# GNSS Code Multipath Mitigation by Cascading Measurement Monitoring Techniques
## 1 Introduction
Stochastic model of measurements and weighting approach: The second approach includes solutions where monitoring metrics are used in weighting schemes to mitigate the effect of stochastic errors. In this approach, the variances of the GNSS measurements are continuously adapted based on monitoring metrics where the contribution of degraded measurements are potentially de-weighted in the position solution. This requires defining a relationship between the metric outputs and degradation in measurement precision and sometimes tuning model parameters [15]. Besides the elevation angle of satellites [16], Signal-to-Noise Ratio (SNR) and equivalently C/N\({}_{0}\) are well-known quality metrics investigated for the purpose of GNSS stochastic models and measurement weighting schemes. References [17; 18; 19] investigate the relationship between measurement precision and corresponding C/N\({}_{0}\) to develop the _SIGMA-\(\epsilon\)_ and _SIGMA-\(\Delta\)_ stochastic models to cope with signal attenuation, diffraction and NLOS conditions. Although initially developed for carrier phase measurements, it has been shown that these models are also beneficial for pseudoranges as discussed by References [20; 21; 22]. More recently, Reference [23] exploited C/N\({}_{0}\) measurements as a quality metric to weight GNSS measurements under multipath environments. Further investigations reported by Reference [24] examine the effectiveness of a C/N\({}_{0}\)-based weighting scheme for different multipath scenarios. Results show that although the C/N\({}_{0}\)-based solutions generally show improvement in positioning performance, as will be discussed later in this paper, they do not properly deal with gross errors caused by multipath. 3. Multipath detection for excluding or de-weighing affected measurements: Modern multi-constellation receivers are equipped with hundreds of channels resulting in an unprecedented level of measurement redundancy. Checking for measurement failures and selecting those least distorted by gross errors such as multipath are much less likely to result in degraded geometry than in the past. This requires design and implementation of proper algorithms to detect and exclude (or de-weight) affected measurements. Note that the term \"exclusion or de-weighting\" is used here to emphasize the fact that beside excluding detected measurements, the effect of gross errors caused by multipath can be reduced through de-weighting but not fully excluding these measurements. Although similar in methodology, this concept differs from stochastic weighting of measurements (discussed above) where the variances of the GNSS measurements are continuously adapted based on designed monitoring metrics to mitigate the effect of stochastic errors. References [25; 26] are a sample of recent work that show multipath errors can be specifically reduced by detecting and isolating the affected measurements when it does not significantly degrade solution geometry. Given the above, this paper investigates the use of measurement monitoring techniques to mitigate the effect of pseudorange multipath errors. In Section 2, a brief background is presented on the weighted Least-Squares (LS) solution for pseudorange-based positioning and the use of Dilution of Precision (DOP) to monitor the quality of the geometry. The three monitoring approaches, namely multipath error correction, stochastic weighting, and detection/exclusion (or-de-weighting) are discussed in Section 3. The main focus is on the third, where affected measurements are detected, excluded or de-weighted from the position solution. A C/N\({}_{0}\)-based multipath detection metric is investigated for a single-frequency receiver and two Differential C/N\({}_{0}\) (DC/N\({}_{0}\)) and Geometric-free (GF)-based detection metrics are presented and compared for a dual (multi) frequency receiver. Detection, exclusion and de-weighting strategies, used in this research, are discussed in Section 4.