One of the main challenging task in parameter estimation is to be able to compute in a reasonable time a very accurate solution by considering a huge number of observations. We present a parallel implementation of an incremental least squares solver based on orthogonal transformations that uses minimal data storage and enables us to tackle these very large least squares. Then we address the accuracy of the results by defining computable estimates for the conditioning of the solution or of its components and we interpret these condition numbers in terms of statistical quantities, including the variance-covariance matrix. Finally, we present an example of application in the area of space geodesy with real physical data (project from the European Space Agency).

(Seminar CMUC-LCM)