ER-CRLB: An Extended Recursive Cramér–Rao Lower Bound Fundamental Analysis Method for Indoor Localization Systems

Abstract

We propose an extended recursive Cramér-Rao lower bound (ER-CRLB) method as a fundamental tool to analyze the performance of wireless indoor localization systems. The ER-CRLB fully models the complicated indoor environment, e.g., the sequential position state propagation, the target-anchor geometry effect, the non-line-of-sight (NLOS) identification, and the related prior information. First, we use an abstract function to represent the entire wireless localization system model. Then, the unknown vector of the ER-CRLB consists of two parts: The first part is the estimated vector, and the second part is the auxiliary vector that helps improve the estimation accuracy. Accordingly, the Fisher information matrix (FIM) of the ER-CRLB is divided into two parts, namely, the state matrix and the auxiliary matrix. Based on this idea, ER-CRLB can be a practical fundamental limit to denote the system which fuses multiple information in the complicated environment, e.g., recursive Bayesian estimation based on the hidden Markov model, the map matching method and NLOS identification and mitigation methods. When only a small set of unknown vectors is estimated in the system, the ER-CRLB is equivalent to the other CRLBs of the wireless indoor localization system as well. However, the ER-CRLB is more adaptable than other CRLBs when considering more unknown important factors. We employ the ER-CRLB to analyze the time-of-arrival (TOA) range-based indoor localization system. The influence of the hybrid line-of-sight (LOS)/NLOS channels, the building layout information, and the relative height differences between the target and anchors are analyzed. It is demonstrated that the ER-CRLB exploits all the available information for the indoor localization systems and serves as a fundamental limit of the unbiased estimation accuracy.