Optimal and Robust State Estimation

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.

《最佳和強健的狀態估計：有限脈衝響應（FIR）和卡爾曼方法》是一本關於批次狀態估計器和遞迴形式的綜合研究。本書首先介紹了狀態估計方法並提供了簡要的歷史概述。接下來，本書討論了有限脈衝響應（FIR）狀態估計器的特性。後續章節介紹了概率和隨機過程的基礎知識，討論了可用的線性和非線性狀態估計器，處理了最佳FIR濾波，並考慮了有限記憶批次和遞迴算法。

本書還涵蓋了解決q-lag FIR平滑問題，介紹了後退視野（RH）FIR狀態估計方法，以及發展了在干擾下的FIR狀態估計理論。書末討論了不確定系統的FIR狀態估計理論，並提供了幾個有效使用FIR狀態估計器的應用案例。本書涵蓋的關鍵概念包括：

- 狀態估計方法的整體概述，源於需要知道實際系統的內部狀態，而輸入和輸出都是已知的。
- 最佳、最佳無偏、最大似然和無偏強健的有限脈衝響應（FIR）結構。
- FIR狀態估計方法以及無限脈衝響應（IIR）和卡爾曼方法。
- 成本函數和FIR和IIR狀態估計的最關鍵特性。

《最佳和強健的狀態估計：有限脈衝響應（FIR）和卡爾曼方法》適用於微波工程、系統工程和機器人學等領域的專業人士，他們希望在理論和實際應用中解決有限脈衝響應（FIR）估計問題。修讀狀態估計相關課程的研究生和高年級本科生也可以使用本書，以獲得寶貴的知識基礎，並在所選的研究領域中更加熟練。

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.

YURIY S. SHMALIY博士是墨西哥瓜納華托大學的教授。他擔任多個科學期刊的編輯委員會成員，並且是IEEE的Fellow。他還發展了有限脈衝響應（FIR）狀態估計理論，發表了許多主題演講和全體會議演講，他的離散正交多項式被稱為離散Shmaliy矩。

SHUNYI ZHAO博士是中國江南大學的教授。他目前的研究興趣包括統計信號處理、貝葉斯估計理論以及故障檢測和診斷。