In this article, we propose a new geomagnetic localization scheme, named ILoA, to address error accumulation and global localization. Global localization is a fundamental problem that determines the initial pose under global uncertainty. Moreover, error accumulation using inertial navigation systems (INS) impacts robustness and drift error, making it challenging to achieve reliable estimation. The magnetic field in indoor space generates a unique signature/anomaly, which can be used as a local feature. Earth's magnetic field can be easily influenced by ferromagnetic material from the indoor environment due to its weak intensity. The magnetic field vector measured by a magnetometer depends on the orientation of the sensor, which we term a direction variant. We devise a novel approach to identify location and heading through the direction-variant augmented vector. Since a magnetic field vector under varying poses can produce many different vectors, the geomagnetic map is trained with the transformation. We present experiments in two testbeds, covering open space, showing that the proposed method using the magnetic field vector is efficient for global localization and accuracy compared with a state-of-the-art approach.