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The paper generalizes an RPEM based on a restricted nonlinear state space ODE model, to handle also nonlinear measurement equations. The coefficients of a multi-variable polynomial that models one right hand side component of the ODE are estimated, thereby avoiding overparameterization. It is discussed why this restricted model can also handle ODEs with more complicated right hand side structures. The paper also generalizes related results on scaling of the sampling period to the nonlinear output equation case. As an illustration, the RPEM was applied to simulated data obtained from a second order nonlinear drum-boiler model. A first order, four parameter, nonlinear model resulted in accurate modeling of the output power over a wide range of fuel flows.