This paper presents a novel precision position-sensing methodology using two-axis Hall-effect sensors, where the absolute multi-degree-of-freedom (DOF) positioning of a device above any magnet matrix is possible. Magnet matrices have a periodic magnetic field about each of its orthogonal axes, which can be modeled using Fourier series. This position-sensing methodology was implemented on a Halbach-magnet-matrix-based magnetic-levitation (maglev) stage. It enables unrestricted translational and rotational ranges in planar motions with a potential 6-DOF motion-measuring capability. A Gaussian least-squares differential-correction (GLSDC) algorithm was developed and implemented to estimate the maglev stages position and orientation in three planar DOFs from raw Hall-effect-sensor measurements. Experimental results show its position resolution of better than 10m in translation and 100rad in rotation. The maximum rotational range achieved so far is 16deg, a factor of 100 improvement of a typical laser interferometers rotational range of a few milliradians. Classical lead-lag compensators were designed and implemented on a digital signal processor (DSP) to close the control loop at a sampling frequency of 800Hz for the three planar DOFs using the GLSDC outputs. Calibration was performed by comparing the Hall-effect sensors outputs against the laser-interferometer readings, which improved the positioning accuracy by correcting the GLSDC error. The experimental results exhibit better than a micrometer repeatability. This multi-DOF sensing mechanism is an excellent cost-effective solution to planar micro-positioning applications with unrestricted three-axis travel ranges.