Performance of Time Delay Estimation and Range-Based Localization in Wireless Channels

by Ning Liu

Institution: University of California – Riverside
Department: Electrical Engineering
Year: 2010
Keywords: Electrical Engineering
Record ID: 1890161
Full text PDF: http://www.escholarship.org/uc/item/5b60509s


This thesis studies the performance of time delay estimation and the range-based localization schemes in wireless multipath channels. The research focuses on the localization schemes based on time-of-arrival and time-difference-of-arrival measurements. In multipath environments, time delay measurements suffer from the errors due to weak line-of-sight and rich non-line-of-sight (NLOS) signal paths. Instead of proposing range measurement algorithms, the thesis is devoted to develop theoretical performance lower bounds used as benchmarks to guide algorithm design and provide insight into the behavior of time delay estimation (TDE).The author develops Ziv-Zakai bounds (ZZBs) on Bayesian estimation of time delay, for known pulsed signal and frequency hopping waveforms that propagate through unknown random multipath channels following Rayleigh/Rician distribution, with a uniform prior on the delay. The bounds do not assume channel knowledge at receivers, providing more realistic and tighter performance limits than the average bound that assumes channel knowledge. The ZZBs also present good performance prediction for maximum a posteriori estimator, tracking a wide range of signal-to-noise ratios. The ZZB for wideband frequency hopping waveforms reveals the performance benefit for TDE from frequency diversity over frequency-selective fading channels. To evaluate the ZZB, the author proposes a moment generating function approach. The closed-form expressions for independent flat-fading channels enable easy study of the effects of SNR, frequency diversity, and channel statistics on TDE.The TDE errors lead to time-based ranging errors that in turn cause positioning errors and deteriorated localization performance. The thesis models the NLOS range measurement error as a deterministic or random positive bias, following widely adopted distributions for time delay over multipath channels. The error analysis for typical estimators shows that the MSE and bias performance is determined by the statistics of measurement bias and noise, the beacon array geometry and the estimator type.