The problem of distributed estimation of a parametric function in space is stated as a maximum likelihood
estimation problem. The function can represent a parametric physical ¯eld generated by an object or be a
deterministic function that parameterizes an inhomogeneous spatial random process.
In our formulation, a sparse network of homogeneous sensors takes noisy measurements of the function. Prior
to data transmission, each sensor quantizes its observation to L levels. The quantized data are then communicated
over parallel noisy channels to a fusion center for a joint estimation.
The numerical examples are provided for the cases of (1) a Gaussian-shaped ¯eld that approximates the
distribution of pollution or fumes produced by an object and (2) a radiation ¯eld due to a spatial counting
process with the intensity function decaying according to the inverse square law. The dependence of the mean-
square error on the number of sensors in the network, the number of quantization levels, and the SNR in
observation and transmission channels is analyzed. In the case of Gaussian-shaped ¯eld, the performance of the
developed estimator is compared to unbiased Cramer-Rao Lower Bound.