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Particle filters have been widely used in positioning problems, to post-process the noisy location sensor measurements. In this paper, instead of the commonly used Prior Importance Function for particle filtering, we have formulated and applied the Optimal Importance Function. Unlike other importance functions, the Optimal Importance Function minimizes the variance of particle weights and thus resolves the degeneracy problem of particle filters. In this work, we have derived a closed form formula for the Optimal Importance Function using map-independent random walk velocity motion model and a GMM sensor error. Due to the generality of the proposed method, it can be used for a wide range of moving objects in different environments. Simulation results support the validity of modeling assumptions and the advantage of applying an Optimal Importance Function in indoor localization and positioning.