Data Assimilation: A Mathematical Introduction

"The mathematical style of the book is accessible to post-graduate students and combines formal mathematics with intuitive arguments and summaries of higher level results. ... the book is a good guide on dynamic data assimilation. ... the book suitable as a reference book for modelling on coordinates, whenever the sample space has a Euclidean vector space structure." (Vera Pawlowsky-Glahn, zbMATH 1353.60002, 2017)

"This book provides a Bayesian perspective of data assimilation, with a focus on smoothing and filtering problems with generic dynamical models. ... The authors also provide many numerical results, focusing on simple models that help the reader easily grasp the important properties of the underlying algorithms. In my opinion, this book is well suited to a graduate level course on data assimilation for applied mathematicians." (David T. B. Kelly, Mathematical Reviews, December, 2016)
"The authors have used a collection of dynamical systems examples throughout the book. ... Exercises are also given at the end of each chapter. The first half of this book would be very suitable as a graduate level textbook and concise reference on discrete time approaches to the data assimilation problem from a Bayesian point of view. The second half of the book ... will primarily be of interest to researchers working in this area." (Brian Borchers, MAA Reviews, maa.org, May, 2016)