Recovering Wiener-Hammerstein nonlinear state-space models using linear algebra**This work was supported in part by the Fund for Scientific Research (FWO-Vlaanderen), by the Flemish Government (Methusalem), by the Belgian Government through the Inter-university Poles of Attraction (IAP VII) Program, by FWO project G.0280.15N, by the ERC Starting Grant SLRA under contract 258581, and by the ERC Advanced Grant SNLSID under contract 320378. Mariya Ishteva is an FWO Pegasus Marie Curie Fellow.