A Survey on Wireless Position Estimation <s> Time Difference of Arrival (TDOA) <s> A maximum likelihood (ML) estimator is developed for determining time delay between signals received at two spatially separated sensors in the presence of uncorrelated noise. This ML estimator can be realized as a pair of receiver prefilters followed by a cross correlator. The time argument at which the correlator achieves a maximum is the delay estimate. The ML estimator is compared with several other proposed processors of similar form. Under certain conditions the ML estimator is shown to be identical to one proposed by Hannan and Thomson [10] and MacDonald and Schultheiss [21]. Qualitatively, the role of the prefilters is to accentuate the signal passed to the correlator at frequencies for which the signal-to-noise (S/N) ratio is highest and, simultaneously, to suppress the noise power. The same type of prefiltering is provided by the generalized Eckart filter, which maximizes the S/N ratio of the correlator output. For low S/N ratio, the ML estimator is shown to be equivalent to Eckart prefiltering. <s> BIB001 </s> A Survey on Wireless Position Estimation <s> Time Difference of Arrival (TDOA) <s> The authors present an exact solution to the problem of maximum-likelihood time-delay estimation over arbitrary observation time T. That is, the standard assumption T>> tau /sub c/+d/sub max/ made in the derivation of the asymptotic maximum-likelihood (AML) estimator, where t/sub c/ is the correlation time of the various processes involved and d/sub max/ the maximum permissible delay, is relaxed. The exact maximum-likelihood (EML) processor is shown to consist of a special finite-time beamformer, followed by a scalar postprocessor based on the eigenvalues and eigenfunctions of a certain integral equation. The solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities (PSD). The performance of EML and AML are compared by means of computer simulations for a first-order low-pass PSD. The results show that EML can lead to a significant improvement in performances (bias, variance, large errors) when the condition T>> tau /sub c/+d/sub max/ is not satisfied. > <s> BIB002 </s> A Survey on Wireless Position Estimation <s> Time Difference of Arrival (TDOA) <s> The expectation-maximization (EM) algorithm is presented as a means of performing passive, high-resolution, intersensor time difference of arrival (TDOA) estimation in the presence of correlated multipath interference and noise. The approach presented here assumes that the signal can be represented as a bandlimited complex Gaussian process, but is otherwise unknown. Within the EM algorithm, a conditional mean estimate of the transmitted signal spectrum is generated and used to determine the direct-path and multipath delays and complex amplitudes associated with each received signal. The delay/amplitude estimator takes the form of nonlinear least-squares optimization problem. The structure of the algorithm is described and its performance demonstrated through simulation. <s> BIB003 </s> A Survey on Wireless Position Estimation <s> Time Difference of Arrival (TDOA) <s> Subscriber radio location techniques are investigated for code-division multiple-access (CDMA) cellular networks. Two methods are considered for radio location: measured times of arrival (ToA) and angles of arrival (AoA). The ToA measurements are obtained from the code tracking loop in the CDMA receiver, and the AoA measurements at a base station (BS) are assumed to be made with an antenna array. The performance of the two methods is evaluated for both ranging and two-dimensional (2-D) location, while varying the propagation conditions and the number of BS's used for the location estimate. <s> BIB004 </s> A Survey on Wireless Position Estimation <s> Time Difference of Arrival (TDOA) <s> From the Publisher: ::: Wireless Location in CDMA Cellular Radio Systems investigates methods for wireless location in CDMA networks and analyzes their performances. Techniques for measuring location parameters (AoAs, ToAs, etc.) are presented along with algorithms for calculating position from those parameters. Several impairments to accurate location are covered and analyzed including multipath propagation, non-line-of-sight propagation, and multiple-access interference. Many of the topics in this book are also applicable to FDMA- and TDMA-based communication networks. <s> BIB005
In the absence of synchronization between the target node and the reference nodes, the TDOA estimation can be performed if there is synchronization among the reference nodes BIB005 . In this case, the difference between the arrival times of two signals traveling between the target node and the two reference nodes is estimated, which determines the position of the target node on a hyperbola, with foci at the two reference nodes, as shown in Figure 4 . One way to estimate TDOA is to first estimate TOA for each signal traveling between the target node and a reference node, and then to obtain the difference between the two estimates. Since the target node and the reference nodes are not synchronized, the TOA estimates include a timing offset, which is the same in all estimates as the reference nodes are synchronized, in addition to the time of flight. Therefore, the TDOA estimate can be obtained as whereτ i , for i = 1, 2, denotes the TOA estimate for the signal traveling between the target node and the ith reference node. For the TDOA estimates obtained as in (8), the accuracy limits can be deduced from the CRLB expression in Section 2.3. Namely, it is concluded that the accuracy of TDOA estimation increases as effective bandwidth and/or SNR increases. Another way to implement TDOA estimation is to perform cross-correlations of the two signals traveling between the target node and the reference nodes, and to calculate the delay corresponding to the largest cross-correlation 8 Sinan Gezici value. The cross-correlation function is given by BIB004  where r i (t), for i = 1, 2, represents the signal traveling between the target node and the ith reference node, and T is the observation interval. From (9), the TDOA estimate is calculated as Although the cross-correlation based TDOA estimation in (10) works well for single path channels and white noise models, its performance can degrade considerably over multipath channels and/or colored noise. In order to improve the performance of the cross-correlation scheme in (9) and (10), generalized cross-correlation (GCC) techniques are proposed BIB001 , BIB002 , BIB003 . In GCC based TDOA estimation, filtered versions of the signals are cross-correlated, which corresponds to shaping the cross-power spectral density (cross-PSD) of the transmitted signals, in order to provide robustness against colored noise  .