ISO/TR 16158:2021 pdf – Space systems — Avoiding collisions among orbiting objects.
They are derived from past observations of satellites. Ephemerides are time-ordered sets of position and velocity within which one interpolates to estimate the position and velocity at intermediate times. Ephemerides need to span the future time interval of interest, where the equations of motion having been propagated by the provider. Observations are measurements of satellite position and velocity from one or more well-characterized and registered instruments. The recipient can use those observations to estimate the evolution of the trajectory either through direct numerical integration of governing equations or by developing orbital elements for subsequent propagation. ISO/TR 11233 describes the way a provider’s orbit determination scheme is codified. There are normative formats for orbital elements and ephemerides (see ISO 26900). See CCSDS 503.0-B-2 for normative formats for transmitting observations. It is extremely important to realize that trajectory estimates are derived from measurements that cannot be precise such as spheres. Therefore, they are called “estimates. ” The input information can include characterized uncertainties. Uncertainty in any of the independent variables or parameters introduces imprecision in all the dependent variables that describe the evolution. The appropriate expression of uncertainty is, therefore, a square matrix whose dimension is the number of elements of the state, called a state vector. If uncertainties are not provided or are wrong, one cannot determine properly the probability that two objects can collide. 5.1.2 Propagating all orbits over the interval of interest All orbits being under consideration are best forecasted by the model in which they were created. Since orbit determination and propagation are uncertain, the propagation scheme can be well suited for this interval.
5.2 Initial filtering 5.2.1 All against all The most complete process would examine each object in orbit against all others over the designated time span. Most techniques eliminate A-B duplication, defined as screening B against A in addition to A against B. Therefore, the number of screenings necessary is not the factorial of the number of satellites. It is impossible to know how many objects orbit the Earth. Many escape perception. The best a satellite operator can do is to consider those that have been detected. One cannot screen against unknown objects that one estimates can be present. 5.3 Eliminating infeasible conjunctions 5.3.1 General Much of the population in orbit physically cannot encounter many other satellites during the period of interest. For example, even if uncontrolled, geostationary satellites 180 degrees apart in longitude are not threats to each other. 5.3.2 Sieve Sieve techniques employ straightforward geometric and kinematic processes to narrow the spectrum of feasible conjunctions based on the minimum separation between orbits. They are based variously on orbit geometry, numerical relative distance functions, and actual orbit propagation.
5.3.3 Toroidal elimination Toroidal elimination eliminates objects by determining which mean orbits can touch a toroidal volume defined by the orbit of the satellite of interest and a keepout volume cross-sectional area. 5.3.4 Apogee-perigee filters This approach eliminates satellites whose apogees are lower than the perigee of the satellite of interest and perigees are sufficiently greater than the apogee of the satellite of interest. The criterion for sufficiency is based either on operator experience or risk tolerance. Risk can be quantified with techniques of signal detection and receiver operating characteristics discussed subsequently. Volumetric screening is of the same nature, eliminating satellites whose orbits are outside the volume of space described by the orbit of the satellite of interest. 5.3.5 Statistical errors Since each of these techniques relies on trajectory information that is imprecise, these filters will suffer from Type I failure to identify real threats and Type II errors (including satellites that are not threats). Filter parameter selection is based on the user’s tolerance for both kinds of errors. Every filtering scheme will include events that can have been discarded and discarded events that ought to have been included.