Covariance inflation plays an important role in the ensemble Kalman filter (EnKF) to prevent filter from divergence or to handle model errors. However the inflation factor needs to be tuned and tuning a parameter in EnKF is expensive. Wang and Bishop (2003), followed by Miyoshi (2005), adaptively estimated the inflation factor from the innovation statistics . Although the results were satisfactory it is obvious that this inflation factor estimation method relies on the information of observation errors covariance R which is not perfectly known in practice. Recent diagnostic works (Desroziers et al, 2005, Talagrand 1999, Cardinali et al. 2004, Chapnik et al. 2005, and others) suggest some statistics to diagnose observation errors. In this study we adaptively estimate observational errors (for each type of instrument) and the inflation factor for the background error simultaneously within the EnKF. Our results for the Lorenz-96 model examples show that without the accurate observation error statistics, a scheme for adaptively estimating inflation alone does not work. By contrast, the simultaneous approach works perfectly in the perfect model scenario and in the presence of random model errors. For the case of systematic model bias, although it underestimates the observation error variance, our algorithm produces analyses that are comparable with the best tuned inflation value. The SPEEDY model experiments indicate that our method is able to retrieve the true error variance for different types of instrument separately when applied to a more realistic high-dimension model.