# GNSS Code Multipath Mitigation by Cascading Measurement Monitoring Techniques
## 4 Detection, Exclusion and De-Weighting Strategies
### Exclusion and De-Weighting of Affected Measurements  
Once multipath is detected, its effect can be reduced by excluding or de-weighting the affected measurement(s). The critical point is the effect of exclusion or de-weighting on measurement geometry. Poor geometry may magnify the effect of remaining errors on position solution. Since position is the major concern, PDOP is adopted as a quality metric to monitor the effect of exclusion or de-weighting on measurement geometry. The strategy allows the exclusion or de-weighting of detected measurements for the epochs where the corresponding PDOP values, before and after exclusion or de-weighting, remain at a fair level (e.g., below 8 as discussed by [20,34]). The following three geometry-based approaches are investigated. Although not based on rigorous statistical theory, the proposed methods can reduce or potentially eliminate the effect of multipath, as it will be shown in the data analysis section. **Measurement subset testing:** This includes exclusion of a subset of the detected measurements which have the least impact on measurement geometry below the tolerable PDOP threshold. This is done by calculating PDOP for several different combinations of detected measurements in order to locate the subset with the least impact on measurement geometry. Although optimized in finding the subset with least impact on geometry, measurement subset testing is computationally heavy. With \(N_{s}\) satellites tracked and \(N_{d}\) detected as affected by multipath, the \(\sum\limits_{n=1}^{N_{d}}\left( \begin{array}{c}N_{s}\\ n\end{array} \right)\) combinations must be tested. Due to the computational burden of this method, an alternative solution is considered in this research labeled _consecutive exclusion_ and is explained as follows. **Consecutive exclusion:** Detected measurements can be consecutively excluded until the PDOP exceeds a tolerable threshold. The detected measurements are sorted based on an exclusion priority, which can be determined based on different criteria such as the value of corresponding CMC, C/N0, elevation and residuals or the effect of each on the measurement geometry. The last criterion is used in this paper where the maximum number of PDOP adjustments is given by \(\sum\limits_{i=0}^{N_{d}-1}\left(N_{d}-i\right)\). Figure 1 shows this procedure when the effect of each exclusion on measurement geometry is considered as the exclusion priority. Although not optimized to determine the best subset in terms of geometry, consecutive exclusion is preferred to subset testing when the number of affected measurements increases due to its lower computational burden. In the case of a single multipath detection, both methods are equivalent [35]. This methodology is similar to the _Data Snooping_ reliability test that is usually performed using least-squares residuals [27]. **Iterative change of measurement weights or de-weighting**: This method retains all measurements but iteratively reduces their contribution to the solution if multipath is detected. This differs from measurement stochastic weighting which aims to deal with stochastic errors rather than gross errors caused by multipath. The main idea is based on the _Danish method_[20; 21] which changes the weight of measurement according to normalized residuals. Here, based on the monitoring results, the procedure iteratively decreases the contribution of the detected measurements by increasing the corresponding variance factors. The method continues until the tolerable PDOP threshold is exceeded. Figure 2 shows the geometry-based iterative change of measurement weights using a  
Figure 1: Consecutive Exclusion: Based on applying a series of consecutive tests to exclude the detected measurements until the tolerable PDOP threshold is satisfied. Exclusion priority is defined based on the effect of each single exclusion on measurement geometry. pre-defined increasing function (e.g., linear or exponential).