Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a three dimensional tool for depicting the variability of probability of collision (Pc) inputs to Pc estimates. The depictions generated by the various embodiments may be used to quantify the quality of Pc input data required to yield actionable Pc estimates. Various embodiments may provide a graphical user interface (GUI) for a computing device that may display a three dimensional depiction of the variability of Pc inputs to Pc estimates.

Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a three dimensional tool for depicting the variability of probability of collision (Pc) inputs to Pc estimates. The depictions generated by the various embodiments may be used to quantify the quality of Pc input data required to yield actionable Pc estimates. Various embodiments may provide tools for depicting Pc validation results. Various embodiments may provide a GUI for a computing device that may depict Pc validation results.

Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a volumetric approach to determining orbital encounters that may determine the number of encounters over a specified length of time. Such information may be used to determine how often during an orbit or period of time an object might trigger a conjunction warning for a neighboring satellite. The various embodiments may be used as a planning and characterization tool to estimate satellite encounter rates for a prospective orbit regime and may provide an efficient, in-line approach to assess the number of encounters occurring within a user-specified span of time.

Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a three dimensional tool for depicting the variability of probability of collision (Pc) inputs to Pc estimates. The depictions generated by the various embodiments may be used to quantify the quality of Pc input data required to yield actionable Pc estimates. Various embodiments may provide a graphical user interface (GUI) for a computing device that may display a three dimensional depiction of the variability of Pc inputs to Pc estimates.

Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a three dimensional tool for depicting the variability of probability of collision (Pc) inputs to Pc estimates. The depictions generated by the various embodiments may be used to quantify the quality of Pc input data required to yield actionable Pc estimates. Various embodiments may provide tools for depicting Pc validation results. Various embodiments may provide a GUI for a computing device that may depict Pc validation results.

Abstract: Systems, methods, devices, and non-transitory media of the various embodiments provide for a volumetric approach to determining orbital encounters that may determine the number of encounters over a specified length of time. Such information may be used to determine how often during an orbit or period of time an object might trigger a conjunction warning for a neighboring satellite. The various embodiments may be used as a planning and characterization tool to estimate satellite encounter rates for a prospective orbit regime and may provide an efficient, in-line approach to assess the number of encounters occurring within a user-specified span of time.

Abstract: A system and method for detection of anti-satellite vulnerability of an orbiting platform. An engagement volume processing unit receives a maximum impulse velocity of an SBI launched from a carrier platform of interest, a maximum time of flight (TOF) until intercept, and orbital data of the carrier platform of interest. A family of interceptor imparted velocities in a VNC frame is determined. The engagement volume processing unit applies the family of velocities over “N” release points using a carrier platform propagator to determine an engagement volume. A display and alert processing unit generates a visual representation of the engagement volume and sends the visual representation to the display device for display.

Abstract: A system and method for assessing the risk of conjunction of a rocket body with orbiting and non-orbiting platforms. Two-body orbital dynamics are used to initially determine the kinematic access for a ballistic vehicle. The access may be represented in two ways: as a volume relative to its launcher and also as a geographical footprint relative to a target position that encompasses all possible launcher locations.

Abstract: A system and method for assessing the risk of conjunction of a rocket body with orbiting and non-orbiting platforms. Two-body orbital dynamics are used to initially determine the kinematic access for a ballistic vehicle. The access may be represented in two ways: as a volume relative to its launcher and also as a geographical footprint relative to a target position that encompasses all possible launcher locations.

Abstract: A system and method for detection of anti-satellite vulnerability of an orbiting platform. An engagement volume processing unit receives a maximum impulse velocity of an SBI launched from a carrier platform of interest, a maximum time of flight (TOF) until intercept, and orbital data of the carrier platform of interest. A family of interceptor imparted velocities in a VNC frame is determined. The engagement volume processing unit applies the family of velocities over “N” release points using a carrier platform propagator to determine an engagement volume. A display and alert processing unit generates a visual representation of the engagement volume and sends the visual representation to the display device for display.

Abstract: A system and method for assessing the risk of conjunction of a rocket body with orbiting and non-orbiting platforms. Two-body orbital dynamics are used to initially determine the kinematic access for a ballistic vehicle. The access may be represented in two ways: as a volume relative to its launcher and also as a geographical footprint relative to a target position that encompasses all possible launcher locations.

Abstract: Collision probability analysis for spherical objects exhibiting linear relative motion is accomplished by combining covariances and physical object dimensions at the point of closest approach. The resulting covariance ellipsoid and hardbody are projected onto the plane perpendicular to relative velocity by assuming linear relative motion and constant positional uncertainty throughout the brief encounter. Collision potential is determined from the object footprint on the projected, two-dimensional, covariance ellipse. To accommodate nonlinear motion in accordance with the disclosed embodiments, the dimension associated with relative velocity is reintroduced by segmenting the collision tube volume into a plurality of mitered tube sections modeled as bundles of parallelepipeds in Mahalanobis space. Disclosed embodiments compute the probability of each parallelepiped as the combined object passes through the space, and sums.

Abstract: Collision probability analysis for spherical objects exhibiting linear relative motion is accomplished by combining covariances and physical object dimensions at the point of closest approach. The resulting covariance ellipsoid and hardbody are projected onto the plane perpendicular to relative velocity by assuming linear relative motion and constant positional uncertainty throughout the brief encounter. Collision potential is determined from the object footprint on the projected, two-dimensional, covariance ellipse. To accommodate nonlinear motion in accordance with the disclosed embodiments, the dimension associated with relative velocity is reintroduced by segmenting the collision tube volume into a plurality of mitered tube sections modeled as bundles of parallelepipeds in Mahalanobis space. Disclosed embodiments compute the probability of each parallelepiped as the combined object passes through the space, and sums.

Abstract: Maximum conjunction probability calculations are refined by addressing rectangular object shapes, even though their orientation may not be known. Object dimensions and relative miss distance, coupled with the aspect ratio of the projected combined covariance, are used to determine the size and orientation of the covariance as well as the object orientation that produces the maximum probability. In treating the objects as rectangles instead of spheres, the probability calculation becomes more realistic by accounting for object shape. In the absence of object attitude information, a footprint is created that completely defines the region where the two objects might touch. This footprint can then be rotated to determine the orientation that produces the largest probability, making it the most conservative estimate for the given conjunction conditions.

Abstract: Maximum conjunction probability calculations are refined by addressing rectangular object shapes, even though their orientation may not be known. Object dimensions and relative miss distance, coupled with the aspect ratio of the projected combined covariance, are used to determine the size and orientation of the covariance as well as the object orientation that produces the maximum probability. In treating the objects as rectangles instead of spheres, the probability calculation becomes more realistic by accounting for object shape. In the absence of object attitude information, a footprint is created that completely defines the region where the two objects might touch. This footprint can then be rotated to determine the orientation that produces the largest probability, making it the most conservative estimate for the given conjunction conditions.

Abstract: A computationally efficient analytical method determines when two quadric surfaces, such as ellipsoids surfaces, share the same volume by adding an extra dimension to the solution space for providing extradimensional product matrices defining degenerate quadric surfaces. The method then examines computed eigenvalues associated the product matrices to determine when the two quadric surfaces share the same volume or when surface projected areas based on viewing angle share the same area. The method provides direct share volume results based on comparisons of the eigenvalues that can be rapidly computed. The method can be use for collision avoidance detection where the objects are modeled by quadric surfaces.

Abstract: A computationally efficient analytical method determines when two quadric surfaces, such as ellipsoids surfaces, share the same volume by adding an extra dimension to the solution space for providing extradimensional product matrices defining degenerate quadric surfaces. The method then examines computed eigenvalues associated the product matrices to determine when the two quadric surfaces share the same volume or when surface projected areas based on viewing angle share the same area. The method provides direct share volume results based on comparisons of the eigenvalues that can be rapidly computed. The method can be use for collision avoidance detection where the objects are modeled by quadric surfaces.