Irrigation is an important component of the terrestrial water cycle, but it is often poorly accounted for in models. Recent studies have attempted to integrate satellite data and land surface models via data assimilation (DA) to (1) detect and quantify irrigation, and (2) better model the related land surface variables such as soil moisture, vegetation, and evapotranspiration. In this study, different synthetic DA experiments are tested to advance satellite DA for the estimation of irrigation. We assimilate synthetic Sentinel-1 backscatter observations into the Noah-MP model coupled with an irrigation scheme. When updating soil moisture, we found that the DA sets better initial conditions to trigger irrigation in the model. However, large DA updates to wetter conditions can inhibit irrigation simulation. Building on this limitation, we propose an improved DA algorithm using a buddy check approach. The method still updates the land surface, but now the irrigation trigger is not based on the evolution of soil moisture, but on an adaptive innovation outlier detection. The new method was tested with different levels of model and observation error. For mild model and observation errors, the DA outperforms the model-only 14-day irrigation estimates by about 30% in terms of root-mean-squared differences, when frequent (daily or every other day) observations are available. The improvements can surpass 50% for high forcing errors. However, with longer observation intervals (7 days), the system strongly underestimates the irrigation amounts. The method is flexible and can be expanded to other DA systems and to a real world case.