Magnitude - Delay Least Mean Squares Equalization for Accurate Estimation of Time of Arrival

Multipath signals are known to be the main source of error in localization procedures; they are generated by the reflection from different objects through non-line of sight (NLOS) paths and overlap with the line of sight (LOS) signal. The time delay and strength of the LOS signal are critical parameters for ranging which are both affected by the overlapped NLOS components. The situation is worse when the frequency bandwidth (BW) is limited that inherently leads to decrease in the resolution of system obeying the Fourier limit (
$3^\ast 10^{\wedge }8$
/BW). Leveraging the classical super-resolution techniques such as Maximum Likelihood (ML), MUSIC and compressive sensing (CS), the Fourier limit can be overcome but at the cost of having higher complexity and more computational time. In this paper, the Magnitude-Delay Least Mean Squares Equalization (MD-LMSE) is proposed uniquely for super-resolution time delay estimation. The proposed estimation algorithm is based on the recursive time domain Least Mean Squares (LMS) minimization, which is established through an equalizer structure. The MD-LMSE approach provides high accuracy, super resolution and low computational time that makes it suitable for real time implementation. The proposed MDLMSE algorithms is used through an experimental setup consisting one LOS signal and one NLOS signal to improve the range resolution of a narrowband system 95% with low error of 6.66%.The obtained results verify that the proposed approach is a good candidate for accurate ranging, especially in low frequency applications (with limited bandwidth) by enabling higher penetration depths.