In order to realize a thin, compact, efficient, and fuel-flexible power-generation system, we have been developing and investigating a free-piston engine linear generator (FPEG), which consists of a two-stroke combustion chamber and an adjustable gas spring chamber. This paper proposes a novel observer algorithm that has two advantages. First, the piston position can be interpolated at high accuracy beyond the resolution of the piston position sensor, which improves the accuracy and stability in controlling the combustion parameters, such as ignition timing and compression ratio. Second, the pressure in the gas spring chamber and the coefficient of damping (lubrication condition) are estimated simultaneously and independently. In this paper, the principle of the developed observer algorithm is described and tested through simulation and experimentation using the developed FPEG system. Based on the simulation, the output of the position sensor (resolution: 0.55 mm) was interpolated with an accuracy of ±0.1 mm. Based on the experimental results for the estimation of pressure in the gas spring chamber and the coefficient of damping, the feasibility of sensorless monitoring of the pressure in the gas spring chamber and the coefficient of damping has been verified.