2018 Volume 100 Issue 6 Pages 193-200
This study proposed to use the approximate standard deviation as an indicator of the accuracy of an area measured by Global Navigation Satellite System (GNSS) receivers. The standard deviation of the area was derived mathematically based on the shoelace formula using the position of the vertices of the plot and the standard deviation of position errors. The approximate value of the standard deviation was calculated using measured GNSS positions and position errors, instead of theoretical true values, because GNSS cannot measure the true position and its error. This paper gives a mathematical description of the derivation of the standard deviation of the area from GNSS-derived coordinates and those errors. The degree of approximation was also evaluated using a numerical simulation. The results showed a goodness of the approximation such that the error rate of the approximate standard deviation was within ±3％ of the measured values in 90％ of the cases in the simulation. The paper also showed examples of the application of the proposed index in GNSS measurement of area.
