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, exact distance measurement is not directly available and must be estimated from information such as received signal strength (RSS), time of arrival, or time difference of arrival. This letter considers bias and variance issues in estimating powers of distances from RSS affected by practical log-normal shadowing. We show that the underlying estimation problem is inefficient and that the maximum likelihood estimate yields a bias and a mean-square error (MSE) that both increase exponentially with the noise power. We then characterize the class of unbiased estimates and show that there is only one estimator in this class, but that its MSE also grows exponentially with the noise power. Finally, we provide the linear minimum mean-square error (MMSE) estimate and show that its bias and MSE are both bounded in the noise power.