TABLE OF CONTENTS One theoretical tool of utility in analyzing limitations on the performance of localization techniques is the use of the Cram r Rao bound. The Cram r Rao bound (CRB) is a well-known lower bound on the error variance of any unbiased estimator, and is defined as the inverse of the Fisher information matrix (a measure of information content with respect to parameters). The CRB can be derived for different assumptions about the localization technique (e.g. TOA-based, RSS-based, proximity-based, node/network localization).
The CRB has been used to investigate error performance of K-level quantized RSSI-based localization [155]. A special case is K = 2, which corresponds to proximity information (whether the node is within range or not). The lower bound can be improved monotonically with K, with about 50% improvement if K is large compared with just using proximity alone. On the other hand, K = 8 (three bits of RSS quantization) suffices to give a lower bound that is very close to the best possible. It is also found that the MLE estimator, which is a biased estimator, provides location errors with variance close to that observed with the CRB.
CRB analysis has also been used to investigate the performance of network localization under different densities, and shown to give similar trends to the iterative/collaborate multilateration technique [184]. The CRB-based analysis suggests that localization accuracy improves with network density, with diminishing returns once each node has about 6 8...
