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The reconstruction of a deterministic data field from binary-quantized noisyobservations of sensors which are randomly deployed over the field domain isstudied. The study focuses on the extremes of lack of deterministic control inthe sensor deployment, lack of knowledge of the noise distribution, and lack ofsensing precision and reliability. Such adverse conditions are motivated bypossible real-world scenarios where a large collection of low-cost, crudelymanufactured sensors are mass-deployed in an environment where little can beassumed about the ambient noise. A simple estimator that reconstructs theentire data field from these unreliable, binary-quantized, noisy observationsis proposed. Technical conditions for the almost sure and integrated meansquared error (MSE) convergence of the estimate to the data field, as thenumber of sensors tends to infinity, are derived and their implications arediscussed. For finite-dimensional, bounded-variation, andSobolev-differentiable function classes, specific integrated MSE decay ratesare derived. For the first and third function classes these rates are found tobe minimax order optimal with respect to infinite precision sensing and knownnoise distribution.

Non-Parametric Field Estimation using Randomly Deployed, Noisy, Binary Sensors