Spatial Coordinate Transformations with Noisy Data

The parametric transformation of spatial coordinates between different reference frames is traditionally dealt with a stepwise approach which imposes a suboptimal treatment in the presence of noisy data. The chapter explains briefly the drawbacks of this approach and then presents an alternative scheme for spatial coordinate transformations that improves the classic stepwise solution when using noisy coordinates of known stochastic structure. The proposed methodology is simple in principle, although its numerical implementation with nonlinear parametric models is a bit more involved and it relies on the joint least squares adjustment of the observed coordinates using their full stochastic model over all points of interest. The mathematical framework and the related properties of this “stacking” approach are presented in detail, along with a numerical example that demonstrates its feasibility for practical problems in geospatial applications