Geodetic Data Collection Techniques - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 43

Principles of Satellite Laser Ranging

SLR is a physical distance-measuring method, using the laser as its light source and
the time of flight of the optical pulse for measurements. Its main features are:
1. The output power of the laser can reach orders of magnitude of 10 9 W and its
optical energy density per unit area can be greater than that of the surface of the
sun. Thus, the effective distance of the laser can reach the artificial Earth
satellites tens of thousands of kilometers away, or even the lunar surface.
2. The laser spectrum is very sharp and has a halfwave width of about 5 , which
benefits from adopting a narrow-band filter to eliminate sky background noise in
a receiving optical system and to improve signal-to-noise ratio in observation.
3. The divergence angle of light beam output by the laser is very small, at about
1 mas. Through the optical system alignment, the divergence angle can be
further compressed. Therefore, the light energy can still be concentrated within
a very small scope far away.
4. The laser burst of a pulsed laser can reach a very small order of magnitude in
width. Because the pulse width is one of the main factors in determining ranging
accuracy, the laser ranging can be very accurate.

Due to the aforementioned characteristics of the laser, it is possible to realize
long-distance laser ranging. There are three methods of laser ranging: the pulse
method, phase method, and interference method. The pulse method is usually
applied in SLR. Its basic principle is very simple: laser pulse signals are sent
from a laser ranger placed at the observation station to a laser satellite equipped
with a back-reflecting prism and go back to the receiving system of the rangefinder
after being reflected by the tested satellite. If the time difference t between the

sending and receiving of these laser pulse signals is measured, we can get the
distance

ʔ

ˁ between the satellite and the station according to the formula:

1
2 c

ˁ ¼ ʔ t, ð 2 : 11 Þ

where c is the velocity of light. Suppose the equation of motion of satellites in the
Earth-Centered Inertial (ECI) Coordinate System is:

X

¼ F X ð ; P d ; t Þ , X tðÞ¼ X 0 , ð 2 : 12 Þ

(r, r 0 ) T or X where X is the satellite's state vector at an instant of time t; X ¼ ¼ ˃ ,

˃ being the six Keplerian elements; X 0 is the satellite's state vector at initial time t 0 ;

and P d is the physical parameter to be estimated. Then the solution of (2.12) can be
expressed as:

:

Q X 0 , P d , d t

X ¼ ð 2 : 13 Þ

ʘ O is the satellite's observed quantity (i.e., the distance between the
satellite and the Earth); its corresponding theoretical value

Suppose

ʘ C canthenbedefinedas: