Estimation of the duration of the scale unit of TAI with primary frequency standards

Frequency measurements of primary frequency standards (PFS) are reported more or less regularly to the BIPM to improve the accuracy of TAI. Data from the several PFS are combined to compute an estimation of the duration of the scale unit of TAI. The algorithm used to this purpose "weights" the different evaluations via filter coefficients that depend on the uncertainty of the evaluation, on the time elapsed between the interval of evaluation of the PFS and that of the calculation, and on the model that represents the instability of the free atomic scale (echelle atomique libre, EAL). We discuss in this paper problems encountered with the filtering algorithm, and we propose a tentative solution. We discuss the model that could be chosen to represent the instability of EAL