Deterministic and stochastic parameters in inertial survey adjustment

Abstract

In the adjustment of inertial position surveys the additional parameters describing the systematic errors of individual traverses can be considered as deterministic or stochastic. The paper deals with various aspects of the deterministic or stochastic approach by way of a standard functional model. If purely deterministic parameters are set up, the solvability of the least squares problem depends on redundant observations like coordinate discrepancies of forward and backward runs or coordinate differences at cross-over points of traverse networks. Inequalities are presented to handle the configuration problem for any net and for several ways of introducing parameter sets. Also condition equations being geometrically explainable are developed solving the datum problem in free adjustment applications. Based on the Ebersberger Forst campaigns with a large amount of Ferranti, Honeywell and Litton data, numerical investigations into the stochastic properties of the additional parameters and the observations follow. It turns out that additional parameters for Honeywell and Litton data can be considered as stochastic parameters while for Ferranti data significant azimuth and time dependent effects can be found. The investigations of true errors show that in case of the deterministic adjustment approach a diagonal covariance matrix can be introduced and in case of stochastic additional parameters a first order Gauss-Markov process serves as a good approximation for the stochastic behaviour of the observations.