Published on *GEOG 862: GPS and GNSS for Geospatial Professionals* (https://www.e-education.psu.edu/geog862)

$$s=\frac{\left(m\xb7n\right)}{r}+\frac{\left(m\xb7n\right)\left(p-1\right)}{r}+k\xb7m$$

where

s = the number of observing sessions,

r = the number of receivers,

m = the total number of stations involved

Finding the Number of Sessions

The illustrated survey design calls for 10 sessions, but the calculation does not include human error, equipment breakdown, and other unforeseeable difficulties. It would be impractical to presume a completely trouble-free project. The FGCC proposed the following formula for arriving at a more realistic estimate

But n, p, and k require a bit more explanation. The variable n is a representation of the level of redundancy that has been built into the network, based on the number of occupations on each station. The illustrated survey design includes more than two occupations on all but 4 of the 14 stations in the network. In fact, 10 of the 14 positions will be visited three or four times in the course of the survey. There are a total of 40 occupations by the 4 receivers in the 10 planned sessions. By dividing 40 occupations by 14 stations, it can be found that each station will be visited an average of 2.857 times. Therefore the planned redundancy represented by factor n is equal to 2.857 in this project.

The experience of a firm is symbolized by the variable p in the formula. The division of the final number of actual sessions required to complete past projects by the initial estimation yields a ratio that can be used to improve future predictions. That ratio is the production factor, p. A typical production factor is 1.1.

A safety factor of 0.1, known as k, is recommended for GPS projects within 100 km of a company’s home base. Beyond that radius, an increase to 0.2 is advised.

The substitution of the appropriate quantities for the illustrated project increases the prediction of the number of observation sessions required for its completion:

$$s=\frac{\left(m\cdot n\right)}{r}+\frac{\left(m\cdot n\right)\left(p-1\right)}{r}+k\cdot m$$ $$s=\frac{\left(14\right)\left(2.857\right)}{4}+\frac{\left(14\right)\left(2.857\right)\left(1.1-1\right)}{4}+\left(0.2\right)\left(14\right)$$ $$s=\frac{\left(40\right)}{4}+\frac{\left(4\right)}{4}+\left(2.8\right)$$ $$s=10+1+2.8$$ $$s=14\text{sessions(roundedtothenearestinteger)}$$

In other words, the 2-day, 10-session schedule is a minimum period for the baseline plan drawn on the project map. A more realistic estimate of the observation schedule includes 14 sessions. It is also important to keep in mind that the observation schedule does not include time for on-site reconnaissance.