We consider the simultaneous reconstruction of the state vector and unknown parameters for a special class of non-linear parameter-dependent systems. The approach suggested here consists of two stages. First, the state is reconstructed by a reduced order unknown input observer. Second, this observer is augmented by a filter to obtain the desired parameter. The design procedure is straightforward and may be used for an online estimation of the unknown parameter. In contrast to previous work on adaptive systems, we do not require a persistence of excitation. The approach is illustrated on two non-linear cell models.