# Benefits and Impact of Joint Metric of AOA/RSS/TOF on Indoor Localization Error
## 2 Related Works  
Depending on the ranging metric, the existing indoor localization solutions in wireless networks can be commonly classified into three categories, AOA-based, RSS-based and TOF-based indoor localization [17]. The performance of RSS-based indoor localization highly depends on the physical layout, propagation loss and channel interference, while the NLOS propagation property may seriously degrade the performance of AOA-based and TOF-based indoor localization due to the difficulty of detecting the direct signal path and measuring the time of flight of the signal, respectively [18]. Thus, the metric by using the AOA, RSS or TOF solely is vulnerable to environmental changes. To solve this problem, the authors in [19] proposed to use the metric of RSS/TOF to conduct the localization based on the determining likelihood function, which is used to depict the relations between the measurements and distances. The authors in [20] presented a scheme in which the metrics of RSS and AOA are integrated to restrain the NLOS fading. The authors in [21] developed an efficient approach to localize the mobile sensors using the metrics of TOF and AOA with the help of multiple seeds adopted to obtain adequate observations. There are batches of studies analyzing the error bound of localization by using the FIM. The authors in [22] selected the CRLB to investigate the localization error by performing the unbiased Gaussian range estimation based on the metric of AOA. In [23], the authors proposed to use the information inequality-based Position Error Bound (PEB) to analyze the error performance of TOF-based cooperative localization. The authors in [24] investigated the impact of the bandwidth and sampling rate of the receiver on the accuracy of the radar localization systems based on the Cramer-Rao bounds of the TOF and TDOA. In [25], the authors derived the error bound of the RSS-based localization for the uncertain network topology by using the Fisher information and Cramer-Rao inequality. Similarly, the authors in [26] analyzed the CRLB of the localization by selecting the Signal Strength Difference (SSD) as the location fingerprint. In addition, the bound of localization error helps greatly in designing effective localization algorithms, as well as providing valuable suggestions for the construction of superior localization systems by revealing the error trends, which are associated with the network deployment. In [27], the authors quantifies via the Cramer-Rao bound on location estimators, which use measured TOF or RSS. The authors in [28] realized the highly-accurate positioning of the sensors by using the metrics of RSS and TOF. Different from the literature above, which analyzed the unbiased localization problem, the authors in [29] analyzed the impact of various parameters in system design, as well as the biased measurements on positioning performance and meanwhile derived an asymptotic expression for positioning mean-square error in the network-based multilateral localization system. The mathematical analysis in [29] is based on the CRLB and maximum likelihood theory. Furthermore, the authors in [30] studied the deterministic CRLBs for the estimation of the specular multipath parameters and target locations in an asynchronous direct sequence code division multiple access system, which operates over the specular multipath fading channel. However, the existing literature mainly focused on the analysis of the localization error bound by selecting the AOA, RSS or TOF solely as the metric. Different from these, we investigate the error bound with respect to the JMART used for the indoor localization. The most important contribution of this paper is to derive the error bounds by using the AOA, RSS, TOF and JMART respectively for the unbiased localization problem. To achieve this goal, on the one hand, we use the deviation \(\sigma\) to approximately describe the multipath effect, which is also used in [22; 23; 24; 25; 26].