In the tokamak ASDEX Upgrade, Integrated Data Analysis (IDA) is used to infer plasma quantities, such as electron density, using heterogeneous data sources. Essential is forward modeling from the parameter space into the data space with physically reasonable models for probabilistic evaluation. This paper presents a new forward model for O-mode profile reflectometry, a necessary prerequisite for Bayesian inference and inclusion in IDA. An efficient forward model based on the analytic solution for a piece-wise linear density description allows IDA to overcome problems associated with the established determination of cut-off locations via Abel inversion and Bottollier-Curtet's method. Instead of using a hard-coded initialization for densities below the first measured cut-off density, other diagnostics, such as the lithium beam, are used to analyze the shape of the initial part of the profile. Error propagation from the measured data, and other uncertain sources, to the uncertainties in the density profile and also its gradient is an intrinsic property of the probabilistic approach, which benefits from the joint analysis. Missing or ambiguous data do not prevent the profile evaluation, but only increase the uncertainty for densities in the affected range. Density profiles together with their uncertainties are determined by the joint analysis of complementary diagnostics, with the newly added reflectometry closing a gap in the outer core region. A stand-alone inversion based on the new forward model, including uncertainty quantification, is introduced, optionally providing an n(R) profile with uncertainties and a gradient. This method is a candidate for real-time analysis, providing error bars.
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