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Phase-based 3D localization of radio-frequency (RF) markers has high sensitivity and accuracy. However, phase measurements suffer from oscillator phase noises, wavelength ambiguities, and multi-path interferences. Additionally in the near field, antenna detuning and medium inhomogeneity render the phase-distance relation nonlinear and non-monotonic and bring forth extra ambiguities, especially with obstructed line-of-sight (LoS). In this work, we present a novel precision localization framework which leverages spatially diverse redundant channels to resolve ambiguities without relying on broad bandwidth. First, measured differential phases were used to accurately retrieve differential distances from spline-fitted phase-distance curves. Then, distances from multiple channels were combined to generate 3D location estimates. Finally, location ambiguities were removed by taking different channel subsets to identify one unambiguous location using spatial clustering. An experimental multiple-input multiple-output (MIMO) network was implemented by a Universal Software Radio Peripheral (USRP) platform and harmonic RF markers to demonstrate millimeter-level 3D localization at sub-1GHz carrier frequencies within heavy multi-path ambient, simulating the condition inside building structures.