Measurement uncertainty of height differences - TNL5

6.6 Measurement Uncertainty of Height Differences

The expression of the combined standard uncertainty of a height difference can be evaluated as:

σISO-EDM, σo, σc, σj will be the same as those used in the combined standard uncertainty of distances.

In the least squares adjustment by observation equations, in order to construct the weight matrix P, the inverse of the square of the standard deviation will be entered for each value, whether angular or distance measurements.

The values of the standard deviations are affected by the equipment configuration.

García Balboa, J. L., Ruiz Armenteros, A. M. & Mesa Mingorance, J. L. (2011). Evaluación de la incertidumbre de medida de ángulos, distancias y desniveles medidos con instrumentación topográfica. Mapping 149, 6-27.

Distance Equation

Distance observations contain the following information: origin and target stations, observed distance, standard deviation and residual. The general formula is:

where:

Azimuth Equation

Azimuth observations consist of origin and target stations, observed azimuth, calculated azimuth, standard deviation and residual. The general formula is:

where:

Angular Equation

Angular observations consist of origin and target stations, observed angle, calculated angle, standard deviation and residual. The general formula is:

where:

I = current station

B = previous station

F = next station

Vertical Equation

Vertical observations indicate the differences between observed and calculated height differences. The general formula is:

where:

García Balboa, J. L., Ruiz Armenteros, A. M. & Mesa Mingorance, J. L. (2011). Evaluación de la incertidumbre de medida de ángulos, distancias y desniveles medidos con instrumentación topográfica. Mapping 149, 6-27. (http://coello.ujaen.es/publicaciones/Garcia-Ruiz-Mesa_2011_Mapping_Evaluacion_incertidumbre.pdf, last accessed: August 2013)

García-Asenjo, L., Hernández, D. & Llácer, C. (2004). Estudio de la influencia de las correcciones geodésicas sobre trabajos topográficos realizados a partir de mediciones clásicas y de GPS. VIII Congreso Nacional de Topografía y Cartografía TOPCART2004.

Wolf, P.R. & Ghilani, C.D. (1996). Adjustment computations: statistic and least squares in surveying and GIS.

Brinker, R. C. & Minnick, R. (1995). The Surveying Handbook.