# GNSS Code Multipath Mitigation by Cascading Measurement Monitoring Techniques
## 3 Measurement Monitoring Techniques for Multipath Mitigation
### Multipath Detection for Excluding or De-Weighing Affected Measurements  
Along with the stochastic modeling of the measurements, gross errors caused by multipath can be specifically reduced by detecting and excluding or de-weighting affected measurements. Thanks to the development of multi-GNSS constellation receivers, this approach is increasingly effective as the redundancy is sufficiently large to detect and exclude (or de-weight) faulty measurements. Two conventional C/N\({}_{0}\)-based detection metrics are discussed and a new Geometry-free (GF) monitoring metric is then presented for more reliable multipath detection. * C/N\({}_{0}\) as a single-frequency monitoring metric for detection  
In addition to being used in stochastic modelling of measurements, C/N\({}_{0}\) is conventionally used for detection of degraded measurements [29; 30]. Under multipath conditions, C/N\({}_{0}\) fluctuates as a result of the superposition of direct and one or more reflected signals. These fluctuations can be monitored to de-weight or exclude affected measurements. * Differential C/N\({}_{0}\) (DC/N\({}_{0}\))-based monitoring metric for detection  
Having measurements on more than one carrier frequency provides auxiliary information that can be used for multipath detection. Depending on the phase lag of the reflected signal with respect to the direct signal, multipath interference on the measured C/N\({}_{0}\) can be either constructive or destructive. However, as the phase lag is frequency dependent, the C/N\({}_{0}\) is affected differently on each frequency. Thus, by differencing C/N\({}_{0}\) measurements, multipath can be detected. The desired detection metric is defined as  
\[m_{DC/N_{0},i}(k)=(C/N_{0})_{i}^{f1}(k)-(C/N_{0})_{i}^{f2}(k)-\Delta C_{i}^{f1 /2}(k), \tag{12}\]  
where \(m_{DC/N_{0},i}(k)\) is the differential C/N\({}_{0}\)-based detection metric for the \(i\)th satellite at the \(k\)th monitoring epoch, \((C/N_{0})_{i}^{f1}(k)\) and \((C/N_{0})_{i}^{f2}(k)\) the corresponding C/N\({}_{0}\) values (in dB-Hz) for \(f1\) and \(f2\) frequencies and \(\Delta C_{i}^{f1/2}(k)\) is the corresponding nominal C/N\({}_{0}\) differences (between \(f1\) and \(f2\)) under multipath-free conditions. \(\Delta C_{i}^{f1/2}(k)\) is mostly a function of satellite elevation due to non-proportional frequency-based receiver antenna gain for different elevation angles. \(\Delta C_{i}^{f1/2}(k)\) can either be estimated by time-averaging or modeled through calibration or the use of a reference antenna. As an advantage, differencing two or more C/N\({}_{0}\) measurements (in dB-Hz) from different carrier frequencies cancels out the effect of frequency-independent and proportional frequency-dependent parameters and the rest can be calibrated more easily based on receiver antenna gain for different arrival directions. By differencing the measured C/N\({}_{0}\) values on two frequencies, two scenarios are considered. First, when the deviation from the nominal value occurs with opposite signs on two frequencies the multipath signature is magnified. Second is the case when the C/N\({}_{0}\) deviations occur with the same sign on two frequencies resulting in lower multipath visibility in the output of the differential metric. Hence, the detection procedure will be more reliable if three (or more) frequencies are used since the phase of the multipath on three frequencies is less likely to be consistent than two [30]. The output of C/N\({}_{0}\) differences will also be an indication of multipath for at least one of the constituent frequencies, but it is not possible to distinguish which one. For both single-frequency C/N\({}_{0}\) and DC/N\({}_{0}\)-based detection metrics, for a given Signal-to-Multipath Ratio (SMR), a shorter multipath delay imposes a greater effect on the monitoring metrics because the direct and reflected correlation peaks will be closer to each other, resulting in a larger distortion of the computed C/N\({}_{0}\) value.