Distance estimation from received signal strength under log-normal shadowing: Bias and variance

In source localization one estimates the location of a source using a variety of relative position information. Many algorithms use certain powers of distances to effect localization. In practice, such distances are not directly available but must be deduced from information such as received signal strength (RSS) or time difference of arrival. This paper considers bias and variance issues in estimating powers of distances from RSS affected by log-normal shadowing. We show that the underlying estimation problem is inefficient and that the maximum likelihood estimate yields a bias and error variance that both increase exponentially with the noise power. By considering the class of twice differentiable estimators, we show that there is a unique unbiased estimator in this class, but that its error variance also grows exponentially with the noise power. Finally, we propose an estimate the bias and error variance of which are both bounded in the noise power.