# Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks
## 1 Introduction  
Location estimation plays a key role in many applications, and is today attracting a great interest from both industry and academia. This process is sustained by the increasing widespread use of interconnected smart devices, which have the potential to enable seamless position capabilities at significantly reduced development costs. Indeed, besides the undisputed importance of the ultimate localization accuracy, the low-complexity requirement has been recently regarded as a fundamental need in most resource-constrained operational contexts, such as body area networks and wireless sensor networks (WSNs). In this respect, the design of localization solutions able to exploit the received radio frequency signals in an opportunistic way, without requiring any additional hardware, is of great practical interest. Several approaches have been proposed in the literature to tackle the problem of node localization by leveraging information extracted from existing terrestrial technologies [1; 2; 3; 4; 5; 6]. Among others, range-based solutions have been widely employed in popular terrestrial localization systems, especially in WSNs, where they are preferred to range-free techniques [7; 8] thanks to their reduced complexity. Range information can be obtained by exploiting different characteristics of the received signals, namelyreceived signal strength (RSS) [9; 10; 11; 12; 13; 14; 15; 16], time (difference) of arrival (TOA/TDOA) [17; 18; 19; 20], and angle of arrival (AOA) [21; 22; 23; 24; 25]. Hybrid approaches combining different types of measurements have also been proposed. For instance, references [26; 27; 28; 29; 30; 31; 32] investigated novel localization schemes based on the combined use of RSS and AOA measurements, which are able to achieve improved estimation performance. Although interesting, these techniques require enhanced hardware and processing capabilities that are usually not available on-board low-cost sensor nodes employed in typical WSN deployments; more precisely, AOA-based methods are not appealing in such contexts owing to the increased complexity and costs associated with multiple antennas. TOA/RSS solutions better fit the requirements of low-cost contexts, thanks to their simplicity and ready availability, and the hybrid (joint) approach is interesting for its improved accuracy [33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. A theoretical study of the localization performance achievable using joint TOA/RSS measurements has been conducted in [33]. By providing the exact expression of the Cramer-Rao lower bound (CRLB), authors showed that such hybrid schemes can offer significant improvements in the estimation accuracy with respect to the case where RSS-only or TOA-only measurements are used. In [34], authors addressed the problem of target localization in presence of mixed line-of-sight (LOS)/non-line-of-sight (NLOS) scenarios. In a first step, the algorithm classifies all the links as either LOS or NLOS according to a parametric Nakagami distribution; then, the position is estimated through a weighted least squares (WLS) approach that considers the sole TOA measurements for those links identified as LOS and the RSS measurements for the NLOS paths. A novel algorithm to tackle the problem of target localization in adverse NLOS environments has been proposed in [35]. In this work, authors tried to mitigate the detrimental effects of NLOS biases on both RSS and TOA measurements by recasting the original (non-convex) problem as an approximated generalized trust region sub-problem. The ultimate target position estimate is then obtained by applying a bisection procedure based on an iterative squared range WLS approach. In [36], same authors addressed the more challenging scenario in which all paths are in NLOS. By assuming a partial knowledge of the NLOS biases affecting the collected measurements, the highly-dimensional localization problem can be approximated to a min-max problem in which the NLOS biases are treated as known nuisance parameters.