# Location Estimation in Sensor Networks - Setting

Setting

Let denote the position of interest. A set of sensors acquire measurements contaminated by an additive noise owing some known or unknown probability density function (PDF). The sensors transmit measurements to a central processor. The th sensor encodes by a function . The application processing the data applies a pre-defined estimation rule . The set of message functions and the fusion rule are designed to minimize estimation error. For example: minimizing the mean squared error (MSE), .

Ideally, sensors transmit their measurements exactly to the processing center, that is . In this settings, the maximum likelihood estimator (MLE) $hat{theta} = frac{1}{N}sum_{n=1}^N x_n$ is an unbiased estimator whose MSE is $mathbb{E}|theta-hat{theta}|^2 = text{var}(hat{theta}) = frac{sigma^2}{N}$ assuming a white Gaussian noise . The next sections suggest alternative designs when the sensors are bandwidth constrained to 1 bit transmission, that is =0 or 1.

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