5-43. Loop Closure Checks. Postprocessing criteria are aimed at an evaluation of a single baseline.
To verify the adequacy of a group of connected baselines, one must perform a loop closure on the
baselines formulated. When GPS baseline traverses or loops are formed, their linear (internal) closure
should be determined in the field. If the job requires less than third-order accuracy (1:10,000 or 1:5,000)
and the internal loop/traverse closures are very small, a formal (external) adjustment may not be
a. The internal closure determines the consistency of the GPS measurements. Internal closures are
applicable for loop traverses and GPS networks. It is required that one baseline in the loop be
independent. An independent baseline is observed during a different session or on a different day.
Many of the better postprocessing software packages come with a loop closure program. Refer to the
manufacturers' postprocessing user's manual for the particulars of the loop closure program included
with the hardware. If the postprocessing software package does not contain a loop closure program, the
user can perform the following loop closure computation:
Step 1. List the ΔX, ΔY, ΔZ, and the distance components for all baselines used in the loop closure.
Step 2. Sum the ΔX, ΔY, ΔZ, and the distance components for all baselines used in the loop closure.
Step 3. Add the square of each of the summations together and take the square root of this sum.
This resultant value is the misclosure vector for the loop.
Step 4. The loop misclosure ratio is calculated as follows:
Loop misclosure ratio = m/L
= misclosure for the loop
= total loop distance (perimeter distance)
The resultant value can be expressed as 1:loop misclosure ratio. All units for the expressions are stated
in terms of the units used in the baseline formulations (such as meters, feet, or millimeters).
b. External closures are computed in a manner similar to internal loops. External closures provide
information on how well the GPS measurements conform to the local coordinate system. Before the
closure of each traverse is computed, the latitude, the longitude, and the ellipsoid height must be
converted to geocentric coordinates (X, Y, and Z). If the ellipsoid height is not known, geoid-modeling
software can be used with the orthometric height to get an approximate ellipsoid height. The external
closure aids the surveyor in determining the quality of the