# Hybrid TOA/RSS Range-Based Localization with Self-Calibration in Asynchronous Wireless Networks
## 1 Introduction
Similarly to [35], the final target location is estimated by resorting to a robust bisection procedure within a generalized trust region framework. It is worth noting that almost all the aforementioned localization schemes based on hybrid TOA/RSS measurements require that a partial or even perfect knowledge of the model parameters is available. Moreover, in most cases all the nodes in the network are implicitly assumed to be perfectly synchronized among each other. Although these assumptions are typically used to reduce the high dimensionality of the cost functions involved in the position estimation process, in practical WSN deployments, nodes are not synchronized to the same clock and all the model parameters are unknown, hence the need to be adaptively estimated \"on the field\". Furthermore, in most operational scenarios, such as indoor environments and urban areas, the presence of dynamic obstacles (people, vehicles, etc.) introduces significant modifications in the surrounding environments, leading to channel characteristics that are non-stationary over time. Therefore, to address the problem of target localization in real applications, a preliminary calibration phase aimed at estimating the unknown channel parameters at run-time should be performed. On the one hand, such a procedure must be as simple as possible in order to suit multiple real-time re-calibrations even in low-cost applications; on the other hand, it must be fully automatic, that is, it should not require any external assistance, including human interventions and frequent configurations--for this reason, such a feature can be also called _self-calibration_. In this paper, we address the problem of target localization based on the combined use of TOA and RSS measurements under the realistic case of self-calibrated parameters. This work is motivated by the analysis conducted in [43], where it is highlighted the biased nature of the distance estimates obtained via RSS-only ranging in case of self-calibrated channel parameters. The main objective of this paper is to investigate how a dynamic estimation of the TOA and RSS model parameters will impact the ultimate position estimation performance of joint TOA/RSS range-based localization. To this aim, we extended our previous work [44] by considering, in addition to the hybrid TOA/RSS range estimator proposed therein, a preliminary self-calibration stage and a final position estimation stage. In particular, differently from [44] where all the parameters are assumed to be known, in this paper, we consider the more realistic case where the model parameters are estimated \"on the field\" according to a self-calibration procedure (described in Section 3.1). Moreover, we explicitly address the problem of nodes synchronization by including the clock offsets in all the considered models, as opposed to [44], where nodes are assumed to be synchronized. Our results show that using estimated parameters in place of the ideal (true) ones introduces detrimental non-linear effects that cannot be easily mitigated, and may lead to localization errors that can be significantly bigger than those obtained assuming a perfect knowledge of the environment; nonetheless, the provided algorithm is able to perform the whole localization task in a real environment and in a fully automatic (unsupervised) way. Summarizing, the paper provides a two-fold contribution. First, we formalize the hybrid TOA/RSS localization problem in presence of synchronization errors among all the nodes in the network, and derive the corresponding joint maximum likelihood (ML) estimator of target position and nuisance parameters. As we will see, such an estimator does not admit a closed form solution; moreover, due to the large number of nuisance parameters in the final cost function, a numerical optimization is practically unfeasible.