Bayesian model updating is an effective method to predict and calibrate models based on prior distribution and observation data. Uncertainties in engineering experiments， such as instrumental accuracy， human errors and environmental interference， can cause inaccuracy of observation data， which in turn result in uncertainty of posterior distribution parameters， bringing new challenges to Bayesian updating. To obtain the accurate posterior sample distribution under the observation uncertainty， the Bayesian updating problem under the observation uncertainty is studied. By equivalently transforming the Bayesian updating problem under the observation uncertainty into a reliability analysis problem involving interval and random variables， a new Bayesian updating model is established. A single-layer and a double-layer Kriging algorithms for estimating the established model are proposed， which can efficiently achieve quantitative Bayesian model updating under the observation uncertainty. The application of the proposed model and method in wing and other structures shows that the established model can accurately measure the influence of observation uncertainty on posterior distribution parameters， achieve the complete update of input variable distribution parameters under observation uncertainty， and effectively reduce the uncertainty of input variable distribution parameters. The single-layer Kriging algorithm can efficiently provide the average estimates of the posterior sample distribution， while the double-layer Kriging algorithm can accurately provide the complete value interval of posterior sample distribution parameters. Compared with the Monte Carlo method， the two proposed algorithms significantly reduce the number of calls to the original model while ensuring the accuracy， enhancing the computational efficiency of Bayesian updating under observation uncertainty.