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While self-mixing interferometry(SMI) has proven to be suitable for displacement measurement and other sensing applications, its characteristic self-mixing signal shape is strongly governed by the non-linear phase equation which forms relation between perturbed and unperturbed phase of self-mixing laser. Therefore, while it is desirable for robust estimation of displacement of moving target, the algorithms to achieve this must have an objective strategy that can be achieved by understanding the characteristic of extracting knowledge of the perturbed phase from the unperturbed phase. Therefore, it has been proved and shown that such a strategy must not involve sole methods where the perturbed phase is a continuous function of the unperturbed phase (e.g: Taylor series or fixed-point methods) or through successive displacements (e.g: variations of Gauss-Seidel method). The subset of this strategy is to perform spectral filtering of the perturbed phase followed by perturbative or homotopic deformation. A less computationally expensive approach of this strategy is adopted to achieve displacement with a mean error of 62.2nm covering all feedback regimes, when the coupling factor 'C' is unknown.