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This paper addresses the problem of position determination based on coherence of phases of a set of received sinusoidal acoustic waves. It describes an easily implementable test bed to assess the feasibility of carrier-phase-based differential ranging techiques for precise positioning applications in indoor environments. Futhermore, the use of a discrete set of frequencies fits the scope of using signals of opportunity, such as broadcast stations in RF. Acoustic waves are, themselves, relevant for positioning in specific environments, such as underwater. The main subject of the paper is the formulation and solution of the position determination goal as an -dimensional integer optimization problem. This -dimensional problem can be expressed as a weighted least-squares minimization problem with real and integer variables. The associated integer least-squares problem can be solved efficiently in practice as shown. This work is illustrated with some experimental data and a critical analysis of the obtained results.