It is assumed in an estimation problem with an observer that all inputs to a system can be measured and are available. However, there exists a system such as a boiler heating surface in which the observer causes estimated errors because the input called heat absorption is unmeasurable. The authors proposed, in a previous paper, a solution to such a problem for linear systems. This paper presents an extension of the proposed solution to nonlinear systems such as the actual boiler heating surface obtained by applying fuzzy controls to the feedback loops in the observer that track its output to the system output. The authors describe an example for the final superheater in a supercritical pressure once-through boiler and favorable estimated results obtained by simulations for both state variables and the unmeasurable input.