An optimal solution can be obtained through optimization of the uncertainty in each observation. From this set of grid points, which define a space including the real solution, we compute its center of weight, which corresponds to an estimate of the solution, and its variance–covariance matrix. This process is repeated for all equations, and the common section A of the sets of grid points is defined. Then, for each equation an uncertainty is assigned to the corresponding measurement, and the sets of the grid points which satisfy the condition are detected. In our approach, an m -dimensional grid G of points around the real solution (an m -dimensional vector) is at first specified. To overcome these problems, we propose an alternative numerical-topological approach inspired by lighthouse beacon navigation, usually used in 2-D, low-accuracy applications. The adjustment of systems of highly non-linear, redundant equations, deriving from observations of certain geophysical processes and geodetic data cannot be based on conventional least-squares techniques, and is based on various numerical inversion techniques. Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solution with poor error control. The adjustment of systems of highly non-linear, redundant equations, deriving from observations of certain geophysical processes and geodetic data cannot be based on conventional least-squares techniques, and is based on various numerical inversion techniques.
Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based approach Adjustment of highly non-linear redundant systems of equations using a numerical, topology-based.Ībstract.