A method for operating a linear compressor is provided. The method includes estimating an acceleration of the motor of the linear compressor using at least a robust integral of the sign of the error feedback. A position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point is also determined based at least in part on a measured current to the motor of the linear compressor and an estimated acceleration of the motor. The position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point is calculated based at least in part on the position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point and a stroke length of the motor of the linear compressor.