The numerical integration of a non-linear function f(a (t), ap(t),.. a (t)) vith mutually independent variaties a, is considered for the case that the initial conditions for the integration process and time series of a, are determined by experiment. In order to minimize the error in the result of the integration process a technique is developed based on the stochastic characteristics of the measured variables. This technique is applied to the problem of determining aircraft trajectories from in-flight recordings of acceleration components and attitude of the aircraft (Euler angles), starting from given initial conditions for position and speed of the aircraft in addition to a (measured) end condition a minimum-error estimate of the trajectory is derived. Special attention is paid to the folioving aspects of the technique: a comparison to simple non-stoachstic error reduction techniques, the effect of errors in the additional ("updating") information on the resuitin accuracies and the validation of the technique.