# Employing Ray-Tracing and Least-Squares Support Vector Machines for Localisation +
## 1 Introduction  
Localisation in multipath environments has been a challenge for mobile wireless systems. Global Navigation Satellite Systems (GNSS) like GPS have been the default go-to technologies for localisation and navigation, but these have also performed poorly in urban areas because of multipath propagation and blockage of the satellite in urban canyons. GNSS systems are not able to provide indoor localisation and navigation. Multi-GNSS systems improve location accuracy, but still have been reported to have achieved a best-case 2-D accuracy of 40m, in a worst-case urban canyon environment [1]. These issues have instigated research into mobile wireless localisation.  
Positioning systems that make use of mobile radio systems determine the location by first determining the range (distance from the base-station (BS)) of the mobile station (MS) or user equipment (UE). Time delay measurements or the power level of the received signal are used in trilateration and Angle-of-Arrival (AOA) measurements are used in triangulation. For triangulation, the challenge is to determine the true line-of-sight (LOS) angle of arrival at the BS, which is a difficult task in urban multipath environments, when all signals arriving at the BS are in non-line-of-sight (NLOS). In trilateration, the time delay measurements generally consist of a positive bias due to multipath. Both of the above cases give rise to the need for NLOS identification and mitigation.  
The use of Least-Square Support Vector Machines (LSSVMs) to address the challenges of localisation in NLOS environments is becoming popular. Already LSSVMs have been shown tobe effective for NLOS identification and mitigation in urban environments [2]. In this article, we show a direct scheme, that provides for localisation of the mobile station, without needing to go through NLOS identification and mitigation processes [3]. We also compare the performance of both approaches in different environments. Ray tracing data for the greater city of Bristol is used in the study. We use NLOS identification and mitigation, and the localisation algorithms discussed in [2], to compare with the Direct method. Detailed discussion on other NLOS identification and mitigation techniques can be found in [4].  
Related approaches like fingerprinting [5] involve matching the received signal quantities, commonly the received signal strength, to the values that are pre-recorded in the fingerprinting database, for any particular environment. A fingerprinting database is built by taking or collecting measurements per grid, of the area of interest. Positioning accuracy in this scheme, therefore, depends on the grid size used. Fingerprinting requires cell matching before correlation with grids around that cell, whereas the LSSVM method discussed here, handles BS matching and location estimation within the same framework. Also, fingerprinting employs either probabilistic algorithms, such as maximum likelihood, to estimate the position or deterministic algorithms that calculate the similarity between the UE measurement and the database grid-based measurements. Because of the challenges and limitations of fingerprinting, it is commonly considered as an augmenting scheme to other approaches to improve accuracy. Ray-tracing has also been demonstrated to be an effective approach for localisation, including when used together with finger-printing [6; 7; 8].