
A bottom-up approach that enables readers to master and apply the latest techniques in state estimation This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning: Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice MATLAB(r)-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering.
However, to understand recursive least squares, in particular the covariance matrix update you're going to need a firm grounding in probability and statistics. Simon makes the case that probability theory is a less strict pre-requisite than multiple-input-multiple-output (state space) linear systems theory (for which I can recommend Chen's "Linear System Theory and Design").
So I would argue that to understand Kalman filters you need to know state space systems modelling, both continuous time and discrete time discretisation methods (this provides the dynamics that describe the time-update step), plus you need to know enough multivariate statistics to understand how the Kalman filter propagates the gaussian random variables (i.e. the Kalman state) through the dynamics and back and forth through the measurement matrices.
Optimal State Estimation by Dan Simon helped, too: http://www.amazon.com/Optimal-State-Estimation-Nonlinear-App...