Linear compressors are being widely used in a huge variety of applications due to their higher efficiency than traditional rotary compressors. The linear compressor is driven by the Linear Oscillatory Machine (LOM), and the sensor-less control of LOM is very important to make linear compressors more efficient and compatible auxiliary for big systems like refrigerators, air conditioners, etc. A novel piston stroke estimation method has been proposed in this article to obtain the sensor less control the LOM. This method utilizes an improved third-order generalized integrator (TOGI) based novel sliding mode observer (SMO) for LOM piston stroke estimation. In addition to this, an absolute reaching law with a chosen sliding surface has been implemented to further reduce the effects of sliding chattering. The piston stroke signal suffers DC offsets and harmonics due to mismatched machine parameters, nonlinearities of the converter, and first-order integration of back-electromotive force (EMF). In some recent studies, the second-order generalized integrator (SOGI) has been used to reduce pure integral saturation problem, but it has limited attenuation ability against DC components and has considerable steady-state error. Therefore, in order to improve the accuracy of the estimated stroke signals, a new method has been proposed in this article, which can not only solve the integral saturation problem, but also reduce the steady-state error in the piston stroke estimation effectively. The simulation results prove the authenticity of the proposed method.