Location Estimation in Sensor Networks - Unknown Noise Parameters

Unknown Noise Parameters

A noise model may be sometimes available while the exact PDF parameters are unknown (e.g. a Gaussian PDF with unknown ). The idea proposed in for this setting is to use two thresholds, such that sensors are designed with, and the other sensors use . The processing center estimation rule is generated as follows:

$\hat{q}_1=\frac{2}{N}\sum\limits_{n=1}^{N/2}m_A(x_n), \quad \hat{q}_2=\frac{2}{N}\sum\limits_{n=1+N/2}^{N}m_B(x_n)$

$\hat{\theta}=\frac{F^{-1}(\hat{q}_2)\tau_1-F^{-1}(\hat{q}_1)\tau_2}{F^{-1}(\hat{q}_2)-F^{-1}(\hat{q}_1)},\quad F(x)=\frac{1}{\sqrt{2\pi}}\int\limits_{x}^{\infty}e^{-v^2/2}dw$

As before, prior knowledge is necessary to set values for to have an MSE with a reasonable factor of the unconstrained MLE variance.

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