A unified and systematic theoretical framework for solving problems related to finite impulse response (FIR) estimate

Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches is a comprehensive investigation into batch state estimators and recursive forms. The work begins by introducing the reader to the state estimation approach and provides a brief historical overview. Next, the work discusses the specific properties of finite impulse response (FIR) state estimators. Further chapters give the basics of probability and stochastic processes, discuss the available linear and nonlinear state estimators, deal with optimal FIR filtering, and consider a limited memory batch and recursive algorithms.

Other topics covered include solving the q-lag FIR smoothing problem, introducing the receding horizon (RH) FIR state estimation approach, and developing the theory of FIR state estimation under disturbances. The book closes by discussing the theory of FIR state estimation for uncertain systems and providing several applications where the FIR state estimators are used effectively. Key concepts covered in the work include:

• A holistic overview of the state estimation approach, which arose from the need to know the internal state of a real system, given that the input and output are both known
• Optimal, optimal unbiased, maximum likelihood, and unbiased and robust finite impulse response (FIR) structures
• FIR state estimation approach along with the infinite impulse response (IIR) and Kalman approaches
• Cost functions and the most critical properties of FIR and IIR state estimates

Optimal and Robust State Estimation: Finite Impulse Response (FIR) and Kalman Approaches was written for professionals in the fields of microwave engineering, system engineering, and robotics who wish to move towards solving finite impulse response (FIR) estimate issues in both theoretical and practical applications. Graduate and senior undergraduate students with coursework dealing with state estimation will also be able to use the book to gain a valuable foundation of knowledge and become more adept in their chosen fields of study.
About the Author:

YURIY S. SHMALIY, PhD, is a Professor with the Universidad de Guanajuato, Mexico. He serves as an Editorial Board Member in various scientific journals and is an IEEE Fellow. He also developed the theory of FIR state estimation, gave many keynote and plenary lectures, and his discrete orthogonal polynomials are called discrete Shmaliy moments.

SHUNYI ZHAO, PhD, is a Professor with the Jiangnan University, China. His current research interests include statistical signal processing, Bayesian estimation theory, and fault detection and diagnosis.