This application is directed to a
local positioning system having a plurality of wire coils. Each wire coil includes one or more respective turns of wire that have a respective shape and a respective size and are arranged substantially in parallel with a respective wire plane. Each wire coil is configured to be electrically driven by a respective synchronous
electric current carrying a respective
train of pseudo-random waveforms according to a predefined bandwidth. For each wire coil, the respective
train of pseudo-random waveforms includes a first number of waveform periods and is orthogonal to each other
train of pseudo-random waveforms of the wire coils. In some embodiments, a
receiver system is coupled to, and measures, the
magnetic field created by the wire coils during each waveform period. The location of the
receiver system is determined based on measured magnetic data vectors of the
magnetic field.