Customer Reviews

Applied Optimal Estimation

5 star:		(12)
4 star:		(3)
3 star:		(0)
2 star:		(0)
1 star:		(1)

 

 

I received the first copy of the book from my employers when I took a short-course in Kalman Filters to augment my systems knowledge for performing inertial navigation analysis work for missile engineering at TRW in Redondo Beach, CA. That was 20 years or so ago. I can say I have yet to see another book that can match or surpass this one in simplicity in explanations, background materials (linear algebra, linear differential equations, state variable theory - control systems aspect, and random processes), cover many varied areas of applications and nonlinear problems, present the practical discrete-time equations alongside the more theoretically based continuous-time equations and demonstrate their uses and meaning, and discuss practical implemetation issues, schematically depict difficult ideas, equations and concepts through well organized and coherent diagrams and tables, and design manageable and solvable problems as exercises for learning at the end of each chapter, all of these done in a small inexpensive paperback. The book, unlike most others I have read or browsed, does not in any way assume a priori knowledge or basic understanding of Kalman Filters or what they are all about, and presents enough fundamental materials written clearly and lucidly so that any motivated student or worker new to the field can pick up almost everything he or she needs for learning. Though the book is not quite not a theoretical landmark for the mathematically inclined (and makes no bones about it), yet it has enough derivations to make it rigorous in its presentation of the mathematics underlying Kalman Filtering. Perhaps the computer oriented students and professionals will be disappointed because the book predates Matlab, but it did well in the days when analytical software was often custom designed, tailored and developed for engineering and scientific applications. A brief summary - very readable and approachable, unpretentious writing style, a great learning guide for the uninitiated as well as the systems engineering practitioner.

I worked in the aerospace industry from 1980-1991. During my years at the Aerospace Corporation I got this book as a reference to the application of Kalman filtering to orbit determination and estimation problems. So my experience and appreciation for this book is very similar to my colleagues working nearby me at TRW or Hughes Aircraft and cosequently I am in strong agreement with some of the other amazon reviews of Gelb's book. I always found it to be a key reference for me.

I first became acquainted with Kalman filters in 1979 when I was required to write software to track targets on a Navy weapons testing range. We used passive hydrophones together with active pingers on the targets, with the ping sequence identifying each target. We received arrival times for each ping, and had to sort them out and solve the intersecting hyperbolic surfaces of rotation to determine the target's position. Since pings had a significant time interval seperating them, we used Kalman filters to interpolate and extrapolate the target's position. I read Kalman's original 1960 paper on the subject, and several other papers, but I knew of no textbook coverage of the subject.

In the mid-1980's I was in graduate school. There I became aware of Gelb's wonderful book. I wished I had had it 6 years earlier!

A neighbor is an econometric quantitative analyst, and he uses Kalman filters for managing hedge funds.

Now I am involved in modelling glucose and insulin levels in diabetics and Kalman filters look like the technique of choice once again. Out with Gelb's book for a quick review. It seems to be timeless in its value because of the excellent treatment of the subject.

I took an estimation class this semester, and the book required was "introduction to Random Signals and Applied Kalman Filtering" by Brown and Hwang. This book was good for those who want to just apply kalman filters, and assumes that you don't care much about the derivations. But it was my first course in estimation, so I needed to get a complete and in depth introduction to the subject. I searched on amazon, and I found this book. I borrowed it from the library, and it was simply great! I like this type of authors that explain all his proofs, and add this one or two lines that make your life easier. Last week, I ordered it from Amazon to add it to my own library. I recommend it to any serious student in estimation or/and control.

Aboujouj83
http://www.qnhl.com

I purchased this book due to all of the good reviews. However, I am very disappointed in this book. I don't know the difference between myself and the other reviewers, other than my 1 star rating. I can say that I have a PhD in Statistics, and I wanted to know the fundamental properties of Kalman filters so that I could apply them on my own. I do not think that this book is helpful in that regard.

The book is very loose. It seems as though it is written for someone who works with people who build Kalman filters, i.e. someone who only needs a very rough idea about Kalman filters.

In addition, I also did not find the exercises to be helpful. Again, they are very loose, which makes them frustrating. I will provide two examples. You only need to look at Problem 2-1 and Problem 2-3 on page 46.

Problem 2-1
Show that \dot{P}^{-1} = -P^{-1} \dot{P} P^{-1}.

What is \dot{P}? The only reference to a matrix P in Chapter 2 is Eq(2.2-62) on p.39, so we know that P MAY be the covariance matrix of a normal distribution. In general the statement is true if \dot{P} is a skew-symmetric matrix and P is an orthogonal matrix, but this is not mentioned. The statement is also true if P is the covariance matrix in Eq(4.4-1) on p.127. Hence, this problem is out of place at best.

Problem 2-3
Show that A is positive definite iff all of the eigenvalues of A are positive.

The matrix A must be a real and symmetric matrix.


These inaccuracies are littered throughout the text.

If you want to learn about optimal filtering, you should consider "Optimal Filtering" by Anderson and Moore and "Stochastic Processes and Filtering Theory" by Jazwinski. Both books are Dover publication, and the combined price of both books is ~<= the price of this book.

I bought this book over 15 years ago and I still refer to it, and got a second copy when my book fell apart. It's very broad in coverage of all filtering and is a thin paperback with lots of easily understood concepts. A keeper.

This book should be a great reference for all engineering students who are dealing with dynamic systems, at entry level. Moderate advanced mathematics being involved, the book provides clear and straightforward discussion for a variety of estimation techniques. Moreover, I like the examples contained very much, since they offer you hand-on experience for understanding the techniques better.

As you can see from the other reviews, Gelb's book is a classic in the Optimal Estimation. I used Gelb to supplement Brown & Hwang's Applied Kalman Filtering text. Brown & Hwang is very readable, written in a conversational tone. It is also *VERY* application focused and has many Matlab examples. However, in their rush to application, I felt Brown & Hwang did not clearly layout the development of the Kalman (it's all there but it is scattered around). On the other hand, Gelb's book is cogent - both clear and concise. I found that Gelb's development and summarization of Kalman and related optimization schemes gave me the foundational understanding to work Brown & Hwang's applicatios.
For this subject, you definitely need probability (thru matrix representation of covariance, means, etc) and stochastic process. Both Gelb and Brown & Hwang review the requisite probability/stochastic processes , but I would recommend a deeper grounding in the subjects (working thru Papoulis, for example).

This is a concise record of Kalman filtering and related estimation methods. It briefly covers both discrete time and continuous estimators and is particularly useful to extend your knowledge of if you are already familiar with some of the material. Also, the appendix has an interesting comparison of the analogous terms and concepts for estimation and control theory. The book makes a breadth of topics accessible to students, practicing engineers and others.

This is a textbook covering optimal estimation, solutions to stochastic differential equations with clear discussions on implementation. This text is a must have for solving multi-dimensional parameter estimation problems.