Range-based geolocation in fading environments

We consider source geolocation based on range estimates from sensors with known coordinates. In a fading propagation environment, where a line-of-sight (LOS) path may be weak or essentially nonexistent, range estimates may have positive biases. We study this problem by considering a weighted least squares (WLS) location estimator, based on noisy range estimates, each of which is contaminated by additive Gaussian noise and possibly a positive bias. We derive the mean and mean-square error (MSE) of the WLS estimator, showing that in general the estimator produces biased estimates. The error expressions are developed via first-order perturbation analysis. They provide a means to study achievable localization performance, as a function of the measurement bias and variance, as well as the sensor network geometry.