Unknown Noise PDF
We now describe the system design of for the case that the structure of the noise PDF is unknown. The following model is considered for this scenario:
In addition, the message functions are limited to have the form
where each is a subset of . The fusion estimator is also restricted to be linear, i.e. .
The design should set the decision intervals and the coefficients . Intuitively, we would allocate sensors to encode the first bit of by setting their decision interval to be, then sensors would encode the second bit by setting their decision interval to and so on. It can be shown that these decision intervals and the corresponding set of coefficients produce a universal -unbiased estimator, which is an estimator satisfying for every possible value of and for every realization of . In fact, this intuitive design of the decision intervals is also optimal in the following sense. The above design requires to satisfy the universal -unbiased property while theoretical arguments show that an optimal (and a more complex) design of the decision intervals would require, that is: the number of sensors is nearly optimal. It is also argued in that if the targeted MSE uses a small enough, then this design requires a factor of 4 in the number of sensors to achieve the same variance of the MLE in the unconstrained bandwidth settings.
Read more about this topic: Location Estimation In Sensor Networks
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