# Target Localization via Integrated and Segregated Ranging Based on RSS and TOA Measurements
## 1 Introduction  
The aspiration for precise knowledge about the location of objects and/or people has motivated a great deal of scientific research recently [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. This is due to a firm growth of the range of enabling devices and technologies, as well as the need for seamless solutions for location-based services. Besides localization precision, a common requirement for emerging solutions is that they are cost-restrained, both in terms of the financial and computational cost. Therefore, development of different localization strategies from already deployed technologies, e.g., from various terrestrial radio frequency sources is of great practical interest. Among others, these include concepts based on received signal strength (RSS), angle of arrival, time of arrival (TOA), or a combination of them [6; 9; 16; 18; 19; 20; 21; 22]. Much work has been done regarding target localization based on integrated RSS and TOA measurements [18; 19; 20; 21; 22]. The authors in [23] and [20] studied the range estimation problem based on these two quantities. The authors in [23] employed the Newton-Raphson (NR) method to obtain a sub-optimal hybrid RSS-TOA ranging estimator for indoor non-line of sight NLOS environments in a closed-form. A joint ad-hoc (JAH) relaxation of hybrid likelihood function, which offers a good bias-variance trade-off to the derived ranging estimator was proposed in [20]. Although NR and JAHare originally designed for range estimation, after getting the range estimates, their generalization to the target localization problem is straightforward, for example through the use of a squared range approach [24]. In [18; 21], the target localization problem in mixed line of sight (LOS)/NLOS environments was addressed. The authors in [18] first identified the type of the path for all links by using Nakagami distribution and then proposed a weighted least squares (WLS) estimator which utilizes TOA-only/RSS-only measurements if the link is identified as LOS/NLOS. An iterative squared range WLS estimator was proposed in [21]. The authors in [21] partially mitigate the negative influence of NLOS biases by approximating them by a single (mean) parameter, and then applying a simple alternating procedure to get an estimate of the target location. In [22], the authors considered a worst-case scenario in which they assumed that all links are NLOS. Based on this, and the assumption that the magnitude of the NLOS bias is (imperfectly) known, a min-max problem was derived and a robust estimator given in a generalized trust region sub-problem (GTRS) framework was proposed. This work is inspired by the recently published work in [20], where the authors argued that fusion of RSS and TOA measurements does not necessarily bring benefit by default in comparison with RSS-only and/or TOA-only measurements. Based on a theoretical analysis, they determined a formula to compute the value of a _critical distance_, around which the hybrid measurements should offer gain, whereas for links far below or above this value, TOA-only and RSS-only measurements should dominate, respectively. It is a well known fact that RSS measurements are beneficial for short-ranges, whereas the TOA ones are well suited for long-range links [1]. Hence, the intuition presented in [20] is that if one measurement is much more accurate than the other one, there is little or no advantage in coupling them together, i.e., the more accurate measurement should be employed only. Nevertheless, in practice, the real challenge in this case is to know which of the measurements is more accurate. Even though the authors in [20] derived a formula to determine the critical distance, this formula is based on accurate knowledge of certain parameters (for instance, noise powers and path loss exponent (PLE)). This assumption is at least optimistic, since it is very unlikely that it stands in practice.