This thesis develops algorithms in support of a prototype hybrid air-water quadcopter platform: the AquaQuad. We consider the scenario in which AquaQuads with underwater acoustic sensing capabilities are tracking a submerged target from the surface of the ocean using sparse distributed measurements. Multiple nonlinear estimation filters are evaluated for the tracking scenario, resulting in the selection of the unscented Kalman filter (UKF). Geometric positioning effects on estimators are explored through analysis of the horizontal dilution of precision metric. The UKF is then implemented in real-time on quadrotors using time-difference of arrival pseudo-measurements in an instrumented Vicon lab space. The AquaQuads will primarily drift, but possess battery-limited flight capabilities. To increase on-station time, we seek to maximize use of the environment. In addition to solar energy, we take advantage of ocean currents that traditional autonomous platforms seek to reject. A novel sampling-based approach for path-planning is therefore created and lab-tested. The new algorithm, Dead-Reckoning Rapidly-Exploring Random Tree Star (DR-RRT*), combines the infinite-time optimality guarantees of RRT* with the unique AquaQuad mobility requirements. The DR-RRT* develops obstacle-free paths to a goal by linking brief flight and energy-efficient drift segments together, resulting in an energy savings of 27 percent over direct flight.