Space Trajectories. Orbit Determination

Space-based positioning and observation applications require precise knowledge of satellite positions. A satellite's orbit evolves under the effect of numerous perturbations, and must be regularly re-estimated.

The first orbitography methods were developed for astronomy. They used optical observations without distance measurements. Notable successes included Halley's prediction in 1705 of the comet's return in 1758, and Gauss's calculation of the orbit of the asteroid Ceres, enabling it to be re-observed eleven months after its discovery in 1801.

From the 1950s onwards, observation systems underwent a major expansion. A satellite can be tracked by optical, radar or laser means, providing measurements of direction, distance and speed. The measurements are corrected for geometric, optical and atmospheric effects experienced by the electromagnetic signal on its path. A preliminary orbit is calculated from a reduced number of observations, then adjusted by differential correction. Least squares and filtering techniques are used to estimate orbital and dynamic model parameters. Observation of Sputnik I's orbit in 1957 enabled us to estimate the gravitational term J ₂ related to terrestrial flattening. The proliferation of space debris is creating new needs. Surveillance systems such as SSN (Space Surveillance Network) or Graves (French radar system) and orbitography techniques are thus undergoing continuous improvement.

This article describes observation systems and measurement processing, then presents preliminary orbit calculation, least-squares smoothing and Kalman filtering estimation.