Most data assimilation systems do not correct biases during the analysis step, although developing bias-aware assimilation methods is conceptually straightforward. The main challenge is correctly attributing detected biases to their sources and developing applicable models for them. Assimilation may correct the wrong source when multiple sources produce similar biases. This risk increases when more degrees of freedom are added to the system. For example, in a weak-constraint variational analysis, parameters for radiance bias correction support the model-error correction. It is still being determined whether constraints on the correction terms can be designed to ensure that model and observation biases can always be correctly and simultaneously identified in the analysis.