In modern turbocharged engines the power output is strongly connected to the turbocharger speed, through the flow characteristics of the turbocharger. Turbo speed is therefore an important state for the engine operation, but it is usually not measured or controlled directly. Still the control system must ensure that the turbo speed does not exceed its maximum allowed value to prevent damaging the turbocharger. Having access to a turbo speed signal, preferably by a cheap and reliable estimation instead of a sensor, could open up new possibilities for control. This paper proposes a turbo speed estimator that only utilizes the conditions around the compressor and a model for the compressor map. These conditions are measured or can be more easily estimated from available sensors than the conditions on the turbine side. Another approach would be to estimate the turbo speed from the torque balance on the turbo shaft, but this requires estimating the torque provided by the turbine. Sensor information on the turbine side is usually sparse and varies greatly, which decrease the reliability of the estimates on the turbine side. The estimator utilizes an ellipse model for the compressor that outputs pressure ratio as a function of turbo speed and compressor mass flow, alternatively mass flow as a function of pressure ratio and turbo speed. The model is however hard to solve analytically for the turbo speed, which is the state to be estimated. To solve this problem a fixed-point iteration is proposed, where the turbo speed estimation from the previous sample step together with measured mass flow is used to estimate a pressure ratio. The estimation is then compared to the measured pressure ratio and the difference is used to update the turbo speed estimation for the next iteration. The observer is first validated in simulation showing that it converges exactly when the model is perfect. Robustness to model errors and noise is then shown using engine experiments where the observer converges to track the measured turbo speed.