A system, method, and computer program product for reducing processing time related to relative geometry calculations performed for objects in a simulated three-dimensional environment. The method converts three-dimensional location coordinates of each object of a plurality of simulated objects in the simulated three-dimensional environment to coordinates of a two-dimensional grid. Then, a two-dimensional grid area that is associated with the scan of an object is calculated. Objects with two-dimensional grid coordinates that are collocated with the calculated area of the scan are determined and relative geometry calculations for the scan of the object determined to be collocated with the calculated area of the scan is performed.

Determining suitable launch windows to avoid or minimize close approaches between a launch vehicle and orbiting objects. A method and apparatus is disclosed for minimizing close approaches between spacecraft and other objects in space during the launch and early deployment phase of their lifetime, by defining a launch window, utilizing filters to screen certain objects in space from consideration and identifying launch window blackout times to avoid close approaches with the remaining objects in space under consideration.

Apparatuses, methods, and systems of transferring correction information are described. In certain implementations, correction factors relate to stored or calculated values, and a correspondence between a correction factor and a value is indicated by a predetermined order of the correction factors. In one application, a method according to an embodiment of the invention is used to transmit correction factors relating to the positions of physical objects. For example, such a method may be used to transmit correction factors relating to the positions of space vehicles within a Global Positioning Satellite (`GPS`) system.

Mechanisms and techniques provide a system to evaluate operational integrity of a data processing system such as an area augmentation system by obtaining at least one set of distribution data related to information processed by the data processing system. The set(s) of distribution data can include corrections information and integrity bounds information related to the corrections information. The system applies a moment generating function to the set of distribution data to produce a moment bounded distribution data result and compares the moment bounded distribution data result to an integrity limit to determine if the data processing system operates within an acceptable integrity threshold. The system can be used in real-time or non-real time with sets of distribution data that are non-Gaussian, non-symmetric and/or non-unimodal.

A method is provided for determining position integrity in a system having a Global Navigation Satellite System (GNSS) component, such as, for example, a Global Positioning System (GPS) device. For successive alarm limits, with each alarm limit corresponding to a position integrity level, it is determined whether valid position integrity information is available. At the alarm limit at which valid position integrity information is first available, a corresponding position integrity level is determined. If no valid position integrity information is available for any of the alarm limits, a default position integrity level is then designated. An associated apparatus, system, and computer software program product are also provided.