Journal of Applied Geodesy
Editor-in-Chief: Kahmen, Heribert / Rizos, Chris
CiteScore 2018: 1.61
SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064
Adjustment of survey networks by topological grid search
The adjustment of survey networks by a new topological grid search (TGS) approach offers some advantages compared to conventional least squares (LS) solutions. TGS can solve systems of highly non-linear, redundant or rank defect equations, and with integer or real number parameters. The observations of survey (geodetic) data can be combined with models of geophysical processes. In this paper three numerical examples are given to assist with the understanding of the TGS process and to compare it with conventional LS and L1 adjustments. A new investigation of the residuals of the observations is included and the effects of gross errors. The application of TGS to network rank defect problems and to integer parameters is presented in this paper for the first time.
The TGS approach uses an m-dimensional grid of points around starting estimates of the values of the parameters. The method does not require a design matrix that is usually formed from partial derivatives of model equations, as is required in LS and robust L1 norm (L1) solutions. Topologically each observation is tested against the model values calculated for each of the many possible combinations of the grid points. Those grid points which satisfy the set of conditions that the calculated value differs from the observed value by less than some criteria are accepted. From this set of multidimensional grid points, which define a space including the solution, we compute the mean values, which correspond to an estimate of the solution parameters
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