We address adaptive output feedback control of uncertain nonlinear systems with noisy output measurements, in which both the dynamics and the dimension of the regulated system may be unknown, and only the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. A recently developed method proposes the use of a linear error observer that estimates the tracking error and its derivatives. Since the observer is full order, it also estimates the states of the controller, even though these states are exactly known. It has been observed experimentally that the resulting adaptive control architecture is very sensitive to sensor noise. In this paper we provide a specific reduced order observer that significantly reduces sensitivity to sensor noise in adaptive control design. Experimental results on a three degrees of freedom laboratory model helicopter are used to illustrate the effectiveness of the reduced order observer design.