Cramér–Rao Lower Bounds of RSS-Based Localization With Anchor Position Uncertainty

The location awareness is useful in many wireless networking solutions, such as cellular, ad hoc, self-organizing, cognitive radio networks, and so on. The RSS-based, non-Bayesian source localization is of particular interest, due to the presence of the RSS measurements in all radio devices, as well as the instantaneous estimations without extensive training and learning phases. However, most RSS-based localization algorithms usually neglect problems arising from inherent network topology uncertainty. The positions of some measuring anchors, usually assumed to be precisely known in advance, are often a subject of previous estimation, which propagates errors in the source localization procedure and results in performance degradation. A joint localization framework, termed source position estimation for anchor position uncertainty reduction (SPEAR), has been recently proposed as a possible solution to the problem of RSS-based localization in the presence of network topology uncertainty. The framework simultaneously estimates the positions of the sources and the uncertain anchors and serves as robust tool that provides improved source localization performance and more reliable anchor position estimates. This paper focuses on the theoretical assessment of SPEAR's performance by deriving its fundamental lower bounds using the Cramér-Rao information inequality. The main contribution of this paper is the detailed information-theoretic interpretation of the obtained results. The interpretation provides valuable insight into the essence of the SPEAR localization problem because it identifies different position information components in the observed data, discovers how they are mutually related, and determines how they contribute toward the resulting position information. This paper also provides geometric interpretation of the obtained results and illustrates the principles of distribution of position information in space. The theoretical results as well as their information-theoretic and geometric interpretations can be used as a benchmark for RSS-based location-aware systems that operate in the presence of network topology uncertainty.