In this paper the problem of simultaneous robust state and parameter estimation for a class of MIMO non-linear systems under mixed uncertainties (unmodelled dynamics as well as observation noises) it tackled. A switching gain robust 'observer-identifier' is introduced to obtain the corresponding estimates. This is achieved by applying an observer to the so-called nominal extended system, obtained from the original system without any uncertainties and considering the parameters as additional constant states. As it is shown, in general the extended system can lose the global observability property, supposed by valid for the original non-extended system, and a special procedure is needed to provide a good estimation process in this situation. The suggested adaptive observer has the Luenberger type observer structure with switching matrix gain that guarantees a good enough upper bound for the identification error performance index. The Van der Monde generalized transformation is introduced to derive this bound which turns out to be 'tight' (it is equal to zero in the absence of both noises and unmodelled dynamics). The example dealing with an inverted pendulum illustrates the high effectiveness of the suggested approach.