UC San Diego

Physical systems often experience a complexity of behavior which requires many

degrees of freedom to model accurately. In practice, it may be impossible to experimentally

observe all the necessary state variables in a dynamical model. To make quantitative

predictions it becomes necessary to extract information from the observable variables

in order to estimate the entire state of the system. I discuss different approaches to

making estimating these unobservable state variables. In particular, I explore novel ways

of combining data at different times throughout the trajectory of the system to improve

the estimate of the system state at a single time.