One of the fundamental challenges of accurate simulation of turbulent flows is that initial data is often incomplete, which for said flows is a strong impediment to accurate modeling due to sensitive dependence on initial conditions. A continuous data assimilation method proposed by Azouani, Olson, and Titi in 2014 introduced a linear feedback control term to dissipative systems, giving a simple rigorous deterministic method by which to understand the underpinnings of more complex data assimilation algorithms. In this talk, we will focus on how the AOT algorithm and modifications can be improved by knowledge of the dynamics, as well as how the AOT algorithm can yield new insights into the large time behavior of said dynamical systems.