This paper develops an observer for a magnetic field based position sensor. The process model for the magnetic field sensing system is linear while the output equation is highly nonlinear. Previous results on observer design in nonlinear systems have mostly assumed that the output equation is linear, even if the process dynamics are nonlinear. This paper presents a new observer design technique that can rigorously address the presence of nonlinearity in the output equation. The estimation error dynamics of a two degree-of-freedom observer is transformed into a Lure system in which the sector condition for the nonlinearity in the feedback loop is constructed from the element-wise bounds on the Jacobian matrix of the nonlinear measurement equation. The developed observer design technique is applied to non-intrusive estimation of the position of a piston inside a pneumatic cylinder. Experimental results show that the observer can accurately estimate piston position with sub-mm accuracy. The advantages of the nonlinear observer over an extended Kalman Filter are demonstrated. The developed observer has applications in many other problems involving nonlinear output equations.