Finding the infection sources in a network when we only know the network topology and infected nodes, but not the rates of infection, is a challenging combinatorial problem, and it is even more difficult in practice where the underlying infection spreading model is usually unknown a priori. In this paper, we are interested in finding a source estimator that is applicable to various spreading models, including the susceptible-infected (SI), susceptible-infected-recovered (SIR), susceptible-infected-recovered-infected (SIRI), and susceptible- infected-susceptible (SIS) models. We show that under the SI, SIR, and SIRI spreading models and with mild technical assumptions, the Jordan center is the infection source associated with the most likely infection path in a tree network with a single infection source. This conclusion applies for a wide range of spreading parameters, while it holds for regular trees under the SIS model with homogeneous infection and recovery rates. Since the Jordan center does not depend on the infection, recovery, and reinfection rates, it can be regarded as a universal source estimator. We also consider the case where there are k 1 infection sources, generalize the Jordan center definition to a k-Jordan center set, and show that this is an optimal infection source set estimator in a tree network for the SI model. Simulation results on various general synthetic networks and real-world networks suggest that Jordan center-based estimators consistently outperform the betweenness, closeness, distance, degree, eigenvector, and pagerank centrality-based heuristics, even if the network is not a tree.

We consider the problem of tracking a receiver using signals-of-opportunity (SOOPs) from beacons and a reference anchor with known positions and velocities, and where all devices have asynchronous local clocks or oscillators. We model the clock drift at individual devices by a two-state model with unknown clock offset and clock skew and analyze the biases introduced by clock asynchronism in the received signals. Based on an extended Kalman filter, we propose a sequential estimator to jointly track the receiver location, velocity, and its clock parameters using altitude information together with time-difference-of-arrival and frequency-difference-of-arrival measurements obtained from the SOOP samples collected by the receiver and a reference anchor. The receiver was implemented on a software-defined radio testbed, and field experiments are carried out using Iridium satellites as the SOOP beacons. The experiment and simulation results demonstrate that our measurement model has a good fit, and our proposed estimator can successfully track both the receiver location, velocity, and the relative clock offset and skew with respect to the reference anchor with good accuracy.

The goal of a rumor source node in a social network is to spread its rumor to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have accepted the rumor (which are called infected nodes). We model the rumor spreading and source identification problem as a strategic game, where the rumor source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that probes every node within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the rumor source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which the Nash equilibria of the strategic game exist. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.

We propose a novel distributed expectation maximization (EM) method for non-cooperative RF target localization using a wireless sensor network. We consider the scenario where few or no sensors receive line-of-sight signals from the target. In the case of non-line-of-sight signals, the signal path consists of a single reflection between the transmitter and receiver. Each sensor is able to measure the time difference of arrival of the target's signal with respect to a reference sensor, as well as the angle of arrival of the target's signal. We derive a distributed EM algorithm where each node makes use of its local information to compute summary statistics, and then shares these statistics with its neighbors to improve its estimate of the target localization. We show that our distributed algorithm converges, and simulation results suggest that our method achieves an accuracy close to the centralized EM algorithm. We apply the distributed EM algorithm to a set of experimental measurements with a network of four nodes, which confirm that the algorithm is able to localize a RF target in a realistic non-line-of-sight scenario.

We consider the problem of localizing two devices using signals of opportunity from beacons with known positions. Beacons and devices have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cramér-Rao lower bound (CRLB) of device position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival (DTDOA) and frequency-difference-of-arrival (FDOA) that mitigates the effects of clock asynchronism to estimate the device positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations.

We consider the problem of localizing two sensors using signals-of-opportunity from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We analyze the biases introduced by clock asynchronism in the received signals, and derive the Cramér-Rao lower bound (CRLB) for sensor position and velocity estimation errors. We quantify the error caused by beacon clock asynchronism. We also propose an algorithm that mitigates the effects of clock asynchronism to estimate the sensor positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when sensor clock skews have small standard deviations.

We consider the problem of sensor localization in wireless networks in a multipath environment. We propose a distributed and cooperative algorithm based on belief propagation, which allows sensors to cooperatively self-localize with respect to a single anchor node in the network, using range and direction of arrival measurements. In the algorithm, neighboring sensors exchange limited information to update their local mean location estimates and covariance matrices. We show that the covariance matrix for each sensor converges for connected networks, and its mean location estimate converges if all scatters are either parallel or orthogonal to each other. Furthermore, these estimates are asymptotically unbiased. Simulations show that cooperation amongst neighboring nodes significantly improves the localization accuracy.

We consider the problem of localizing two sensors using their TDOA measurements of signals from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We analyze the effect of the clock skews and offsets on the TDOA estimations, and introduce a novel approach using the difference in TDOA (DTDOA) measurements to mitigate the effects of clock skews and offsets on the location estimates. We propose an algorithm for location and velocity estimation based on DTDOA, and perform simulations to verify the robustness of our algorithm to asynchronous local clocks in the beacons and sensors.

Finding locations of the sensor nodes in Wireless Sensor Network has been an active research area in recent years. One important category of approaches uses distance measurements between anchors and sensors to localize the unknown node. However, most approaches assume that the anchor positions are perfectly known, while in practice the anchor positions may not be accurate due to estimation errors as well as observation errors. In this paper, we study the localization of wireless sensor node with erroneous anchors, and propose an EM estimator which iteratively refines the anchor positions and estimates the sensor location. Simulation results shows that the EM estimator converges in a few iterations and outperforms the existing robust least squares algorithm.

In this paper, the problem of clock synchronization for Wireless Sensor Network (WSN) under exponential delay is analyzed based on two-way message exchange mechanism. The Maximum Likelihood Estimator (MLE) for joint estimation of the clock offset and clock skew is derived, and an approximate Cramer-Rao Lower Bound (CRLB) is also developed. Simulation results verify that the proposed estimator gives improved performance compared to an existing algorithm.

In this paper, the problem of clock synchronization is analyzed based on the two-way message exchange mechanism. In order to estimate the clock offset and the clock skew with unknown fixed delay, the maximum likelihood estimator (MLE) and a low-complexity estimator are proposed. Furthermore, their corresponding performance limits and complexities are analyzed. It is found that the MLE achieves the best performance with the price of high complexity, while the newly proposed estimator achieves the same performance as the MLE with low complexity.