# Evaluation of 5G Positioning Performance Based on UTDoA, AoA and Base-Station Selective Exclusion
## 3 Position Solution and Measurement Exclusion
### NLoS BS Exclusion Mechanism  
As already stated, positioning accuracy is hindered by many propagation effects such as multipath and NLoS, which may appear due to surrounding obstacles, particularly in urban environments. These circumstances have gradually increased the request for more accurate and reliable positioning solution, thus requiring the implementation of alternative measures to minimize such degradation. Our contribution towards this problem consists of a method [19] for detecting faulty measurements from BS affected by NLoS propagation. The method monitors the residuals resulting from the WLS positioning solution, inspired by the approach implemented by Receiver Autonomous Integrity Monitoring (RAIM) techniques in GNSS receivers. The fundamental concept behind the proposed technique is to check the redundancy of range measurements obtained from all available BSs in order to detect one faulty transmitter at a time [20]. The technique includes both a Fault Detection (FD) [21] and a Fault Detection and Exclusion (FDE) functionality (see Algorithm 1).  
In conditions of synchronization error among BSs and in the presence of NLoS signals, the proposed method aims to detect large biases induced into the measurements. The workflow diagram of measurement's monitoring depicted in Figure 2 shows the process of its functionality as follows:Calculate the pseudo-range residuals using all BSs in the scenario. Large residuals indicate that a measurement error (bias) might be present. Generally, to perform a fault detection, there must be at least one redundant observation available. Since we are working with TDoA measurements, a minimum of four BSs are needed to compute a 3D position, five BSs to detect a failure and six BSs to detect and exclude the faulty BS.
2. In order to distinguish between bias-free measurements and those subject to abnormal measurements, a measurable scalar parameter is defined to provide information about pseudo-range measurement errors. This parameter, named test statistic, is related to pseudo-range observations, and it is calculated as the normalized root sum square of the pseudo-range measurement residuals.
3. The test statistic is then compared with a detection threshold \(T\). If the test statistic exceeds the given threshold, a bias might be present in the measurements and the faulty BS identification is performed. Otherwise, the solution with all the BSs is used in the scenario.
4. If a failure is detected, we create subsets of BSs by setting one BS as serving for the TDoA measurements and removing one BS from the rest of BSs at a time, so that there will be \((M_{\text{BS}_{\text{TDoA}}}-1)\) subsets, each having \((M_{\text{BS}_{\text{TDoA}}}-1)\) BSs. The detection of the failure is achieved by performing a consistency check through the test statistic parameter for each of the subsets. The subset with the minimum test statistic that does not exceeds the given threshold is chosen to perform the location computation.
5. If the presence of degraded measurement errors is detected, but the faulty BS cannot be identified, the set of BSs that is used for the computation is selected to be the one whose test statistic is the smallest. The candidates' BSs sets (on which the test statistic is calculated) include the \((M_{\text{BS}_{\text{TDoA}}}-1)\) subsets and also the original set with all the available BS in the scenario. In any case, in such situation when the faulty BS cannot be identified, we recognize that the positioning accuracy remains degraded and does not improve as expected.