Vision-aided navigation is the process of fusing data from visual cameras with other information sources to provide vehicle state estimation. Fusing information from multiple sources in a statistically optimal manner requires accurate stochastic models of each information source. Developing such a model for visual measurements presents a number of challenges. Vision-aided navigation systems rely on a set of computer vision methods known as feature detection and tracking to abstract visual camera images into a data source amenable to state estimation. It is nearly universally assumed that the measurements produced by these methods have independent and identically distributed (IID) errors. This study presents evidence that directly contradicts these assumptions. Novel models for visual measurements that eliminate the IID assumption are developed. Estimators are designed around the models and tested. Results demonstrate a significant performance advantage over existing methods and also reveal new challenges and paradoxes that motivate further research. In addition to improving vision-aided navigation models, a set of flexible and robust data-driven estimation techniques are developed and demonstrated on both canonical problems and problems in vision-aided navigation.