Precision Orbit Determination for Earth Observation Systems

The orbit determination problem has its origin in the early efforts of solar system astronomers attempting to describe the motions of the planets and comets as they orbit the Sun. In these studies, the observations of the bodies, as observed from the surface of Earth, were fit to a path through the heavens that was completely described by six parameters. The foundations of modern estimation theory evolved from the early attempts to develop techniques to determine the six fundamental orbital parameters. Three of the parameters determine the orientation of the orbit or trajectory plane in space, and three locate the body in the orbital plane. These six parameters are uniquely related to the position and velocity of the satellite at a given epoch. Six appropriately selected observations will yield a solution for the trajectory. This is the classic orbit determination problem in which there is a match between the number of observations and the parameters to be determined. However, when the number of observations exceeds the number of parameters to be assigned, special techniques were required to allow using all observations. Early activity was followed by a period of intense study, culminating in the current theory for estimating dynamic parameters using observations corrupted by random measurement error. During the past two decades, the requirements for highly accurate determinations of the orbits of near-Earth satellites have been driven by the evolution of the fields of satellite geodesy and satellite oceanography. The ability to use satellite altimeter measurements to obtain accurate, globally distributed, and temporally dense observations of a satellite height as it traverses the ocean surface has opened a new era in oceanography. The ability to use accurate range and range-rate measurements between an orbiting satellite and tracking systems located on Earth's surface has provided a dramatic improvement in the ability to monitor tectonic surface deformation and subsidence and to monitor small but important changes in Earth's rotation. These same measurements, along with satellite-to-satellite measurements, are providing unparalleled views of Earth's gravity field and the gravitational signals from temporal variations in Earth's mass distribution. The advances in each of these fields is tied to the advances in our ability to determine, at high accuracy, the path followed by an Earth-orbiting satellite. The methodology whereby this task is accomplished is referred to as precision orbit determination (POD). The solution of the orbit determination problem involves four fundamental elements: (1) a set of differential equations that describes the motion of the satellite; (2) a numerical integration procedure to obtain a solution of the differential equations; (3) accurate observations of the satellite's motion; and (4) an appropriate estimation method that combines the results of the first three to yield an estimate of the satellite's position, velocity, and appropriate model parameters. These four elements are discussed. POS is used in tracking systems and force model improvement. Keywords: orbit; determinations; concept; satellite motion; orbit estimation; state equations; observation-state relationship; linearization; nonlinear problem; precision orbit determination; tracking systems; force model improvement