On Universal Distributed Estimation of Noisy Fields with One–bit Sensors∗

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one–bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper–bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio–temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain minimal technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per–sensor bitrate and sensing–related network overhead rate simultaneously go to zero. The proposed scheme achieves the order–optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio–temporal fields.