Single Molecule Localization Microscopy (SMLM) has enabled researchers to breakthrough the diffraction limit and obtain nanometer resolution images of macromolecular structures. But due to the time involved in obtaining ample data for proper image, the technique is venerable to many problem including fluctuations due to thermal gradients from surrounding which cause the frames to drift. SMLM relies on the stochastic blinking of fluorophore probes. Thus drift in SMLM could be explicitly modelled as a stochastic state space process. These models could be used to perform drift correction. Two state space models are proposed relying on different properties of SMLM. The first model utilizes shifting of underlying image structure. The state space model for this property is constructed using shift matrices. A system identification method along with image reconstruction method is also derived to form the drift compensation algorithm for this model. This algorithm is further developed to provide adequate performance within low computational time. The second model relies on the position of emitter molecules and utilizes linking or pairing of fluorophore probes in succeeding frame to obtain the output data. Drift compensation algorithm for this model is constructed using Prediction Error Methods (PEM) and Kalman (RTS) smoother. The drift correction algorithm for these two models are also bench-marked with existing algorithms to obtain insight into performance. Furthermore, other properties of these algorithms are explored using simulation dataset and recommendation are provided for improvement and further research.