Non Gaussian State Estimation and the Maximum Correntropy Approach

Preface
Author
Chapter 1 Introduction
1.1 State Estimation
1.2 Motivating examples and applications
1.3 Modeling of Uncertainties and Gaussian Random Variables11
1.4 Conclusion
1.5 References

Chapter 2 Estimation with Weighted Least Squares
2.1 Introduction
2.2 Weighted Least Square Estimator
2.3 Minimum Variance Linear Estimator
2.4 Estimation with prior knowledge
2.5 Maximum Likelihood Estimation (MLE)
2.6 Maximum a Posteriori Estimate (MAP)
2.7 Initial State Estimation
2.8 Cramer-Rao Inequality
2.9 Bayesian Framework for State Estimation
2.10 Conclusions
2.11 References

Chapter 3 Recursive State Estimation: Linear Systems
3.1 Introduction
3.2 Recursive estimators
3.3 Modeling of uncertainties as non-Gaussian
3.4 Correntropy and maximum correntropy criterion
3.5 Correntropy Filter
3.6 Performance Criteria
3.7 Conclusions
3.8 References

Chapter 4 Nonlinear State Estimation
4.1 Introduction
4.2 Estimation with Nonlinear Stochastic Models
4.3 Extended Kalman Filter
4.4 Unscented Kalman Filter
4.5 New Sigma Point Kalman Filter
4.6 Gaussian sum formulations
4.7 Test problem: 3D angles-only target tracking problem
4.8 Conclusions
4.9 References

Chapter 5 Maximum Correntropy Estimation Algorithms for Nonlinear Systems
5.1 Introduction
5.2 Gaussian kernel based maximum correntropy nonlinear state estimation framework
5.3 Cauchy kernel based MC nonlinear state estimation framework
5.4 Convergence Analysis for Cauchy kernel based MC nonlinear estimators
5.5 Illustrative Examples
5.6 Appendix 1: Power series expansion of Cauchy kernel function
5.7 Appendix 2: Derivation of Kalman Gain
5.8 Appendix 3: Generalized Algorithm for Cauchy kernel based nonlinear MC estimator
5.9 Conclusions
5.10 References

Chapter 6 Maximum Correntropy Algorithms for Non Gaussian Systems
6.1 Introduction
6.2 Gaussian kernel based MC nonlinear state estimation MCG CKF
6.3 Cauchy kernel based MC nonlinear state estimation
6.4 Simulation results
6.5 Conclusions
6.6 References

Chapter 7 Angles-only Target Tracking
7.1 Introduction and problem formulation
7.2 Pseudo-linear Estimator
7.3 Bias Compensated PLKF
7.4 PLKF and BC-PLKF-based Maximum Correntropy Es- timator (MC-PLKF & MC-BC-PLKF)
7.5 Maximum Correntropy Unscented and New Sigma Point Kalman Filter
7.6 Simulation Results
7.7 Conclusions
7.8 References

Chapter 8 Tracking and Interception of a Ballistic Target on Reentry
8.1 Introduction
8.2 Mathematical Modelling
8.3 Proportional navigation guidance (PNG) law
8.4 Performance of Estimators in the Presence of Gaussian Noise
8.5 Performance of MC-Based Estimators in the Presence of Non-Gaussian Noise
8.6 Conclusions
8.7 Acknowledgment
8.8 References

Chapter 9 State of Charge Estimation for Battery Management Systems
9.1 Introduction
9.2 Mathematical Modelling
9.3 The Parameter Identification
9.4 SoC Estimation using Unscented Kalman Filter (UKF)
9.5 Comparative Studies Between EKF and UKF Algorithm
9.6 Non-Gaussian Noise in Measurement
9.7 Comparative Studies Between UKF with Gaussian and Non-Gaussian Measurement Noise
9.8 SoC Estimation Using Maximum Correntropy Un- scented Kalman Filter (MC-UKF)
9.9 Conclusions
9.10 Acknowledgment
9.11 References

Biography

Rahul Radhakrishnan was born in Kerala, India in December 1988. He studied Applied Electronics and Instrumentation at the Government Engineering College, Kozhikode, and did M.Tech in Control Systems at National Institute of Technology Kurukshetra. He received the Ph.D. degree in nonlinear filtering and its applications to target tracking problems from the Department of Electrical Engineering, Indian Institute of Technology Patna, Patna, India, in 2018. Before joining as an Assistant Professor with the Department of Electrical Engineering, SVNIT Surat, India, he worked as a post-doctoral fellow in the Department of Chemical Engineering, Indian Institute of Technology Bombay. Presently, he is working as an Assistant Professor in the Department of Electrical Engineering, National Institute of Technology Calicut, India. His main research interest includes nonlinear filtering, aerospace and under□water target tracking, moving horizon estimation, estimation of remaining useful life in energy storage systems, and process control.

Stepan Ozana was born in Bilovec, Czech Republic, in May 1977. He studied electrical engineering at the VSB Technical University of Ostrava, and received the M.Sc. degree in control and measurement engineering, in 2000, and the Ph.D. degree in technical cybernetics, in 2004. In 2015, he was habilitated in technical cybernet□ics. Since then, he has been working as an Associate Professor with the Department of Cybernetics and Biomedical Engineering, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava. He currently gives lec□tures on cybernetics and control systems. His main areas of interest and expertise are modeling and simulation of dynamic systems, control theory, automation, design, implementation, and deployment of control algorithms using soft PLC systems