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We consider positioning in the scenario where only two reliable range estimates, and few less reliable power observations are available. Such situations are difficult to handle with numerical maximum likelihood methods which require a very accurate initialization to avoid being stuck into local maxima. We propose to first estimate the support region of the two peaks of the likelihood function using a set membership method, and then decide between the two regions using a rule based on the less reliable observations. Monte Carlo simulations show that the performance of the proposed method in terms of outlier rate and root mean squared error approaches that of maximum likelihood when only few additional power observations are available.