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A hyperbolic positioning method with antenna arrays consisting of proximately-located antennas and a multi-channel pseudolite is proposed in order to overcome the problems of indoor positioning with conventional pseudolites (ground-based GPS transmitters). A two-dimensional positioning experiment using actual devices is conducted. The experimental result shows that the positioning accuracy varies centimeter- to meter-level according to the geometric relation between the pseudolite antennas and the receiver. It also shows that the bias error of the carrier-phase difference observables is more serious than their random error. Based on the size of the bias error of carrier-phase difference that is inverse-calculated from the experimental result, three-dimensional positioning performance is evaluated by computer simulation. In addition, in the three-dimensional positioning scenario, an initial value convergence analysis of the non-linear least squares is conducted. Its result shows that initial values that can converge to a right position exist at least under the proposed antenna setup. The simulated values and evaluation methods introduced in this work can be applied to various antenna setups; therefore, by using them, positioning performance can be predicted in advance of installing an actual system.