Spatial triangulation in a local, astronomical oriented cartesian coordinate system

For the determination of spatial coordinates of the points of a net-work a local Cartesian coordinate system is introduced, whoze z-axis coincides with the true vertical of an arbitrarily selected central point in the net-work, and whose x-axis is oriented to astronomical north. The observed horizontal directions and vertical angles, which refer to the local verticals of the observation stations, are reduced to parallels to the z-axis and the x-axis. For this purpose the direction of the local vertical in the observation stations and at least the astronomical azimuth of one side of the net-work need to be measured. This method has the advantage, that the number of unknowns for one observation station is reduced from six for the conventional method to four, and that, if the vertical angle and the astronomical azimuth of a line are measured from both sides, a simple control of the measured values is possible before the adjustment. The formulae for the reduction of the measured quantities and the observation equations for the adjustment of reduced azimuths, reduced vertical angles and of distances are derived. The method is checked in a quadrilateral in the Swiss Alps and compared with the conventional ellipsoidal adjustment.