Full Waveform Inversion (FWI) is an iterative inversion method whose purpose is to retrieve high-resolution models of subsurface physical parameters. Because FWI relies on the solution of a non-linear ill-posed inverse problem, uncertainty estimation is a crucial issue in practical applications, both in seismology and exploration seismic. While uncertainty assessment is a strongly desired feature for FWI, it remains a challenging problem. In this presentation, we investigate uncertainty estimation within the framework provided by ensemble data-assimilation strategies. We combine the Ensemble Transform Kalman Filter and FWI. We review the concepts underlying our ETKF-FWI method, discuss its limitations and appeals for uncertainty estimation, and illustrate it on a 2D multiparameter inversion of an exploration scale field dataset.