Covariance inflation plays an important role within the ensemble Kalman filter (EnKF) in preventing filter divergence and handling model errors. However the inflation factor needs to be tuned and tuning a parameter in the EnKF is expensive. Previous studies have adaptively estimated the inflation factor from the innovation statistics. Although the results were satisfactory, this inflation factor estimation method relies on the accuracy of the specification of observation error statistics, which in practice is not perfectly known. In this study we propose to estimate the inflation factor and observational errors simultaneously within the EnKF. Our method is first investigated with a low-order model, the Lorenz-96 model. The results show that the simultaneous approach works very well in the perfect model scenario and in the presence of random model errors or a small systematic model bias. For an imperfect model with large model bias, our algorithm may require the application of an additional method to remove the bias. We then apply our approach to a more realistic high-dimension model, assimilating observations that have errors of different size and units. The SPEEDY model experiments show that the estimation of multiple observation error parameters is successful in retrieving the true error variance for different types of instruments separately. Copyright © 2009 Royal Meteorological Society