This is really an amazing book - it more than fulfilled my expectations.
It starts from the very basics of probability theory and clearly derives
Kalman Filtering, Particle Filtering, Probabilistic Motion and Probabilistic
Perception in the first 6 chapters. From there it moves on to talk about
Localization and Mapping completely separately (which I appreciated, since
the two topics are far easier to comprehend independently) in chapters 7 and
8 and then finally introduces SLAM (the main topic of the book) in chapter
9. From there it goes on to discuss various SLAM algorithms and implementations,
and finally rounds out with planning and control (that is, the practical
application of SLAM algorithms).
I can't imagine a more well-researched academic work. Every point is backed
up with examples and illustrations, and every algorithm is derived rigorously.
Even better, the mathematical derivations are set apart from the main text
so that a more "casual" reader can skip over the derivations and still get
some benefit from the text (and believe me, the math parts of this book are
very involved!). The authors assume a working knowledge of trigonometry,
calculus and linear algebra (although you could likely make some sense of the
book even if you're rusty in any of these areas). However, since the book
is about probability, you'll probably need some background in probability
theory to get any value from this text. Chapter 2 contains a refresher on
probability theory, but I doubt it would be enough to decipher the later
chapters if you had no background in the subject. I found myself having to
go back and look up the details of Bayes Rule and multivariate conditional
probability more than once.
My only gripe with this book is that each chapter includes suggested exercises
(good) but no answers/cross-check (bad). Especially considering the open-ended
nature of the exercises, it's almost not worth attempting them (or even reading
them), since you'll never know if you got the right answer, or were even on the
right track. There's no "student supplement" (at least not as I write this),
so the exercises are fairly pointless.
However, that aside, this is one of the best academic books I've read in a very
long time. I had been struggling through academic papers from IEEE and ACM on
the topic of SLAM, and only comprehending about half of it before I picked up
"Probabilistic Robotics". After reading this book carefully (I actually had
to read it twice to get it all to sink in), I'm actually zipping through the
academic papers, and understanding everything I read. You couldn't ask for a
better introduction to probabilistic robotics and SLAM.