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This work is focused on the study of the maximum likelihood (ML) mobile position estimator when the quality of the available measurements is not a-priori known. Based on a statistical analysis, a polynomial time-evolution model is used to simplify the ML function, finding a closed-form approximation of the ML estimator. Numerical simulations show that the proposed algorithm, with a low implementation complexity, attains the Cramer Rao lower bound (CRB) for all reasonable observed window lengths and for any arbitrary distribution of the measurement variances. Although the mathematical development of this closed-form position estimator is quite dense, the obtained algorithm has a very low complexity implementation.