Distributed adaptive quantization for wireless sensor networks: A maximum likelihood approach

We consider distributed parameter estimation using quantized observations in wireless sensor networks (WSN) operating in a noisy channel environment. Due to bandwidth constraints, each sensor quantizes its local observation into one bit of information. Previously, adaptive quantization(AQ) schemes were developed under the assumption of perfect communication links between the sensors and the fusion center (FC). In this paper we propose an adaptive quantization scheme for a WSN with channel links modeled as binary erasure channels. A first-order Hidden Markov Model (HMM) framework is introduced to model the adaptive quantization scheme. The introduction of a HMM framework aids in the systematic design of an estimator. To address the significant problem of bit erasures, we propose an Expectation-Maximization (EM) based estimator. Theoretical closed form solutions for the Cramer-Rao lower bounds are developed for the proposed estimation problem under certain assumptions. We analyze the performance of the proposed quantization scheme and estimator under different criteria. Numerical simulation results are shown for the proposed adaptive quantization and EM parameter estimation scheme under different scenarios. The simulation results indicate that the proposed quantization scheme and estimator are robust and can provide superior performance for erasure rates up to 10 %.

In this paper, we consider non-Bayesian parameter estimation in wireless sensor networks (WSNs) with multiple sensors that have different quantization resolutions. Quantized measurements provide improved performance in the sense of energy consumption, communication bandwidth, and hardware complexity, but are less informative than analog, unquantized measurements and may lead to poor estimation performance. In this paper we assume that the WSN contains two types of sensor nodes: 1-bit, quantized measurements and TO-bit, unquantized measurements. We introduce the maximum-likelihood (ML) estimator for this case and derive the Fisher scoring method in order to implement it. The Cramer-Rao lower bound (CRB) has been developed for the considered model. In addition, we characterize the sample allocation rule that determines how many sensors are selected for quantized and unquantized measurements in order to minimize the sum of the CRB and linear sensors costs. Finally, we present simulations that show for the linear Gaussian model the ML estimator achieves the CRB and examine the use of additional analog measurements as a tool for improving robustness.

We examine distributed estimation of the average power of a random signal in wireless sensor networks (WSNs). Due to stringent bandwidth/power constraints, each sensor quantizes its observation into one bit of information and sends the quantized data to a fusion center, where the signal power is estimated. We firstly introduce two fixed quantization (FQ) schemes, with the first using a single threshold and the second employing a pair of symmetric thresholds. The maximum likelihood (ML) estimators associated with the two FQ schemes are developed, and their corresponding Cramer-Rao bounds (CRBs) are analyzed. We show that the FQ approach, especially the second one, can achieve an estimation performance close to that of a clairvoyant estimator using unquantized data if the optimum quantization threshold is available; however, the optimum threshold is dependent on the unknown signal power, and as the threshold deviates from its optimum value, the performance degrades rapidly. To cope with this difficulty, we propose a distributed adaptive quantization (AQ) approach by which the threshold is dynamically adjusted from one sensor to another in a way such that the threshold converges to the optimum threshold. Our analysis shows that the proposed AQ approach is asymptotically optimum, yielding an asymptotic CRB equivalent to that of the FQ approach with optimum threshold.

In this paper, we study distributed estimation with wireless sensor networks (WSN) when channel estimation is imperfect. A robust distributed maximum likelihood (ML) estimator of the unknown parameter is proposed, which improves the performance of the traditional ML estimator with imperfect channel estimation. By maximizing the effective signal to noise ratio (SNR) at the fusion center (FC), we find that the optimal length of the training sequence is the square root of the length of the quantized observation at each node. Simulations are provided to evaluate the performance of the robust method and to validate the theoretical optimal length.

In this paper, the distributed estimation in wireless sensor network using optimal task scheduling is considered. The main goal is to maximize network lifetime where it consists of a fusion center and a set of sensor nodes. Lifetime defined as the number of rounds accomplished before network becomes nonfunctional. In order to prolong network lifetime, we determine the optimal number of active sensor nodes and the number of samples provided by each of them using linear optimization problem. Sensor observations are quantized into messages and then forwarded to a fusion center where a final estimation is performed based on degree of certainty. Simulation results show that our optimal proposed algorithm has achieved significant efficiency when compared with other heuristic methods.

This paper proposes a distributed incremental quantization and estimation scheme by which each sensor can make a maximum likelihood estimation (MLE) of the unknown parameter based on its local observations and the quantized messages transmitted by the previous sensor. We derive the upper bound of the estimation mean squared error (MSE) of the proposed scheme, and propose the bit allocation algorithms, which minimize the total required bandwidth while ensuring a given MSE performance. Simulation results demonstrate that the proposed scheme requires much less bandwidth, but achieves around 40% MSE reduction compared with the distributed adaptive quantization and estimation scheme.

We consider distributed estimation algorithms in a large Wireless Sensor Network (WSN) with a star topology. The local estimates computed by each sensor must be collected in a fixed amount of time by the network's Fusion Center (FC) and processed to produce a global estimate. When the amount of time available is not sufficient to collect a local estimate from every node, a strategy that enables the most reliable estimates to be collected first must be developed. In this paper, we develop such an algorithm for a WSN whose FC uses a Best Linear Unbiased Estimator (BLUE) and collects the local estimates on a collision channel. The proposed schemes use population splitting that is based on the reliabilities of the local estimates. The time available for data collection is divided into frames and each frame is subdivided into slots. The slots in the first frame are used to collect the most reliable local estimates, the next frame of slots is used to collect the next most reliable set of local estimates, etc. As the performance of the schemes depends on the reliability thresholds, the number of bits representing the estimates, and the number of time slots in a frame, we formulate time-constrained optimization problems and derive methods to obtain the optimal values of these parameters. An interesting result shows that the optimal reliability thresholds do not maximize the channel's throughput.

Wireless Sensor Networks (WSNs) are traditionally employed to collect spatial and temporal data characterizing various events. These data are then used to solve inference problems such as object detection, counting, classification, estimation and tracking. Distributed solutions provided by WSNs are often cost effective and characterized by high performance indices.;In this work, we model and simulate a distributed sensor network composed of radiation detectors and analyze its ability to make inferences. Radiation detectors are deployed over a known area. A radiological point source is positioned in the interior of the area. Detectors take measurements of the field generated by the point source and transmit them (without any interaction with one another) to a remotely installed super computer (called here Fusion Center) for a joint processing. To minimize consumption of resources such as power in the network and transmission bandwidth, the measurements are locally preprocessed prior to transmission. Our model assumes two Gaussian channels, observation and transmission. The first channel distorts data at the receiver end of each sensor during data acquisition. The second channel distorts data during transmission. Sensor measurements are modeled as an inhomogeneous spatial counting random process (Poisson process). The location of the radiological point source in the area and the strength of the field generated by the substance are unknown parameters. The goal of the FC is to estimate these parameters from the distributed measurements provided by the WSN. To find the distributed estimates, we adopt the Maximum Likelihood approach. This approach requires knowledge of the joint probability density function of the distributed measurements observed by the FC. Since the joint probability density of the data observed at the FC is nonlinear in unknown parameters, we propose an iterative approach to solve for the maximum likelihood estimates of these parameters. The solution is a combination of the Bisection and Secant approaches adjusted to seek solution in a multidimensional parameter space. The performance of the distributed estimator is measured in terms of the mean square error. It is analyzed with respect to various parameters of the WSN. We vary the following parameters of the network: (1) the number of sensors in the WSN, (2) signal to noise ratio in observation and transmission channels, (3) the strength of the original field, and (4) the number of quantization levels used by a sensor to convert an analog measurement into a digital signal. We also propose a distributed tracking algorithm for monitoring

We consider the lifetime maximization problem for joint estimation in wireless sensor network. In the joint estimation problem, each sensor observes a noise-corrupted version of a physical quantity, then amplifies and forwards the observation to the destination (fusion center) through a wireless channel. The fusion center combines the data and constructs a joint estimate. The sensors may communicate with the destination through either orthogonal or shared channels. We develop algorithms that jointly determine the transmit power of sensors as a function of sensor measurement noises, wireless channel coefficients, and the available battery power at sensors. The objective of the algorithm is to maximize the lifetime of the network, while a certain quality of estimation at the fusion center is maintained throughout the lifetime of the network. It is observed that the present algorithm behaves differently compared to minimum-transmit-power strategies, and performs better in terms of the longevity of the network.

Securing range free localization against wormhole attack using distance estimation and maximum likelihood estimation in Wireless Sensor Networks

The reverberation power spectral density (PSD) is often required for dereverberation and noise reduction algorithms. In this work, we compare two maximum likelihood (ML) estimators of the reverberation PSD in a noisy environment. In the first estimator, the direct path is first blocked. Then, the ML criterion for estimating the reverberation PSD is stated according to the probability density function of the blocking matrix (BM) outputs. In the second estimator, the speech component is not blocked. Instead, the ML criterion for estimating the speech and reverberation PSD is stated according to the probability density function of the microphone signals. To compare the expected mean square error (MSE) between the two ML estimators of the reverberation PSD, the Cramer–Rao Bounds (CRBs) for the two ML estimators are derived. We show that the CRB for the joint reverberation and speech PSD estimator is lower than the CRB for estimating the reverberation PSD from the BM outputs. Experimental results show that the MSE of the two estimators indeed obeys the CRB curves. Experimental results of multimicrophone dereverberation and noise reduction algorithm show the benefits of using the ML estimators in comparison with another baseline estimators.

The problem of distributed estimation of an unknown parameter corrupted by noise is studied in this paper. In consideration of the stringent bandwidth constraint in practical wireless sensor network (WSN) applications, a one-bit quantization scheme is adopted to compress local sensor observations. Imperfect data transmission between local sensors and a fusion center is considered and modeled as a Rayleigh fading channel. The conventional maximum likelihood estimation (MLE) usually involves high computational complexity. In this paper, we propose a simple mean estimator which requires only the mean of the channel gain. It is further modified by utilizing the properties of the intermediate parameter under estimation. Theoretical analysis and simulation results show that the proposed estimators are not only more computationally efficient than MLE, but also achieve near MLE performance over a wide range of the channel SNR and the number of sensors, which makes them suitable for practical resource-constraint WSN applications.

Location estimation in wireless sensor networks (WSNs) has received tremendous attention in recent times. Improved technology and efficient algorithms systematically empower WSNs with precise location identification. However, while algorithms are efficient in improving the location estimation error, the factor of the network lifetime has not been researched thoroughly. In addition, algorithms are not optimized in balancing the load among nodes, which reduces the overall network lifetime. In this paper, we have proposed an algorithm that balances the load of computation for location estimation among the anchor nodes. We have used vector-based swarm optimization on the connected dominating set (CDS), consisting of anchor nodes for that purpose. In this algorithm, major tasks are performed by the base station with a minimum number of messages exchanged by anchor nodes and unknown nodes. The simulation results showed that the proposed algorithm significantly improves the network lifetime and reduces the location estimation error. Furthermore, the proposed optimized CDS is capable of providing a global optimum solution with a minimum number of iterations.

In this paper, we propose a fully distributed algorithm for joint clock skew and offset estimation in wireless sensor networks. With the proposed algorithm, each node can estimate its clock skew and offset by communicating only with its neighbors. Such algorithm does not require any centralized information processing or coordination. Simulation results show that estimation mean-square-error at each node converge to the centralized Cramér-Rao bound with only a few number of message exchanges.

In this paper, we propose a novel model of three points named TP for location estimation in wireless sensor networks (WSNs) with random deployment of anchor nodes. In this model, we select three anchor nodes which have the strongest received signal strength (RSS) for location estimation, the centroid algorithm and the method of intersection of judgment are used to estimate the location of unknown nodes. To further exploit three nearest intersection points in TP, the enhanced TP (ETP) is proposed. The simulation results show that the proposed models outperform MMSE and BML in terms of the localization accuracy for WSNs. Moreover, the localization accuracy of the proposed models in scenario 2 with random deployment of anchor nodes are better than in scenario 1 with planned deployment of anchor nodes. Additionally, compared with MMSE and BML, ETP and TP can reduce the environmental impact on location estimation.