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A turbomachine is a fundamental engineering apparatus meant to transfer energy between a rotor and a fluid. Turbomachines are the core of power generation in many engineering applications such as electric power generation plants, aerospace, marine power, automotive etc. Their relevance makes them both mission critical and safety critical in many fields. To foster reliability and safety, then, continuous monitoring of the rotor is more than desirable. One promising monitoring technique is, with no doubt, the Blade Tip-Timing, which, being simple and non-invasive, can be easily implemented on many different rotors. Blade Tip-Timing is based on the recording of the time of arrival of the blades passing in front of a probe located at a fixed angular position. The non-contact nature of the measurement prevents influences on the measured vibration, that can be recovered for all the blades simultaneously, possibly even online. In this regard, a novel algorithm is presented in this paper for obtaining a good estimate of the vibration of the blades with minimum system complexity (i.e., only one Blade Tip-Timing probe) and minimum computational effort, so to create a simple vibration monitoring system, potentially implementable online. The methodology was tested on a dataset from a SAFRAN turbomachine made available during the Surveillance 9 international conference for a diagnostic contest.