Distributed field estimation with one-bit sensors

Abstract

We study the problem of reconstructing a temporal sequence of unknown spatial data fields in a bounded geographical region of interest at a data fusion center from finite bit-rate messages generated by a dense noncooperative network of noisy low-resolution sensors (at known locations) that are statistically identical (exchangeable) with respect to the sensing operation. The interchangeability assumption reflects the property of an unsorted collection of inexpensive mass-produced sensors that behave in a statistically identical fashion. We view each data field as an unknown deterministic function over the geographical space of interest and make only the minimal assumption that they have a known bounded maximum dynamic range. The sensor observations are corrupted by bounded, zero-mean additive noise which is independent across sensors with arbitrary dependencies across field snapshots and has an arbitrary but unknown distribution but a known maximum dynamic range. The sensors are equipped with binary analog-to-digital converters (ADCs) (comparators) with random thresholds that are independent across sensors with arbitrary dependencies across snapshots and are uniformly distributed over a known dynamic range. These modeling assumptions partially account for certain real-world scenarios that include (i) the unavailability of good initial statistical models for data fields in yet to be well studied natural phenomena, (ii) unknown additive sensing/observation noise sources, (iii) additive model perturbation errors, (iv) substantial variation of preset comparator thresholds accompanying the mass-manufacture of low-precision sensors, (v) significant temperature fluctuations across snapshots affecting hardware characteristics, and (vi) the use of intentional dither signals for randomized scalar quantization. © 2008 Springer-Verlag US.