Adjustment to Cross Section Data to fit Integral Experiments by Least Squares Method

The least squares fit of a hyperplane to uncertain data

Deming least-squares fit to multiple hyperplanes

A method is derived to fit a set of multidimensional experimental data points having a priori uncertainties and possibly also covariances in all coordinates to a straight line, plane, or hyperplane of any dimensionality less than the number of coordinates. The least-squares formulation used is that of Deming, which treats all coordinates on an equal basis. Experimentalists needing to fit a line...

Generalisation of Vector Data Sets by Simultaneous Least Squares Adjustment

Manual cartographic generalisation is a holistic process. However, most automatic approaches so far have been sequential; generalisation operators are applied one at a time in a given order. This has been the case both for model generalisation (generalisation of the conceptual model) and the fine-tuning phase (generalisation of the graphics). Our research seeks to demonstrate that fine-tuning p...

Geocoding Sar-interferograms by Least Squares Adjustment

Several geocoding methods for SAR interferometry are compared. The discussion results in the proposal of a new geocoding model. It is based on a least squares adjustment combining interferometric phase, range, Doppler centroid frequency, flight path and control point data. A complete mathematical framework for the computation of object space coordinates without approximations is presented. This...

Least-Squares Covariance Matrix Adjustment

We consider the problem of finding the smallest adjustment to a given symmetric n × n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and inequalities, and in addition is positive semidefinite. This least-squares covariance adjustment problem is a convex optimization problem, and can be efficiently solved using standard methods when the ...