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Abstract
The problem of the convergence of the collocation solution to the true gravity field was defined long ago (Tscherning in Boll Geod Sci Affini 39:221-252, 1978) and some results were derived, in particular by Krarup (Boll Geod Sci Affini 40:225-240, 1981). The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be really continued down to a Bjerhammar sphere, we have a quite general convergence property in the noiseless case. When noise is present in data, still reasonable convergence results hold true.
"Democrito che 'l mondo a caso pone" "Democritus who made the world stochastic"
Dante Alighieri, La Divina Commedia, Inferno, IV - 136 [PUBLICATION ABSTRACT]