Distributed Quantization-Estimation For Wireless Sensor Networks

Advances in sensor technology, wireless communication technology and microproces-sor technology have led to the development of wireless sensor networks (WSNs), whichare attracting the attention of academia and industry due to its great potential for appli-cation. In the recent years, distributed quantization-estimation for WSNs has become thefocus in the fields of signal processing and network control. Due to power and bandwidthconstraints, the observations of sensors have to be quantized and encoded to digital signalsbefore transmission over wireless channels, and the estimation is obtained based on quan-tized observations, which is certainly di?erent from the traditional estimation based onthe analog-amplitude observations. Moreover, the introduction of networks has broughtmany new uncertainties, such as packet loss and delay, which is a new challenge to manyclassic problems. How to utilize the limited network bandwidth e?ciently and achievethe optimal performance of estimation is the focus of distributed quantization-estimationfor WSNs. Most of the existing works concentrated on the distributed quantization-estimation of static parameter, and generally only considers the designs of quantizer andestimator under the given bit rate of each sensor. However, some other important issues,such as optimal bit allocation under total bandwidth constraint, theoretical optimal per-formance of estimation and distributed quantized state estimation of dynamic system,are still left to be open.This thesis studies distributed quantization-estimation problems for static and dy-namic systems, in which the mean-squared error (MSE) is adopted to measure the perfor-mance of the estimators. The thesis contains three parts: The first part investigates dis-tributed quantization-estimation of deterministic and random parameters with quantizedmeasurements. In the second part, our work focuses on distributed quantized Kalman fil-tering of dynamic system with distributed measurements. The third part studies Kalmanfiltering of dynamic system with real-time encoded signals.Firstly, distributed quantization-estimation of static parameter is investigated. Forthe deterministic parameter case, an unbiased probabilistic quantizer is designed and thelinear optimal unbiased estimator is obtained. Then the optimal bit-allocation under agiven total bandwidth for a two-sensor system is studied. It is found that the optimal bitrate of each sensor is determined by the local signal-to-noise ratio (SNR) and analyticsolution for bit-allocation is obtained, where whether the sensor is activated or not isbasically determined by the total number of quantization levels and the relative coe?cientof SNRs. For the random parameter case, we studies the optimal bit-allocation in terms of the upper bound of MSE for linear quasi-MMSE and the Bayesian Cramer-Rao lowerbound based on the uniform quantization. It is shown that for the high-resolution case,the bit allocation solution for quasi-MMSE is an optimal in the sense that the BCRB ofthe estimator is minimized, and the optimal number of quantization levels is inverselyproportional to the sensor noise variance. Moreover, the optimal quantizer-estimatorand bit-allocation are studied for vector parameters with a set of scalar-observations. Aminimum-MSE estimator is obtained based on the quantized observations. It is found thatthe asymptotic optimal quantizer of each sensor is actually the well-known Lloyd-Maxquantizer, and the asymptotic optimal number of quantization levels is proportional tothe SNR. Furthermore, since the optimal quantization-estimation algorithm has a heavyburden of computation when there is a large number of active sensors, we propose aniterative quantization-estimation algorithm, which reduces the calculation burden largelyand be applicable to network environment with packet loss or delay, which increases therobustness and applicability of algorithm.Secondly, we extend to distributed quantized Kalman filtering for linear discrete-timedynamic system. We propose a new dynamic Lloyd-Max quantizer and the online updatescheme is designed. Then, the optimal recursive quantized Kalman filter is derived basedon the Bayesian principles, and an asymptotically equivalent iterative quantized Kalmamfilter algorithm is presented, which reduces the computational complexity and increasesthe robustness and applicability of algorithm. Furthermore, the stability of the quantizedKalman filter has been analyzed. For an unstable system, it is found that the criticalbit rate to yield stable quantized Kalman filter is determined by quantizer and unstableeigenvalues of system matrix, which are unrelated to the number of sensors or observationnoises.Finally, we study optimal real-time coding Kalman filtering for linear discrete-timedynamic system. This problem can be transformed to the optimal recovery of a GaussianMarkov source, we get optimal recursive structures of encoder and estimator, and theinformation-theoretic rate-distortion function is analyzed. Then, a specific real-time cod-ing Kalman filter is proposed based on the dynamic Lloyd-Max quantizer principle, whosestructures are identical to the optimal structures of encoder and estimator. Moreover, itis shown that the rate-distortion function of the proposed scheme is within a factor ofthe information-theoretic rate-distortion function for the scalar system.The above results answer a fundamental question in distributed signal processing fornetworks: How the quantization a?ects the performance of distributed estimator?...