Advanced Wireless Local Positioning via Compressed Sensing

Wireless local positioning systems are based on measurements of signal time of flights and/or bearing angles to determine the position of an active transmitter in 3-D space. Traditional time-of-flight and angle measurements with such positioning systems require many data samples at high rates to fulfill the Nyquist criterion. Moreover, in multipath channels the ability of classical signal processing methods to resolve the delay and bearing vectors of the multiple transmission paths is strictly limited by the radio frequency bandwidth and aperture size. In this paper, we show that the wireless channel is ideally suited for the application of compressed sensing. We can thus reduce the number of samples without major losses in localization performance, or we can improve the resolution. After introducing a general model of a localization task with multipath propagation, and following the definition of key parameters of existing systems, we review the necessary data processing stages with compressed sensing and verify its excellent applicability. Finally, measurements are presented to verify the theoretical predictions experimentally.