A fast-converging and reliable method for estimating a wind speed at, for example, a wind turbine comprising a rotor carrying a set of variable pitch angle wind turbine blades. The estimated wind speed is iteratively derived using a wind turbine rotor rotational speed, a turbine blade pitch angle, and a derived initial estimated wind speed. The initial estimated wind speed is based on the rotational speed and an initial tip speed ratio. The initial tip speed ratio is selected to be a value greater than a minimum tip speed ratio, wherein the minimum tip speed ratio defines a control region stability limit as a function of the pitch angle. Thus, for a given pitch angle, a minimum tip speed ratio is derived as a limit or boundary point between a stable control region and an unstable control region.