A method for determining a position of a stylus (141, 250), comprising: generating one or more drive signals, each of the one or more drive signals being associated with a particular transmission coil (321-328, 422) of one or more transmission coils (321-328, 422), the one or more transmission coils (321-328, 422) being associated with a display device; generating one or more magnetic fields, each of the one or more magnetic fields being associated with a particular drive signal of the one or more drive signals; sensing one or more voltages, each of the one or more voltages being associated with a particular receiving coil (391-393, 424) of one or more receiving coils (391-393, 424), the one or more voltages being generated by the one or more magnetic fields, the one or more receiving coils (391-393, 424) being associated with the stylus (141, 250); transmitting sensing information based on the one or more voltages from the stylus (141, 250) to the display device, the sensing information including a set of field numbers that represent the sensed magnetic field strength from each of the one or more transmission coils (321-328, 422) to each of the one or more receiving coils (391-393, 424); and determining the position of the stylus (141, 250) within one of a plurality of predetermined regions located above a surface of the display device, the determining the position of the stylus (141, 250) including determining a first region of the plurality of predetermined regions based on the received sensing information, the first region being associated with one or more polynomials describing magnetic fields associated with each of the one or more transmission coils (321-328, 422), the determining the position of the stylus (141, 250) further including determining one or more neighboring regions adjacent to the first region and determining an interpolated position of the stylus (141, 250) based on magnetic field strength data associated with the one or more neighboring regions and the first region. generating one or more drive signals, each of the one or more drive signals being associated with a particular transmission coil (321-328, 422) of one or more transmission coils (321-328, 422), the one or more transmission coils (321-328, 422) being associated with a display device; generating one or more magnetic fields, each of the one or more magnetic fields being associated with a particular drive signal of the one or more drive signals; sensing one or more voltages, each of the one or more voltages being associated with a particular receiving coil (391-393, 424) of one or more receiving coils (391-393, 424), the one or more voltages being generated by the one or more magnetic fields, the one or more receiving coils (391-393, 424) being associated with the stylus (141, 250); transmitting sensing information based on the one or more voltages from the stylus (141, 250) to the display device, the sensing information including a set of field numbers that represent the sensed magnetic field strength from each of the one or more transmission coils (321-328, 422) to each of the one or more receiving coils (391-393, 424); and determining the position of the stylus (141, 250) within one of a plurality of predetermined regions located above a surface of the display device, the determining the position of the stylus (141, 250) including determining a first region of the plurality of predetermined regions based on the received sensing information, the first region being associated with one or more polynomials describing magnetic fields associated with each of the one or more transmission coils (321-328, 422), the determining the position of the stylus (141, 250) further including determining one or more neighboring regions adjacent to the first region and determining an interpolated position of the stylus (141, 250) based on magnetic field strength data associated with the one or more neighboring regions and the first region.