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Dynamic Observers for Unknown Populations
In this dissertation, we discuss dynamic observers to estimate stage-structured populations. We consider linear discrete-time systems for density independent populations and Lur'e systems for density dependent populations. In both cases, we show that the dynamic observers yield estimates that converge exponentially to the vector-valued population. We define and show the existence of optimal observers, and we give easy-to-check necessary and sufficient conditions for the existence of the observers in ecologically reasonable circumstances. We examine the observer's behavior in the presence of uncertainties including error in parameter estimates and measurement noise, and we compare the linear observer to the classical Kalman filter and the nonlinear observer to the extended Kalman filter. A more general class of nonlinearities is briefly discussed and related to observers for stage-structured metapopulations.
Poppelreiter, Nathan, "Dynamic Observers for Unknown Populations" (2019). ETD collection for University of Nebraska - Lincoln. AAI13815156.