Joint localization and time synchronization in wireless sensor networks with anchor uncertainties

Although localization and synchronization share many aspects in common, they are traditionally treated separately. In this paper, we present a unified framework to jointly solve these two problems at the same time. The joint approach is attractive because it can solve both localization and synchronization using the same set of message exchanges. This is extremely important for energy saving, especially for the energy constrained wireless sensor networks. Furthermore, since the accuracy of localization and synchronization is very sensitive to the accuracy of anchor locations and timings, the joint localization and synchronization problem with inaccurate anchor is considered in this paper. A novel generalized total least squares (GTLS) based method is proposed and the Cramer-Rao lower bound (CRLB) for the joint localization and time synchronization is derived. Simulation results show that the mean square error performances of the proposed estimator can attain the CRLB. © 2009 IEEE.published_or_final_versionThe IEEE Conference on Wireless Communications and Networking (WCNC 2009), Budapest, Hungary, 5-8 April 2009. In Proceedings of IEEE WCNC, 2009, p. 1-

Low-complexity maximum-likelihood estimator for clock synchronization of wireless sensor nodes under exponential delays

In this paper, the clock synchronization for wireless sensor networks in the presence of unknown exponential delay is investigated under the two-way message exchange mechanism. The maximum-likelihood estimator for joint estimation of clock offset, clock skew and fixed delay is first cast into a linear programming problem. Based on novel geometric analyses of the feasible domain, a low-complexity maximum likelihood estimator is then proposed. Complexities of the proposed estimators and existing algorithms are compared analytically and numerically. Simulation results further demonstrate that our proposed algorithms have advantages in terms of both performance and computational complexities. © 2011 IEEE.published_or_final_versio

Distributed clock synchronization for wireless sensor networks using belief propagation

In this paper, we study the global clock synchronization problem for wireless sensor networks. Based on belief propagation, we propose a fully distributed algorithm which has low overhead and can achieve scalable synchronization. It is also shown analytically that the proposed algorithm always converges for strongly connected networks. Simulation results show that the proposed algorithm achieves better accuracy than consensus algorithms. Furthermore, the belief obtained at each sensor provides an accurate prediction on the algorithm's performance in terms of MSE. © 2011 IEEE.published_or_final_versio

Symbol timing recovery for generalized minimum shift keying modulations in software radio receiver

A new symbol timing estimator for generalized MSK signals is proposed. It is based on the squaring algorithm and has a feedforward structure. The proposed timing estimator is fully-digital and is suitable for implementation in software radios. The performance in AWGN channel is compared with the Modified Cramer-Rao bound and that of the ML algorithm. The proposed timing estimator is found to have a performance close to that of the ML algorithm, but with a lower implementation complexity.published_or_final_versio

Determining the convergence of variance in Gaussian belief propagation via semi-definite programming

In order to compute the marginal distribution from a high dimensional distribution with loopy Gaussian belief propagation (BP), it is important to determine whether Gaussian BP would converge. In general, the convergence condition for Gaussian BP variance and mean are not necessarily the same, and this paper focuses on the convergence condition of Gaussian BP variance. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence condition of Gaussian BP variance is derived, with the converged variance proved to be independent of the initialization as long as it is greater or equal to zero. It is further proved that the convergence condition can be verified efficiently by solving a semi-definite programming (SDP) optimization problem. Numerical examples are presented to corroborate the established theories.published_or_final_versio

Non-data-aided ML symbol timing estimation in MIMO correlated fading channels

In this paper, the non-data-aided (NDA) maximum likelihood (ML) symbol timing estimator in MIMO correlated channel is derived. It is found that the extended square nonlinearity estimator in [9] is just a special case of the proposed algorithm. Furthermore, the conditional Cramer-Rao bound (CCRB) and the modified Cramer-Rao bound (MCRB) are also established. Simulation results under different operating conditions (e.g., number of antennas and correlation between antennas) are given to assess the performances of the NDA ML estimator and it is found that the mean square errors (MSE)s of the NDA ML estimator i) are close to the CCRBs, but not the MCRBs; ii) are approximately independent of the number of transmit antennas; iii) are inversely proportional to the number of receive antennas and iv) correlation between antennas has little effect on the SE performance.published_or_final_versio

Distributed Clock Skew and Offset Estimation in Wireless Sensor Networks: Asynchronous Algorithm and Convergence Analysis

In this paper, we propose a fully distributed algorithm for joint clock skew and offs et estimation in wireless sensor networks based on belief propagation. In the proposed algorithm, each node can estimate its clock skew and offset in a completely distributed and asynchronous way: some nodes may update their estimates more frequently than others using outdated message from neighboring nodes. In addition, the proposed algorithm is robust to random packet loss. Such algorithm does not require any centralized information processing or coordination, and is scalable with network size. The proposed algorithm represents a unified framework that encompasses both classes of synchronous and asynchronous algorithms for network-wide clock synchronization. It is shown analytically that the proposed asynchronous algorithm converges to the optimal estimates with estimation mean-square-error at each node approaching the centralized Cram ́er-Rao bound under any network topology. Simulation results further show that the convergence speed is faster than that corresponding to a synchronous algorithm.published_or_final_versio

Convergence Analysis of the Variance in Gaussian Belief Propagation

It is known that Gaussian belief propagation (BP) is a low-complexity algorithm for (approximately) computing the marginal distribution of a high dimensional Gaussian distribu- tion. However, in loopy factor graph, it is important to determine whether Gaussian BP converges. In general, the convergence conditions for Gaussian BP variances and means are not nec- essarily the same, and this paper focuses on the convergence condition of Gaussian BP variances. In particular, by describing the message-passing process of Gaussian BP as a set of updating functions, the necessary and sufficient convergence conditions of Gaussian BP variances are derived under both synchronous and asynchronous schedulings, with the converged variances proved to be independent of the initialization as long as it is chosen from the proposed set. The necessary and sufficient convergence condition is further expressed in the form of a semi-definite programming (SDP) optimization problem, thus can be verified more efficiently compared to the existing convergence condition based on compu- tation tree. The relationship between the proposed convergence condition and the existing one based on computation tree is also established analytically. Numerical examples are presented to corroborate the established theories.published_or_final_versio

On Convergence Conditions of Gaussian Belief Propagation

In order to compute the marginal probability density function (PDF) with Gaussian belief propagation (BP), it is impor- tant to know whether it will converge in advance. By describing the message-passing process of Gaussian BP on the pairwise factor graph as a set of updating functions, the necessary and sufficient convergence condition of beliefs in synchronous Gaussian BP is first derived under a newly proposed initialization set. The pro- posed initialization set is proved to be largest among all currently known sets. Then, the necessary and sufficient convergence con- dition of beliefs in damped Gaussian BP is developed, with the allowable range of damping factor explicitly established. The re- sults theoretically confirm the extensively reported conjecture that damping is helpful to improve the convergence of Gaussian BP. Under totally asynchronous scheduling, a sufficient convergence condition of beliefs is also derived for the same proposed initializa- tion set. Relationships between the proposed convergence condi- tions and existing ones are established analytically. At last, numer- ical examples are presented to corroborate the established theories.published_or_final_versio

Tight probablisitic MSE constrained multiuser MISO transceiver design under channel uncertainty

A novel optimization method is proposed to solve the probabilistic mean square error (MSE) constrained multiuser multiple-input single-output (MU-MISO) transceiver design problem. Since the probabilistic MSE constraints cannot be expressed in closed-form under Gaussian channel uncertainty, existing probabilistic transceiver design methods rely on probability inequality approximations, resulting in conservative MSE outage realizations. In this paper, based on local structure of the feasible set in the probabilistic MSE constrained transceiver design problem, a set squeezing procedure is proposed to realize tight MSE outage control. Simulation results show that the MSE outage can be realized tightly, which results in significantly reduced transmit power compared to the existing inequality based probabilistic transceiver design.published_or_final_versio