Neutral buoyancy simulation of the three-dimensional space environment enables long-term training and evaluation for astronaut and robotic operations prior to attempting these activities in space. The underwater environment, however, does not allow use of global positioning system or pseudolite equivalents, and sonar has significant limitations when used in a small, reflective tank. This paper describes an eight-camera visual positioning system (VPS) to provide real-time three-dimensional position and velocity estimates for free-flying neutral buoyancy robots performing tasks such as spacecraft inspection and servicing. A long-baseline calibration procedure is developed to estimate accurate intrinsic and extrinsic calibration parameters. An extended Kalman filter merges camera measurements with robot telemetry to create an optimal three-degrees-of-freedom estimate of translational position and velocity. Static tests indicate VPS is capable of locating a robot with subcentimeter accuracy under ideal conditions, and more typically, three-to four-centimeter accuracy when background clutter or glare influence processed image measurements. A series of dynamic tests show centimeter-level accuracy so long as the vehicle is viewable with multiple cameras, indicating VPS is a viable navigation system for neutral buoyancy operations.