The sensory experience of an organism is shaped by movement, either of the entire body or of individual sensors. Many organisms can exploit sensor motion in ways that enrich the quality of sensory cues and enhance their ability to estimate unknown quantities. For instance, mantids perform peering head movements before striking prey, a behavior thought to aid in depth estimation. A key challenge in sensory neuroscience is to uncover what motivates such behaviors. How can we understand what information is gained via sensor motion? Here, we present a novel computational method for modeling active sensing behaviors. We focus on revealing how specific types of sensor motion might affect the ability of an organism to estimate a task-relevant variable. Our framework leverages Fisher information and the control-theoretic concept observability to answer key questions regarding active sensing, such as what variables can be estimated and what kind of sensors or sensor movements are required. As a case study, we model how a flying insect could estimate properties of ambient wind. We show that active changes in flight trajectories (turns and accelerations) could enhance an insect’s ability to estimate wind direction and magnitude, and that the potency of these maneuvers is highly dependent on the available sensory cues. We show that our framework can predict animal active sensing behaviors by applying our method to real trajectories of freely flying Drosophila. Lastly, we present a framework for leveraging observability to filter sporadic estimates from bouts of active sensing. We show that integrating this filtering approach with an artificial neural network produces accurate estimates of wind direction using Drosophila trajectories. Our framework serves as a powerful computational tool for interpreting why animals move in a sensorimotor context and for generating testable hypotheses about sensory processing.