Applied Optimal Estimation

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 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.

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.