# GNSS Code Multipath Mitigation by Cascading Measurement Monitoring Techniques
## 6 Field Data Analysis
### Static Test
#### 6.1.2 Position Results  
A Least-Squares (LS) solution was used to provide epoch-by-epoch position results. Tropospheric and ionospheric corrections were applied based on [PERSON] [40] and Klobuchar [41] models respectively. A constant weight (no weight) solution was compared with the conventional elevation and C/N\({}_{0}\)-based weighting schemes. While the latter methods showed more or less similar results but better than the constant weight scheme, the C/N\({}_{0}\)-based model [20; 21; 22; 23] was chosen as a benchmark to evaluate the performance of detection and exclusion, CMC-based error correction and the combined methods. First, the performance of the detection and exclusion technique was investigated for GPS L1 positioning. The combination of detection results related to L1 frequency was considered to determine whether a GPS L1 measurement is affected by multipath or not. For exclusion or de-weighting of the detected measurements, the algorithms presented in Section 4.2 were considered. Due to the good visibility of satellites, the exclusion of detected measurements were used to isolate the effect of multipath as it showed higher performance than the iterative de-weighting approach. For exclusion, the consecutive method was used due to its relatively lower complexity compared to subset testing. An empirical value of 8 was chosen as an appropriate PDOP threshold to avoid geometrically poor solutions that would likely not benefit from measurement exclusion. In addition to the PDOP, Figure 10 shows the corresponding east, north and vertical DOP values before and after the detection and exclusion procedure. The DOP values have been calculated based on Equations (6) and (7). At each epoch, the detected measurements were first sorted based on their effect on measurement geometry from low to high and then were consecutively excluded until the tolerable PDOP value was satisfied. As observed, while excluding the affected measurements increases the DOP values, the latter remain under the tolerable thresholds desired to maintain the quality of the measurements geometry at a certain level. This is important since the ultimate position multipath error is a result of both measurement error and geometry. Figure 11 shows position errors for the collected data before (red) and after (blue) detection and exclusion in the local coordinate system. It is observed that there are epochs and intervals where exclusion increases the position errors in all or some directions. However, in conformity with the expectation presented in Section 4.2, by setting the appropriate PDOP threshold, exclusion improves overall position results. In fact, the PDOP threshold value of 8 was empirically determined to benefit from measurement exclusion most of the time. Increasing the threshold (to a larger PDOP) will increase the probability of position degradation (as a result of exclusion). The corresponding mean and RMS values are provided in Table 1 and labeled as A1 and A2. It is observed that positioning performance has improved in all three dimensions. Comparing 3D positioning RMS values, the detection/exclusion technique improves the performance of the C/N\({}_{0}\)-based weight Least-Squares (LS) solution by 27%. Figure 11: GPS L1 frequency position errors—C/N\({}_{0}\)-based LS solution with no correction or exclusion (red) and after detection and exclusion (blue). Figure 10: DOP values for GPS L1 positioning before and after exclusion of detected measurements. The performance of other monitoring solutions was also compared with the conventional C/N\({}_{0}\)-based LS solution as shown in Figure 12. First a C/N\({}_{0}\)-based LS solution with no exclusion or correction was considered, whose positioning results are in red. In the next step, CMC-based multipath corrections were examined where the estimated zero mean CMC values were applied to pseudoranges to alleviate code multipath errors (see Equation (10)). For this scenario, position errors are shown in blue.