Readers interested in the estimation of actual system states on the basis of measurements will be interested in this book, especially if they are looking for an easy method to refresh the related material they know from journal papers and books. Basically, the presented problems concern inferring the conditional probability distributions, where we can measure some random error states and try to guess the real state that produced these measurements. The authors deal with three groups of problems: predicting (where we infer the future state from the past measurements), filtering (inferring the current state from the measurements collected up to now), and smoothing (inferring a state on the basis of the past and future measurements). The obtained conditional probabilities can be used, especially with the use of maximum likelihood (or maximum a posteriori probability) estimators, to guess the actual states. The best-known approach of this kind is Kalman filtering. The author presents this method, along with many of its extensions and novel approaches.
After presenting the context of Bayesian filtering along with notable examples of its usage (for example, in GPS systems) in chapter 1, the author presents the theoretical basis for Bayesian inference in chapter 2, and estimation methods in chapter 3. The chapter also presents the numerical examples that will be elaborated afterward with various approaches. Then, each chapter follows a clear and a regular template: the problem is presented, and then elaborated with various algorithms, along with supporting theorems and their proofs, and basic illustrations of how the given methods perform (this is especially useful as a comparison to methods given in different chapters). At the end, some exercises, which can be solved with a sheet of paper or the supporting MATLAB files, are given.
The following topics are covered: basic Bayesian filtering with the fundamentals of a linear Kalman method explanation (chapter 4), extended and unscented Kalman filtering for nonlinear cases (chapter 5), filtering with general Gaussian functions (chapter 6), and filtering with Monte Carlo approximations or importance sampling (chapter 7). Then, the respective smoothing methods are shown in an analogous way (chapters 8 to 11). At the end, chapter 12 presents how to estimate parameters to support Bayesian estimation methods, and chapter 13 gives some hints about how to select a method from the presented spectrum to solve problems readers might find in their own work.
Although this book is written in a quite formal language, it is easy to read since the author presents ideas in a clear way. While the presentation of ideas is nice, it might be tiring to some due to the repetitive format of the chapters. Additionally, the lack of more elaborated numerical examples might make it difficult for those without a good knowledge of the topic to comprehend all of the ideas. Moreover, some background and well-developed intuitions on probability theory, statistics, calculus, and matrix algebra are necessary to enjoy this work.
Therefore, this is definitely not a work for laymen or undergraduate engineering students. I recommend it to two groups of readers: specialists that need to have the Bayes-related algorithms at hand while hard-coding them, and those who enter the field, and have some knowledge of mathematical modeling and statistical estimation. These two types of readers will take advantage of this concise and elegantly presented information.
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