In this work we propose methods for object localization in 2D using beacons of low frequency quasi-static magnetic field. From a practical point of view, localization in 2D is sufficient for many applications, requiring much less calculations than in 3D, making it more robust and easier to implement in real-time low power applications. The low frequency magnetic field may penetrate foliage, soil, buildings, and many other types of media. This is an important advantage over traditional localization methods such as sonar or radar, where effective operation requires line-of-sight. Another advantage of the low frequency magnetic fields is that there is no direct influence by bad weather conditions and diurnal variations. Opposite to traditional electromagnetic methods, where operational range is usually more than a wavelength, low frequency induction approach results in a relatively limited localization range. Each beacon comprises a coil generating a magnetic field of a unique frequency in the ULF band. The generated magnetic fields are sensed by a search-coil magnetometer. The magnetometer readings are processed to estimate the magnitude and phase of the received beacons signals, which are used to localize the magnetometer. For a moving object, we propose to combine localization together with tracking algorithm using a data fusion approach. The proposed methods have been tested using numerous computer simulations, showing accurate localization results. A prototype was developed and used in field experiments, validating simulation results. The good accuracy together with a simple implementation makes the proposed methods attractive to many real-time low power field applications.