5-15. Number of Pseudorange Observations Needed. Four pseudorange observations are needed to
resolve a GPS 3D position. Only three pseudorange observations are needed for a two-dimensional (2D)
(horizontal) location. There are often more than four pseudorange observations due to the need to
resolve the clock biases contained in both the satellite and the ground-based receiver. In computing the
X-Y-Z coordinates of a point, a fourth unknown (clock bias) must also be included in the solution. The
solution of a 3D position point is simply the solution of four pseudorange observations containing four
unknowns (X, Y, Z, and time).
5-16. Absolute-Positioning Error Sources. There are numerous sources of measurement errors that
influence GPS performance. The sum of all systematic errors or biases contributing to the measurement
error is referred to as a range bias. The observed GPS range, without removal of biases, is referred to as
a biased range or pseudorange. Principal contributors to errors in the final range and overall GPS
readings include errors in the ephemeris, satellite clock and electronics accuracies, tropospheric and
ionospheric refraction, atmospheric absorption, receiver noise, and multipath effects. Other errors
include those induced by DOD S/A and antispoofing (AS). In addition to these major errors, GPS also
contains random observation errors (such as unexplainable and unpredictable time variations). These
errors are impossible to model and correct. The following paragraphs discuss errors associated with
absolute GPS positioning modes. Many of these errors are either eliminated or significantly minimized
when GPS is used in a differential mode because the same errors are common to both receivers during
simultaneous observing sessions.
a. Ephemeris Errors and Orbit Perturbations. Satellite ephemeris errors are errors in the prediction
of a satellite's position, which may then be transmitted to the user in the satellite data message.
Ephemeris errors are satellite dependent and are very difficult to completely correct or compensate for
because the many forces acting on the predicted orbit of a satellite are difficult to measure directly.
Because direct measurement of all forces acting on a satellite orbit is difficult, it is nearly impossible to
compensate or accurately account for those error sources when modeling the orbit of a satellite. The
previously stated accuracy levels are subject to performance of equipment and conditions. Ephemeris
errors produce equal error shifts in the calculated absolute-point positions.
b. Clock Stability. GPS relies heavily on accurate time measurements. GPS satellites carry
rubidium and cesium time standards that are usually accurate to 1 part in 10 trillion and 1 part in 100
trillion, respectively. Most receiver clocks are actuated by a quartz standard accurate to 1 part in 100
million. A time offset is the difference between the time recorded by the satellite clock and the time
recorded by the receiver. Range error observed by the user as the result of time offsets between the
satellite and receiver clock is a linear relationship and can be approximated.
c. Ionospheric Delays. GPS signals are electromagnetic signals and are nonlinearly dispersed and
refracted when transmitted through a highly charged environment like the ionosphere. Dispersion and
refraction of the GPS signal is referred to as an ionospheric range effect because dispersion and
refraction of the
EN0593
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