Ruixin Niu

Fusion of decisions transmitted over Rayleigh fading channels in wireless sensor networks

In this paper, we revisit the problem of fusing decisions transmitted over fading channels in a wireless sensor network. Previous development relies on instantaneous channel state information (CSI). However, acquiring channel information may be too costly for resource constrained sensor networks. In this paper, we propose a new likelihood ratio (LR)-based fusion rule which requires only the knowledge of channel statistics instead of instantaneous CSI. Based on the assumption that all the sensors have the same detection performance and the same channel signal-to-noise ratio (SNR), we show that when the channel SNR is low, this fusion rule reduces to a statistic in the form of an equal gain combiner (EGC), which explains why EGC is a very good choice with low or medium SNR; at high-channel SNR, it is equivalent to the Chair-Varshney fusion rule. Performance evaluation shows that the new fusion rule exhibits only slight performance degradation compared with the optimal LR-based fusion rule using instantaneous CSI.

Target Location Estimation in Sensor Networks With Quantized Data

A signal intensity based maximum-likelihood (ML) target location estimator that uses quantized data is proposed for wireless sensor networks (WSNs). The signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target. The ML estimator and its corresponding Crameacuter-Rao lower bound (CRLB) are derived. Simulation results show that this estimator is much more accurate than the heuristic weighted average methods, and it can reach the CRLB even with a relatively small amount of data. In addition, the optimal design method for quantization thresholds, as well as two heuristic design methods, are presented. The heuristic design methods, which require minimum prior information about the system, prove to be very robust under various situations

Distributed detection and fusion in a large wireless sensor network of random size

For a wireless sensor network (WSN) with a random number of sensors, we propose a decision fusion rule that uses the total number of detections reported by local sensors as a statistic for hypothesis testing. We assume that the signal power attenuates as a function of the distance from the target, the number of sensors follows a Poisson distribution, and the locations of sensors follow a uniform distribution within the region of interest (ROI). Both analytical and simulation results for system-level detection performance are provided. This fusion rule can achieve a very good system-level detection performance even at very low signal-to-noise ratio (SNR), as long as the average number of sensors is sufficiently large. For all the different system parameters we have explored, the proposed fusion rule is equivalent to the optimal fusion rule, which requires much more prior information. The problem of designing an optimum local sensor-level threshold is investigated. For various system parameters, the optimal thresholds are found numerically by maximizing the deflection coefficient. Guidelines on selecting the optimal local sensor-level threshold are also provided.

Decision fusion in a wireless sensor network with a random number of sensors

For a wireless sensor network (WSN) with a random number of sensors, a decision fusion rule that uses the total number of detections reported by local sensors for hypothesis testing, is proposed. It is assumed that the number of sensors follows a Poisson distribution and the locations of sensors follow a uniform distribution within the region of interest (ROI). Both analytical and simulation results for the system level detection performance are provided. This fusion rule can achieve a very good system level detection performance even at very low signal to noise ratio (SNR), if the average number of sensors is sufficiently large. In addition, the problem of choosing an optimum local sensor level threshold is investigated for various system parameters.

Performance Analysis of Distributed Detection in a Random Sensor Field

For a wireless sensor network (WSN) with randomly deployed sensors, the performance of the counting rule, where the fusion center employs the total number of detections reported by local sensors for hypothesis testing, is investigated. It is assumed that the signal power decays as a function of the distance from the target. For both the case where the total number of sensors is known and the wireless channels are lossless, and the case where the number of sensors is random and the wireless channels have nonnegligible error rates, the exact system level probability of detection is derived analytically. Some approximation methods are also proposed to attain an accurate estimate of the probability of detection, while at the same time to reduce the computation load significantly. To obtain a better system level detection performance, the local sensor level decision threshold is determined such that it maximizes the system level deflection coefficient.

Channel Aware Target Localization With Quantized Data in Wireless Sensor Networks

In this paper, we propose a new maximum-likelihood (ML) target localization approach which uses quantized sensor data as well as wireless channel statistics in a wireless sensor network. The novelty of our approach comes from the fact that statistics of imperfect wireless channels between sensors and the fusion center along with some physical layer design parameters are incorporated in the localization algorithm. We call this approach ldquochannel-aware target localization.rdquo ML target location estimators are derived for different wireless channel models and receiver architectures. Furthermore, we derive the Cramer-Rao lower bounds (CRLBs) for our proposed channel-aware ML location estimators. Simulation results are presented to show that the performance of the channel-aware ML location estimators are quite close to their theoretical performance bounds even with relatively small number of sensors and their performance is superior compared to that of the channel-unaware ML estimators.

Energy Aware Iterative Source Localization for Wireless Sensor Networks

In this paper, the source localization problem in wireless sensor networks is investigated where the location of the source is estimated based on the quantized measurements received from sensors in the field. An energy efficient iterative source localization scheme is proposed where the algorithm begins with a coarse location estimate obtained from measurement data from a set of anchor sensors. Based on the available data at each iteration, the posterior probability density function (pdf) of the source location is approximated using an importance sampling based Monte Carlo method and this information is utilized to activate a number of non-anchor sensors. Two sensor selection metrics namely the mutual information and the posterior Cramér-Rao lower bound (PCRLB) are employed and their performance compared. Further, the approximate posterior pdf of the source location is used to compress the quantized data of each activated sensor using distributed data compression techniques. Simulation results show that with significantly less computation, the PCRLB based iterative sensor selection method achieves similar mean squared error (MSE) performance as compared to the state-of-the-art mutual information based sensor selection method. By selecting only the most informative sensors and compressing their data prior to transmission to the fusion center, the iterative source localization method reduces the communication requirements significantly and thereby results in energy savings.

Conditional Posterior Cramér–Rao Lower Bounds for Nonlinear Sequential Bayesian Estimation

The posterior CramerRao lower bound (PCRLB) for sequential Bayesian estimators, which was derived by Tichavsky in 1998, provides a performance bound for a general nonlinear filtering problem. However, it is an offline bound whose corresponding Fisher information matrix (FIM) is obtained by taking the expectation with respect to all the random variables, namely the measurements and the system states. As a result, this unconditional PCRLB is not well suited for adaptive resource management for dynamic systems. The new concept of conditional PCRLB is proposed and derived in this paper, which is dependent on the actual observation data up to the current time, and is implicitly dependent on the underlying system state. Therefore, it is adaptive to the particular realization of the underlying system state and provides a more accurate and effective online indication of the estimation performance than the unconditional PCRLB. Both the exact conditional PCRLB and its recursive evaluation approach including an approximation are derived. Further, a general sequential Monte Carlo solution is proposed to compute the conditional PCRLB recursively for nonlinear non-Gaussian sequential Bayesian estimation problems. The differences between this new bound and existing measurement dependent PCRLBs are investigated and discussed. Illustrative examples are also provided to show the performance of the proposed conditional PCRLB.

Tracking in Wireless Sensor Networks Using Particle Filtering: Physical Layer Considerations

In this paper, a new framework for target tracking in a wireless sensor network using particle filters is proposed. Under this framework, the imperfect nature of the wireless communication channels between sensors and the fusion center along with some physical layer design parameters of the network are incorporated in the tracking algorithm based on particle filters. We call this approach ldquochannel-aware particle filtering.rdquo Channel-aware particle filtering schemes are derived for different wireless channel models and receiver architectures. Furthermore, we derive the posterior Cramer-Rao lower bounds (PCRLBs) for our proposed channel-aware particle filters. Simulation results are presented to demonstrate that the tracking performance of the channel-aware particle filters can reach their theoretical performance bounds even with relatively small number of sensors and they have superior performance compared to channel-unaware particle filters.

Target Localization and Tracking in Noncoherent Multiple-Input Multiple-Output Radar Systems

For a noncoherent multiple-input multiple-output (MIMO) radar system, the maximum likelihood estimator (MLE) of the target location and velocity, as well as the corresponding Cramer-Rao lower bound (CRLB) matrix, is derived. MIMO radars potential in localization and tracking performance is demonstrated by adopting simple Gaussian pulse waveforms. Due to the short duration of the Gaussian pulses, a very high localization performance can be achieved, even when the matched filter ignores the Doppler effect by matching to zero Doppler shift. This leads to significantly reduced complexities for the matched filter and the MLE. Further, two interactive signal processing and tracking algorithms, based on the Kalman filter and the particle filter (PF), respectively, are proposed for noncoherent MIMO radar target tracking. For a system with a large number of transmit/receive elements and a high signal-to-noise ratio (SNR) value, the Kalman filter (KF) is a good choice; while for a system with a small number of elements and a low SNR value, the PF outperforms the KF significantly. In both methods, the tracker provides predictive information regarding the target location, so that the matched filter can match to the most probable target locations, reducing the complexity of the matched filter and improving the tracking performance. Since tracking is performed without detection, the presented approach can be deemed as a track-before-detect approach. It is demonstrated through simulations that the noncoherent MIMO radar provides significant tracking performance improvement over a monostatic phased array radar with high range and azimuth resolutions. Further, the effects of coherent integration of pulses are investigated for both the phased array radar and a hybrid MIMO radar, where only the pulses transmitted and received by colocated transceivers are coherently integrated and the other pulses are combined noncoherently. It is shown that the hybrid MIMO radar achieves significant tracking performance improvement when compared with the phased array radar, by using the extra Doppler information obtained through coherent pulse integration.