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In this paper we present and review a number of fundamental constraints that exist on the propagation of orbit uncertainty and phase volume flows in astrodynamics. These constraints arise due to the Hamiltonian nature of spacecraft dynamics. First we review the role of integral invariants and their connection to orbit uncertainty, and show how they can be used to formally solve the diffusion-less Fokker-Plank equation for a spacecraft probability density function. Then, we apply Gromov's Non-Squeezing Theorem, a recent advance in symplectic topology, to find a previously unrecognized fundamental constraint that exists on general, nonlinear mappings of orbit distributions. Specifically, for a given orbit distribution, it can be shown that the projection of future orbit uncertainties in each coordinate-momentum pair describing the system must be greater than or equal to a fundamental limit, called the symplectic width. This implies that there is always a fundamental limit to which we can know a spacecraft's future location in its coordinate and conjugate momentum space when mapped forward in time from an initial covariance distribution. This serves as an "uncertainty" principle for spacecraft uncertainty distributions.

The primary goal of this study is to track a ground-moving target using a machine-vision system installed on an unmanned helicopter, and to estimate its position if the target becomes unobservable. The machine-vision system is accomplished using real-time color images obtained from a charge-coupled device (CCD) camera mounted on a computer-controlled gimbaled system that can pitch and yaw. To avoid real-time image-tracking failure resulting from a moving target becoming concealed, the Kalman filtering technique is applied to predict the target's follow-on position, so that the camera can continuously track the target. The entire system is initially tested on the ground and then mounted on a helicopter for in-flight testing. The following three cases are shown in the flight tests: (1) an uncovered static target; (2) a moving visible target; and (3) a target that moves in a straight line at a constant speed and becomes temporarily concealed. The vision-based tracking system with the developed algorithm is successfully applied in all three cases.

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