Data assimilation (DA) has been successfully applied to reconstruct paleoclimate. DA combines model simulations and climate proxies based on their error sizes. Therefore, the error information is crucial for DA to work properly. However, they have been treated rather crudely in the previous studies, especially when the proxies are assimilated directly. This study aims at reconstruction skill improvement by estimating observation errors accurately. For this purpose, we conducted offline data assimilation experiments for the last 100 years. Here we assimilate directly stable water isotope ratios recorded in ice cores, tree ring cellulose, and corals. In the presentation, we first show the reconstruction skills' sensitivity to the observation errors. Then, we estimate observation errors using innovation statistics. Lastly, we show the impact of estimating observation errors on reconstruction skills.