Position feedback in a solenoid actuated system typically requires a position sensing device such as a Linear Variable Differential Transformer (LVDT). The goal of self-sensing is to obtain position information directly from the electrical signals to the solenoid actuators, thus obviating the additional cost and footprint of a LVDT or another displacement sensing device. Such measurement is possible due to the position dependence of electrical inductance in the solenoids. This paper proposes a finite-dimensional nonlinear observer for the magnetic flux linkage for the solenoids. Once the flux linkage has been identified, the solenoid position can be determined via the position-inductance relationship. The algorithm has been adapted for actual solenoids modeled as a third-order system that includes two eddy current modes accurate up to 1024 Hz. Implementation on commercially low-cost solenoids (with 5mm stroke) has demonstrated RMS position accuracy up to 0.061mm. The ability to self-sense accurately can enable solenoids to be deployed at low-cost for many motion control applications besides hydraulic valves.