# Robot Localisation Using UHF-RFID Tags: A Kalman Smoother Approach +
## 5 Discussion  
The focus of the presented solution is to determine the best possible estimate of the whole trajectory followed by the agent inside a plant using an EKF-based smoother rather than an EKF. This issue turns to be very relevant in an actual industrial application where the knowledge of set of trajectories followed by the different moving agents is extremely important to detect points of failures as well as to optimise the team trajectories as a whole. As discussed in the Introduction, different RFID-based localisation systems were designed in the literature. Although some solutions rely on the combination of phase and amplitude measurements [26; 33], phase-only measurements prove to be quite effective in indoor environments [21]. To account for the phase ambiguity, different filters were provided that are based on the fusion with wheel encoders, ranging from Unscented Kalman Filters (UKF) [37], Multi-Hypothesis EKF [32] and particle filters [35].  
Nevertheless, this paper marks a non negligible difference since it proposes a smoother EKF-RTS to deal with the peculiarity of the phase measurements, which inherently need measurement differences to retrieve useful quantities. In particular, we presented an EKF-RTS smoother to reconstruct the whole trajectory of a unicycle-like vehicle moving in an industrial environment. The analysis of the uncertainty affecting the estimates in a realistic warehouse scenario with only four RFID tags is presented and compared with a standard EKF approach. We have also proved that the smoother may be endowed with a tuning parameter, i.e., the length of the observation window \(n\), whose value leverages between the performance of the filter and the computational requirements. Another important feature that is totally missed in the cited literature, is related to the robustness of the solution when measurements are missing, which again marks a notable performance improvement with respect to a filter-based solution, i.e., the EKF. We have additionally explicitly accounted for the relative robot displacement between consecutive RFID tag phase readings, which may jeopardise the solution performance. This tradeoff was also analysed and exposed in the experimental section, where on-field results have been collected and a specific collection of data has been conceived and reported.  
To summarise, the proposed smoother-based solution proved to be more effective of a standard filter and demonstrated its viability, effectiveness and feasibility in a real-time scenario by means of the tuning parameter \(n\). The shortcomings and the advantages of the proposed solution have been throughly exposed and discussed with simulations and experiments.  
**Author Contributions:** Conceptualisation, F.S. and D.F.; software, F.S. and A.M.; methodology, validation, resources, writing, review and editing, all the authors. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported in part by University of Pisa within the Project AURORA of the \"Bando Dimostratori Tecnologici\" (D.R 1528, 13 September 2018), in part by the Regione Toscana (FOR FESR 2014-2020-Line 1--RD Strategic Projects) under Project IREAD4.0 (CUP number: 7165.24052017.112000028) and in part by the Italian Ministry of Education, University and Research (MIUR) through the PRIN project no. 2017 NS9 FY entitled \"Realtime Control of 5G Wireless Networks: Taming the Complexity of Future Transmission and Computation Challenges\". The views and opinions expressed in this work are those of the authors and do not necessarily reflect those of the funding institution.