Precise Orbit Determination
for Low Earth Orbit Satellites
David Hobbs
Lund Observatory, Sweden.
http://www.astro.lu.se
ABSTRACT: The precise orbit determination problem is to accurately determine the position and velocity vectors of an orbiting satellite.
With the ever increasing sophistication of satellites in low Earth orbit the ability to precisely predict the position and velocity of the
satellite is extremely important. This need has been amplified in recent years by the development of Earth observation and meteorological
satellites, which need to make measurements of the Earth’s atmosphere, gravity field, sea surface height, etc., with unprecedented
precision. This has led to the development of advanced numerical methods, which allow a precise orbit to be calculated on the basis of
observation data from GPS signals, as measured by the LEO satellite. Additionally, the observation data is often required by the user in
“near real-time” (for use in, for example, numerical weather prediction simulations). This means that the data must be downloaded from
the satellite every orbital revolution, and must then be processed to an accuracy of less than one meter in position and distributed to
users within approximately one hour of downloading. This task presents a formidable challenge, but, with the use of numerical estimation
methods, accuracies of 2-3 cm in position can be achieved, well within requirements. Some example missions which have heavily relied
on precise orbit determination are listed below.
The precise orbit determination problem is to accurately determine the ephemeris of
an orbiting satellite. To achieve this, estimates of the position and velocity of the
orbiting vehicle are made based on a sequence of observations. This is usually
accomplished by integrating the equations-of-motion, starting from a reference
epoch to produce predicted observations. This initial orbit is generally not very
accurate but is a good starting point from which to construct a state vector which can
then be used in a least squares algorithm to obtain a better estimate of the
observations. The state vector is composed of the position vector, the velocity vector,
empirical forces and measurement model parameters. Components of the satellite’s
state vector at a reference epoch are then adjusted to minimize the observation
residuals in a least squares sense. Thus, to solve the orbit problem one needs:
•Equations-of-motion describing the forces acting on the satellite and, possibly, the
covariance of the process noise if a Kalman filter is employed.
•The relationship between the observed parameters and the satellite’s state vector.
•A least squares estimation algorithm.
Orbit determination methods can be verified by means of independent measurements.
An analysis of worst-case scenarios, in which the usual error sources are maximized,
is show to the right. Additionally, the impact of processing the data under near real
time conditions is illustrated. Despite such adverse conditions, the orbital accuracy is
still shown to be sufficient for, for example, radio occultation experiments.
The unique design of the GRACE mission (twin satellites flying in formation) has lead
to an improvement of several orders of magnitude in these gravity measurements and
allows much improved resolution of the broad-to-finer-scale features of Earth's
gravitational field over both land and sea.
To measure gravity from space, the two identical GRACE satellites fly in the same
orbit -- one 220 km (137 miles) ahead of the other. As the pair circles the Earth,
areas of slightly stronger gravity will affect the lead satellite first, pulling it away from
the trailing satellite. An accelerometer is used to distinguish gravity influences from
those of air drag. The K-band ranging instrument is capable of measuring the
distance between the satellites with a precision better than the width of a human hair.
By monitoring this distance, GRACE is able to detect fluctuations in the gravitational
field and, therefore, differences in the density of the Earth's surface beneath the
satellites. The data is combined with GPS data to produce a map of the gravity field
approximately once a month.
CHAMP (CHAllenging Minisatellite Payload) is a German small satellite mission for geoscientific and
atmospheric research and applications, managed by GFZ. With its highly precise, multifunctional and
complementary payload elements (magnetometer, accelerometer, star sensor, GPS receiver, laser retro
reflector, ion drift meter) and its orbit characteristics (near polar, low altitude, long duration) CHAMP has
generated, for the first time, simultaneously highly precise gravity and magnetic field measurements over a 5
year period. This permits the detection of, not only the spatial variations of both fields, but also their variability
over time. The CHAMP mission opened a new era in geopotential research and become a significant contributor
to the Decade of Geopotentials.
In addition, with the radio occultation measurements onboard the spacecraft and the infrastructure developed
on ground, CHAMP became a pilot mission for the pre-operational use of space-borne GPS observations for
atmospheric and ionospheric research and applications in weather prediction and space weather monitoring.
The TOPEX/Poseidon satellite orbited the Earth, completing one cycle of 127 revolutions
around it about every 10 days. (The satellite made one revolution in 112 minutes.) During
one cycle, the satellite collected the sea level height measurements for over 90% of the icefree oceans of the entire globe at all times using two on-board state-of-the-art altimeters
one by NASA for 90 % of the time and the other by CNES for 10 %.
Simply stated, TOPEX/Poseidon measured the sea level by using two on-board radar
altimeters to measure the altitude of the satellite above the sea surface while three
independent satellite tracking systems measured the distance between the satellite and the
center of the Earth (geocenter). Then, the altimetry measurements were subtracted from the
satellite position to find the height of the ocean above the geocenter, which is the sea level.
Using laser ranging systems, satellites can be tracked with an accuracy in the centimeter to
decimeter range. Alternatively, space-based radio tracking systems like GPS, allow the
differential processing of concurrent ground-based pseudorange and carrier phase
measurements within a global network. When this is combined with detailed models of the
spacecraft and the associated atmospheric drag, solar radiation pressure and geopotential,
the result is an orbit determination, accurate to a few centimeters.