# Analysis of the Relationship between Scintillation Parameters, Multipath and ROTI
## 1 Introduction  
Ionospheric scintillation is one of the main error sources that can reduce the quality of positioning outputs or even lead to loss of lock on satellites, and hence can cause significant errors in Global Navigation Satellite System (GNSS) receiver operation [1]. A series of methods have been implemented to mitigate scintillation effects on positioning. For instance, in [PERSON] et al. [2], the tracking error variances of GNSS receiver phase locked loop (PLL) and delay locked loop (DLL) is used to modify the least squares stochastic model and the positioning accuracy was shown to be improved by 17-21%. Furthermore, [PERSON] et al. [3] attempted to exclude scintillation affected satellites from the positioning calculation with the technique of receiver autonomous integrity monitoring (RAIM) specific for precise point positioning (PPP), which considerably improved the PPP accuracy. Loss of signal lock and cycle slips are the primary problems under scintillation, which are relatively severe when using asingle satellite constellation. Therefore, it was proposed that the data of GPS and GLONASS could be integrated to obtain more reliable positioning solutions under moderate to strong scintillation [4], which improves the accuracy of the positioning output by 60% compared to using GPS alone. By using these approaches, the effects of scintillation can be mitigated to a certain extent. However, specialized receivers that can generate the scintillation indices, namely the amplitude scintillation index (S4) and phase scintillation index (\(\sigma_{\varphi}\)) [5] are not available worldwide, which limits the application of these approaches. Though the S4 index can be computed with low-cost receivers or common geodetic GNSS receivers [6; 7], the \(\sigma_{\varphi}\) index cannot be generated in the same way. In order to overcome this problem, it is proposed to investigate the relationship of two parameters, namely multipath (MP) and rate of change of total electron content index (ROTI), that can be obtained from standard generic receivers to represent scintillation indices (S4 and \(\sigma_{\varphi}\)). Studies on the relationship between scintillation and MP or ROTI were initiated respectively by [PERSON] et al. [8] and [PERSON] et al. [9]. According to [PERSON] [8], a certain relationship can be observed between MP and scintillation parameters. Specifically, MP has a negative influence on the presentation of ionospheric scintillation [8]. [PERSON] et al. [10] also demonstrated an agreement between MP and scintillation parameters. It has been demonstrated previously that ROTI can be used to indicate the occurrence of scintillation [9]. It has been further demonstrated that the correlation between ROTI and scintillation parameters is strong with a correlation coefficient exceeding 0.6 on average, even higher than 0.8 sometimes [11]. In this paper, the relationship between MP and ROTI with S4 and \(\sigma_{\varphi}\) in both the spatial and temporal domains is investigated. Additionally, propagation patterns of all four parameters are studied to investigate the spatial similarity over time. The purpose of this study is to investigate the relationship of S4 and \(\sigma_{\varphi}\) with MP and ROTI. Several objectives are set as follows:  
1. Compare the time series plots of the four parameters to observe the temporal relationship to confirm if during periods of scintillation all parameters are similarly affected. 2. Thereafter, two types of 2D maps are constructed, mean value maps and occurrence percentage maps, where the former is to evaluate whether abnormally high value areas are in similar spatial regions and the latter is to investigate the referred areas with clearer outputs. As scintillation mainly occurs at night and in the early morning local time, the maps are first generated with a period of 6 h.
3. Furthermore, the maps with 5 min periods are generated to observe the relationship during times when the largest variations of the parameters are observed. 4.