Abstract:
In this talk I will introduce the Kalman Filter and explore its application to data assimilation.  The Kalman Filter attempts to estimate unknown variables in a system where there is noise both in observations of the system and the mathematical models describing the system.  This talk will be introductory in nature with two illustrative examples.  The first  example will use data given by a 2-dimensional system determined by a linear ODE.  The second example will use data generated by the Hodgkin-Huxley model for action potentials.  These two examples will shed light on the assumptions made with the Kalman Filter and how modifying these assumptions affects the results of the filter.