Linear Estimation

Rating:
Summary: Well-organized, readable, beautiful
Review: I came to this book with a need to become familiar with Kalman filters. I've read the first two chapters so far with great pleasure. Professor Kailath develops the material beautifully; his profound mastery of the field is evident in every paragraph. The material is concentrated, but is presented in a highly readable compelling style. The reader is expected to be comfortable with the basics of linear systems theory, probability, and matrix analysis, although extensive appendices provide the necessary background.

Rating:
Summary: Linear Estimation from A to Z.
Review: Kailath, Sayed, and Hassibi do an excellent job of explaining what is a fairly complicated subject. This book is best-suited for scholars who desire a deep understanding of estimation theory. Engineers who want to quickly understand how to implement a Kalman Filter might be better off buying Adaptive Filter Theory by Simon Haykin.

The first chapter provides a good overview of the book, although it makes the most sense once the subject matter of the rest of the book has been digested a bit. A consistent framework emphasizing innovations (or the new information which appears at any iteration) is used throughout the book, and both continuous and discrete-time techniques for stochastic estimation are given nearly equal treatment, although the real-world engineer is likely to be interested in the latter.

Professor Kailath's articulate nature and knack for the clever anecdote or one-liner shines throughout the book, making it, while very mathematical in nature, quite readable for the motivated student.

Rating:
Summary: Linear Estimation from A to Z.
Review: Kailath, Sayed, and Hassibi do an excellent job of explaining what is a fairly complicated subject. This book is best-suited for scholars who desire a deep understanding of estimation theory. Engineers who want to quickly understand how to implement a Kalman Filter might be better off buying Adaptive Filter Theory by Simon Haykin.

The first chapter provides a good overview of the book, although it makes the most sense once the subject matter of the rest of the book has been digested a bit. A consistent framework emphasizing innovations (or the new information which appears at any iteration) is used throughout the book, and both continuous and discrete-time techniques for stochastic estimation are given nearly equal treatment, although the real-world engineer is likely to be interested in the latter.

Professor Kailath's articulate nature and knack for the clever anecdote or one-liner shines throughout the book, making it, while very mathematical in nature, quite readable for the motivated student.

Rating:
Summary: Wonderful and insightful
Review: This is one of the best engineering textbooks I have read, period. Although the subject matter is not for the faint-hearted, the authors' attention to pedagogical details shine throughout (repetition is the key to learning). The Kalman filter is introduced naturally as a consequence of a general framework for obtaining the best linear estimator of a random variable given others (earlier observations), and the geometric intuition is stressed repeatedly.

No important issue is omitted, including a very complete treatment of numerical issues and fast algorithms. My only gripe is with the assumption that all model parameters are KNOWN; in other words, the important aspect system identification (parameter estimation, learning, or whatever you call it in your field) is left to other textbooks.

Moreover, and no minor accomplishment, is the amazingly small number of typographical errors (at least up to where I have read so far; a bit over half the book), which is remarkable given the dense mathematical contents.

All in all, I would give it 6 stars if possible. Everything is there: it transmits a deep intuition for the matter, a places it in its historical context through interesting and amusing notes; it leaves the reader fulfilled but not overwhelmed.