Details

Autor(en) / Beteiligte

• Eichhorn, Heinrich
• Clary, Warren G.

Titel

Least Squares Adjustment with Relatively Large Observation Errors, Inaccurate Initial Approximations, or Both

Ist Teil von

• Monthly notices of the Royal Astronomical Society, 1974-02, Vol.166 (2), p.425-432

Ort / Verlag

Oxford, UK: Oxford University Press

Erscheinungsjahr

1974

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• This paper concerns least squares adjustment problems in which the condition equations are non-linear in both the observations and the adjustment parameters (‘unknowns’). We present a solution algorithm which takes into account the second (as well as the first) order derivatives in the adjustment residuals (observation errors) and the corrections to the initially available approximations to the adjustment parameters. The inclusion of second order terms in the adjustment residuals is necessary whenever the adjustment residuals themselves cannot be regarded as negligible as compared to the adjustment parameters, that is, whenever the linearized condition equations would no longer be practically equivalent to the rigorous ones. The conventional solution techniques would then not lead to the ‘best’ estimators for the adjustment parameters in the sense of least squares. (An example for this situation is the determination of the orbit of a narrow visual double. The errors in the measured distance may then be relatively large compared to the angular size of the semi major axis.) The consideration of second order terms in the parameter corrections is completely independent of the second order terms in the adjustment residuals. It may be of advantage when the first approximation values for the adjustment parameters are so bad that the usually employed Newton-type iterations converge either not at all or only very badly. The inclusion of the second order terms will speed up the convergence toward the definitive values, and will sometimes bring about convergence when a strictly linear approach would be divergent.