKF uses unscented transformation to approximate the probability density function with Gaussian approximation, and its accuracy is higher than the EKF. For high-dimensional nonlinear systems, its accuracy and stability will be significantly reduced [43]. Compared with the EKF and the UKF, the PF can get higher estimation accuracy for nonlinear systems, but its timeliness is very poor [44]. For the sake of computation efficiency and estimation accuracy, the UKF is more recommended than the PF [45]. Therefore, a high-performance nonlinear filtering algorithm named cubature Kalman filter (CKF) was proposed in [46], and its estimation accuracy and numerical stability are better than the UKF [47]. In order to ensure the symmetry, positive (semi) qualitative and improve the estimation accuracy of CKF, the SCKF is presented in [46] based on the square-root form of the error covariance matrix.
SARSA in extended Kalman Filter for complex urban environments positioning
Published in International Journal of Systems Science, 2021
Chen Chen, Xiang Wu, Yuming Bo, Yuwei Chen, Yurong Liu, Fuad E. Alsaadi
In recent decades, much effort has been spent to propose appropriate data fusion methods (Hu et al., 2021, 2020; Liu et al., 2021) for measurement from GNSS and INS. As a fundamental filter, KF has extensive applications in the INS/GNSS integrated navigation system (Baozhu et al., 2006; Jiang et al., 2017). Some observations (e.g. the velocity and the acceleration) are introduced into the state vector to increase the rank of the observation matrix and the bandwidth of the filter. Then the navigation accuracy and system robustness can be improved. However, these observations' state functions and observation functions are usually nonlinear, which cannot be appropriately filtered by KF, which is designed to process the data generated by the linear system. In order to solve this problem, the extended Kalman Filter (EKF) was proposed. In the EKF, the nonlinear system model has been simply linearised by utilising the first-order Taylor Expansion (Bugallo et al., 2007; Zhang et al., 2020). The EKF is a mature and reliable method improved by the KF, which can deal with nonlinear systems (Ma et al., 2021, 2020). In order to obtain the optimal estimation, it is crucial to get the prior information of noise covariance matrices, including the process and measurement of noise covariance matrices (Ding et al., 2020; Zou, Wang, Hu, et al., 2020; Zou, Wang, Zhou, et al., 2020). In the EKF, the noises are modelled as zero-mean Gaussian noise. The performance of the EKF will degrade if the values of noise covariance matrices are inappropriate.