## 1 Introduction
[PERSON] and [PERSON] [12] developed a multi-degrees-of-freedom method for obtaining the vibration parameters of mistuned rotating blades. The method was implemented on simulated and measured data and a good match with strain gauge measurements was reported. Recently, [PERSON] et al. [13] suggested a revision for two-parameter plot method. They actually proposed an alternative procedure to determine the Engine Order (EO) and the vibration amplitude and they compared their results with the results obtained by the strain gauges measurements. The methods introduced so far are recognized as indirect methods, they require measurements data from one or two sensors. All samples of the deflection signal recorded by the sensors over the entire resonance region are used for the vibration parameters identification. In addition, there exist other types of analysis methods called direct methods in which at least four probes are employed for analyzing tip timing data. Least-squares Sine fitting algorithm presented by [PERSON] [14] is the most common direct method used for parameters identification. The method is based on a fitting procedure for each value of rotational speed. This procedure is the basis of almost all commercial BTT packages developed for industry. Three new direct methods, known as determinant method, global autoregressive and global autoregressive with instrumental variables, were developed by [PERSON] [15]. They used a simple lumped parameter model of a multi-bladed system to simulate BTT data for synchronous vibrations and they compared the results of the three methods with Monte Carlo simulations. [PERSON] [16] in his PhD thesis in 2010, introduced a multi-frequency Sine fitting method for identifying simultaneous resonances and also he investigated the capability of the BTT technique to replace the strain gauges. [PERSON] et al. [17] presented a resonance parameter identification method which eliminates the need for a once-per revolution sensor. Recently, [PERSON] et al. [18] proposeda novel concept based on sensor waveform analysis in order to estimate the vibration properties via global optimization technique. [PERSON] et al. [19] presented a novel simulator based on a finite element reduced order model of a bladed disk assembly for the generation of BTT data and assessed the performance of three principal BTT algorithms. [PERSON] et al. [20] employed a latest generation BTT system to study the synchronous vibration of shrouded bladed disk, a new positioning for the BTT optical sensors was tested and an original method was suggested to detect the deflection shape of the bladed disk with small mistuning pattern. [PERSON] et al. [21] recently applied a BTT measurement set-up for design validation of a heavy duty gas turbine. The vibration parameters of the blades in the compressor and turbine sections were determined by the Sine fitting analysis method and the damping and amplitude of the blades were also reported. The present paper is focused on the analysis of the BTT measurement data in the particular case when, even if the vibrating mode is isolated from the other modes, the corresponding peak in the frequency response is not single but two very close peaks are present. This type of dynamic response with two very close peaks can occur quite often in the case of bladed disks. It is generally related to the fact that the bladed disk is not perfectly cyclic symmetric and a so called \"mistuning\" phenomenon is present. In particular it happens in the case of \"small mistuning\" where the cyclic symmetry is not completely destroyed, but two slightly different frequencies are associated to the same mode shape, and, as a result, the corresponding resonance peak is split in two peaks. If this is the case, for the post processing of BTT data, the classical method based on 1 degree of freedom (1 DOF) model, introduced by [PERSON] and [PERSON] [9], does not work.