Dimensionality Reduction, Compression and Quantization for Distributed Estimation with Wireless Sensor Networks

The distributed nature of observations collected by inexpensive wireless sensors necessitates transmission of the individual sensor data under stringent bandwidth and power constraints. These constraints motivate: i) a means of reducing the dimensionality of local sensor observations; ii) quantization of sensor observations prior to digital transmission; and iii) estimators based on the quantized digital messages. These three problems are addressed in the present paper. We start deriving linear estimators of stationary random signals based on reduced-dimensionality observations. For uncorrelated sensor data, we develop mean-square error (MSE) optimal estimators in closed-form; while for correlated sensor data, we derive sub-optimal iterative estimators which guarantee convergence at least to a stationary point. We then determine lower and upper bounds for the Distortion-Rate (D-R) function and a novel alternating scheme that numerically determines an achievable upper bound of the D-R function for general distributed estimation using multiple sensors. We finally derive distributed estimators based on binary observations along with their fundamental error-variance limits for pragmatic signal models including: i) known univariate but generally non-Gaussian noise probability density functions (pdfs); ii) known noise pdfs with a finite number of unknown parameters; and iii) practical generalizations to multivariate and possibly correlated pdfs. Estimators utilizing either independent or colored binary observations are developed, analyzed and tested with numerical examples.