This textbook’s significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes’ theorem. Unique for this book is the “top-down” derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today’s popular data-assimilation methods.
This strategy is the opposite of most textbooks and reviews on data assimilation that typically take a bottom-up approach to derive a particular assimilation method. E.g., the derivation of the Kalman Filter from control theory and the derivation of the ensemble Kalman Filter as a low-rank approximation of the standard Kalman Filter.
