Drilling into offshore deep water, high-pressure high-temperature reservoirs is a very challenging process. The most important task in these drilling operations is to control bottomhole pressure. Many automatic control systems for drilling operations are based on models calculating wellbore pressure, flow and downhole hydraulics. Closed loop control systems, for example Managed Pressure Drilling, are examples of systems that may involve such real-time calculations. Therefore a high degree of accuracy in pressure and flow predictions is crucial to the performance of automatic drilling applications. In this paper the key uncertain model parameters and the bottom-hole pressure are estimated using joint unscented Kalman filter based on only available top-side measurements. The results of simulations show accurate estimation of the bottom-hole pressure and uncertain parameters, even in transient periods for example the scenario of pipe connection operations, where there is no available bottom-hole pressure measurement, and flow through the bit.