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This paper gives an overview of an empirical cross-calibration technique developed for the Surface Water Ocean Topography mission (SWOT). The method is here used to detect and to mitigate two spatially coherent errors in SWOT topography data: the baseline roll error whose signature is linear across track, and the baseline length error whose signature is quadratic across track. Assuming that topography data are corrupted by coherent error signatures that we can model, we extract the signatures, and we empirically use the error estimates to correct SWOT data. The cross-calibration is tackled with a two-step scheme. The first step is to get local estimates over cross-calibration zones, and the second step is to perform a global interpolation of local error estimates and to mitigate the error everywhere. Three methods are used to get local error estimates: 1) we remove a static first guess reference such as a digital elevation model, 2) we exploit overlapping diamonds between SWOT swaths, and 3) we exploit overlapping segments with traditional pulse-limited altimetry sensors. Then, the along-track propagation is performed taking the local estimates as an input, and an optimal interpolator (1-D objective analysis) constrained with a priori statistical knowledge of the problem. The rationale of this paper is to assume that SWOT's scientific requirements are met on all errors but the ones being cross-calibrated. In other words, the algorithms presented in this paper are not needed at this stage of the mission definition, and they are able to deal with higher error levels (e.g., if hardware constraints are relaxed and replaced by additional ground processing). Even in our most pessimistic theoretical scenarios of baseline roll and baseline length errors (up to 70 cm RMS of uncorrected topography error), the cross-calibration algorithm reduces coherent errors to less than 2 cm (outer edges of the swath). Residual errors are subcentimetric for very low-frequency errors (e.g- , orbital revolution). Sensitivity tests highlight the benefits of using additional pulse-limited altimeters and optimal inversion schemes when the problem is more difficult to solve (e.g., wavelengths of less than 1000 km), but also to provide a geographically homogeneous correction that cannot be obtained with SWOT's sampling alone.