Ziv-Zakai Time Delay Estimation Bound for Ultra-Wideband Signals

Abstract-Sensor positioning is an important task of location-aware wireless sensor networks. In most sensor positioning systems, sensors and beacons need to emit ranging signals to each other. Sensor ranging energy should be low to prolong system lifetime, but sufficiently high to fulfill prescribed accuracy requirements. This motivates us to investigate ranging energy optimization problems. We address ranging energy optimization for an unsynchronized positioning system, which features robust sensor positioning (RSP) in the sense that a specific accuracy requirement is fulfilled within a prescribed service area. We assume a line-of-sight (LOS) channel exists between the sensor and each beacon. The positioning is implemented by time-of-arrival (TOA) based two-way ranging between a sensor and beacons, followed by a location estimation at a central processing unit. To establish a dependency between positioning accuracy and ranging energy, we assume the adopted TOA and location estimators are unbiased and attain the associated Cramér-Rao bound. The accuracy requirement has the same form as the one defined by the Federal Communication Commission (FCC), and we present two constraints with linear-matrix-inequality form for the RSP. Ranging energy optimization problems, as well as a practical algorithm based on semidefinite programming are proposed. The effectiveness of the algorithm is illustrated by numerical experiments.Index Terms-Cramér-Rao bound, localization, semidefinite programming, wireless sensor networks.

Section: Commentsmentioning

confidence: 99%

Ranging Energy Optimization for Robust Sensor Positioning Based on Semidefinite Programming

Wang

Leus

Huang

2009

“…To evaluate the accurateness of in (31) and in (50), we consider the pulse in (21) with GHz, ns, and dB. In Fig.…”

Section: Asmentioning

confidence: 99%

“…ONLINEAR estimation of deterministic parameters suffers from the threshold effect [2]- [11]. This effect means that for a signal-to-noise ratio (SNR) above a given threshold, estimation can achieve the Cramer-Rao lower bound (CRLB), whereas for SNRs lower than that threshold, estimation deteriorates drastically until the estimate becomes uniformly distributed in the a priori domain of the unknown parameter.…”

mentioning

confidence: 99%

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Mallat

Gezici

Dardari

et al. 2014

Abstract-In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramér-Rao lower bound at low and medium signal-to-noise ratios (SNRs) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accuracy of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.Index Terms-Nonlinear estimation, threshold and ambiguity phenomena, maximum likelihood estimator, mean-squared error, upper and lowers bounds, time-of-arrival.

“…In Section V, the a priori, begin-ambiguity and end-ambiguity thresholds are computed numerically using the MSEA in (6). The asymptotic threshold is computed using and the ALBs in (8) and in (9).…”

Section: A Numerical Computationmentioning

confidence: 99%

“…N ONLINEAR deterministic parameter estimation is subject to the threshold effect [2]- [9]. Due to this effect the signal-to-noise ratio (SNR) axis can be split into three regions (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Statistics of the MLE and Approximate Upper and Lower Bounds–Part II: Threshold Computation and Optimal Pulse Design for TOA Estimation

Mallat¹,

Gezici

Dardari

et al. 2014

Abstract-Threshold and ambiguity phenomena are studied in Part I of this paper where approximations for the mean-squared error (MSE) of the maximum-likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate upper and lower bounds are derived. In this part, we consider time-of-arrival estimation and we employ the MIE to derive closed-form expressions of the begin-ambiguity, end-ambiguity and asymptotic signal-to-noise ratio (SNR) thresholds with respect to some features of the transmitted signal. Both baseband and passband pulses are considered. We prove that the begin-ambiguity threshold depends only on the shape of the envelope of the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape of the ACR. We exploit the results on the begin-ambiguity and asymptotic thresholds to optimize, with respect to the available SNR, the pulse that achieves the minimum attainable MSE. The results of this paper are valid for various estimation problems.Index Terms-Maximum likelihood estimator, mean-squarederror, nonlinear estimation, optimal signal design, signal-to-noise ratio, threshold and ambiguity phenomena, time-of-arrival.