Accurately estimating the state of a dynamical system is of fundamental importance in a variety of applications, from engineering challenges to everyday life. This task is complex because uncertainties typically affect the dynamical behaviour as well as the available observations of the (hidden) state. The goal of this chapter is to provide a comprehensive overview, from the probabilistic problem statement to methods for its solution. In particular the focus will be on filtering problems for time-continuous state evolution equations and time-discrete observations. It will be shown that, except for very few cases, the filtering problem has no closed-form solution, which is generally infinite-dimensional. Hence, several practical algorithms to find an approximate solution are presented.


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    Fundamentals of Kalman-Filtering Software

    Musoff, Howard / Zarchan, Paul | AIAA | 2009


    Fundamentals of Kalman filtering : a practical approach

    Zarchan, Paul / Musoff, Howard | TIBKAT | 2009


    Appendix A. Fundamentals of Kalman-Filtering Software

    Musoff, Howard / Zarchan, Paul | AIAA | 2005


    Fundamentals of Kalman filtering: a practical approach

    Zarchan, Paul / Musoff, Howard | TIBKAT | 2015


    Fundamentals of Kalman filtering : a practical approach

    Zarchan, Paul / Musoff, Howard / American Institute of Aeronautics and Astronautics | LUH institutes collections | 2005