Angles-only initial orbit determination (IOD)

摘要

A methodology for initial orbit determination of an object about an astronomical body searches a grid of possible boundary values on the range-to-object over the observation interval to find the grid point and corresponding initial orbit that best fits all of the more than three (N) angles-only observations according to an error metric. The search is conducted by solving a boundary-value problem for different grid points. The state vector is propagated to determine estimated observation directions for the remaining N−2 observations. The grid point (and initial orbit) that best fit all of the observations is selected. For efficiency, the search may start with a broad but coarse initial grid and increase the resolution of the grid as the search converges to a solution.

主权项

1. A method of determining an object's initial orbit about an astronomical body, comprising:
receiving n angle-only observation directions (do1, do2, . . . don) of the object at times (t1, t2, . . . , tn) where n is greater than three, said angle-only observation directions measured using one or more angle-only sensors from known observation positions (o1, o2, . . . , on), on one or more platforms; and one or more computer processors configured to execute the steps of: generating a search grid in ri and Δr=rj−ri with a sampling resolution where ri and rj are a range-to-object of the different ith and jth observations; for different combinations of ri and Δr,
solving a boundary-value problem as a function of (oi, oj), (doi, doj) (ri, Δr) to determine a state vector of a three-dimensional position and a velocity of the object at time ti;converting the state vector to an orbital element set that describes the object's initial orbit including elements of semi-major axis a, eccentricity e, inclination i, longitude of ascending node Ω, argument of perigee ω, and true anomaly ν;using Kepler's equation to compute the true anomaly ν at times tk for k=1 to n, k not equal i or j for the remaining n−2 observations to propagate the orbit;using the resulting orbital element sets of the propagated orbit to estimate object locations at times tk for k=1 to n, k not equal i or j;computing estimated observation directions (de1, de2, . . . den) from the known observation positions (o1, o2, . . . on) to the estimated object locations at tk for the remaining n−2 observations; andcomputing an error metric based solely on the differences between the measured and estimated observation directions at times tk for the remaining n−2 observations; identifying the (ri, Δr) pair on the search grid at which the error metric represents a best fit to all of the measured observation directions; and reporting an orbital element set corresponding to the identified (ri, Δr) pair that describes the object's initial orbit.