A magnetoresistive sensing device is provided. A first sensed magnetic-field component in parallel with the x-axis and a second sensed magnetic-field component in parallel with the y-axis of an external magnetic field forming a first inclination angle with the x-axis and a second inclination angle with the y-axis are determined. A virtual plane is defined so as to render a magnetic-field component perpendicular to the virtual plane of the external magnetic field is essentially zero. The first inclination angle and the second inclination angle are adjusted with reference to the virtual plane. An x-axis magnetic-field component in parallel with the x-axis, a y-axis magnetic-field component in parallel with the y-axis and a z-axis magnetic-field component in parallel with the z-axis of the external magnetic field are estimated according to the adjusted first inclination angle, the adjusted second inclination angle, the first sensed magnetic-field component and the second sensed magnetic-field component.