Effects of GNSS Receiver Tuning on the PLL Tracking Jitter Estimation in the Presence of Ionospheric Scintillation

Ionospheric scintillation is an interference characterized by rapid and random fluctuations in radio frequency signals when passing through irregularities in the ionosphere. It can severely degrade the performance of Global Navigation Satellite System (GNSS) receivers, thus increasing positioning errors. Receivers with different tracking loop bandwidths and coherent integration times perform differently under scintillation. This study investigates the effects of GNSS receiver tracking loop tuning on scintillation monitoring and Phase Locked Loop (PLL) tracking jitter estimation using simulated GNSS data. The variation of carrier to noise density ratio (C/N0) under scintillation with different tracking loop settings is also studied. The results show that receiver tuning has a minor effect on scintillation indices calculation. The levels of C/N0 are also similar for different PLL bandwidths and integration times. Additionally, the tracking jitter is estimated by theoretical equations and verified using the relationship with the PLL discriminator output noise, which is calculated using the post‐correlation measurements. Novel approaches are further proposed to calculate 1‐s scintillation index, which enables to compute the tracking jitter at a rate of 1 s. It is found that 1‐s tracking jitter can successfully represent the signal fluctuations levels caused by scintillation. This work is valuable for developing scintillation sensitive tracking error models and is also of great significance for GNSS receiver design to mitigate scintillation effects.


Introduction
Ionospheric scintillation refers to the rapid and random fluctuations in radio frequency signal amplitude and phase. It occurs when signals traverse through ionospheric irregularities. The probability of scintillation occurrence is strongly related to solar and geomagnetic activity (Basu et al., 1988). Aarons (1982) suggested that scintillation is more frequent in equatorial regions and auroral to polar regions.
Scintillation is one of the most challenging error sources for Global Navigation Satellite System (GNSS). Because of scintillation, GNSS signals become noisier, thus receiver performance is degraded. The effects of scintillation on receiver take place notably at the tracking stage (Sreeja et al., 2011). On the one hand, the rapid fluctuations caused by scintillation in the incoming carrier phase will increase the Phase Locked Loop (PLL) tracking errors, which lead to a higher probability of cycle slip (Humphreys et al., 2010); when the increased tracking error exceeds the pull-in range of the discriminator, a loss of phase lock may occur (Kaplan & Hegarty, 2017). On the other hand, the amplitude fluctuations caused by scintillation may decrease the carrier to noise density ratio (C/N0); when it is lower than the receiver threshold, the Delay Locked Loop (DLL) will declare a loss of lock event, which causes signal loss. The increased probability of losing lock and a large tracking error will contribute to an increase in code and carrier phase measurement errors, leading to a degraded GNSS positioning accuracy (Guo, Aquino, Veettil, et al., 2019;Pi et al., 2017).
Much effort has been made to analyze and model the effects of ionospheric scintillation on GNSS receivers. Knight and Finn (1998) studied scintillation stochastic models and developed an approach to evaluate the scintillation effects on Global Positioning System (GPS). They pointed out that the levels of scintillation required to cause signal loss depends on the receiver tracking loop bandwidth, filter order, and discriminator type. In the study of Hegarty et al. (2001), a scintillation signal model was developed and GPS scintillation signals were generated. It was found that the typical noncoherent DLLs are relatively robust to signal fluctuations caused by scintillation, while PLLs are generally more susceptible to scintillation effects. To calculate the scintillation induced tracking error, Conker et al. (2003) proposed the PLL and the DLL tracking error variance equations to calculate tracking errors caused by different error sources. The 1-min scintillation indices and 1-min averaged C/N0 were input to those equations in the study to evaluate the tracking error variances caused by scintillation. An extended model was developed by Moraes et al. (2014) to describe the effects of the scintillation on GPS receivers. By processing scintillation data recorded in Brazil, the tracking error variance was estimated and receiver performance was analyzed. Vadakke Veettil et al. (2018) built statistical models to estimate the standard deviation of the receiver PLL tracking errors as a function of scintillation levels exploiting the models in Conker et al. (2003) and Moraes et al. (2014) using the scintillation data recorded over 4 years at low and high latitudes. Guo, Aquino, and Vadakke (2019) analyzed the signal intensity fading due to scintillation. The results showed that signal fading caused by scintillation can increase the receiver tracking error.
The effects of receiver PLL tracking loop bandwidth tuning on scintillation monitoring have been discussed in the literature. Orus-Perez and Prieto-Cerdeira (2011) compared the scintillation indices observed by two different commercial scintillation monitoring receivers, that is, Novatel GSV4004B and Septentrio PolaRxS. Results showed that both receivers present comparable performance in scintillation monitoring. Rougerie et al. (2016) studied the effects of GNSS receiver PLL bandwidth tuning on scintillation indices calculation. They suggested that receiver tuning has almost no effect on S4 and Phi60 calculation. The cut-off frequency can affect the shape of the phase spectrum. However, these analyses only focus on scintillation indices estimation with different receivers or receiver tracking loop parameters. The effects of receiver tuning on tracking jitter estimation under scintillation are not considered.
To address the above limitation, a hardware simulator is used to generate GNSS signals affected by different levels of scintillation. An ionospheric scintillation monitoring receiver (ISMR) is connected to the simulator to record the GPS scintillation data. The scintillation indices and C/N0 observed for different tracking loop parameters are studied. The PLL tracking jitter is estimated using the theoretical models with receiver tuning. Discriminator output noise levels are calculated to verify the values of the estimated tracking jitters. This study focuses on (1) understanding the effects of receiver tuning on scintillation monitoring and tracking jitter estimation under scintillation; (2) verifying the relationship between the tracking jitters estimated by theoretical models and calculated by the PLL discriminator output. Novel approaches are also proposed to calculate the 1-s scintillation indices, which enables to estimate the jitter at 1-s intervals. Scintillation data processing and scintillation indices calculation are introduced next, followed by the description of PLL tracking loop models and tracking jitter estimation methods under scintillation. The experimental set up and scintillation data processing flow are then introduced. Results and discussions are provided next. Conclusions and remarks are given at the end.

Ionospheric Scintillation
The S4 and Phi60 indices are used to characterize amplitude and phase scintillation intensity, respectively, which relate to fluctuations in amplitude and phase of radio frequency signals caused by ionospheric irregularities. S4 is defined as the standard deviation of the detrended signal intensity normalized by its mean over 60 s (Van Dierendonck et al., 1993;Van Dierendonck, 1999): where P det is the detrended signal intensity and ⟨·⟩ denotes arithmetic mean. The intensity detrending is accomplished by applying a sixth-order low pass Butterworth filter to the measured intensity P, which is calculated by  10.1029/2019SW002362

Space Weather
where I corr and Q corr are the 50 Hz post-correlation In-phase and Quadra-phase measurements, respectively. Readers interested in the intensity detrending process may refer to Van Dierendonck et al. (1993) and Van Dierendonck and Arbesser-Rastburg (2004) for more details.
As the ambient noise in the receiver also causes signal intensity fluctuation, the S4 total calculated by Equation 1 needs to be corrected to remove the ambient noise contribution. According to Van Dierendonck et al. (1993), the ambient noise contribution is given by where c/n 0 is fractional form of C/N0, calculated by c/n 0 = 10 0.1*C/N0 . Thus, the corrected S4 is calculated as (Van Dierendonck et al., 1993) The corrected S4 is employed to carry out the analysis in this study.
Phi60 is defined as the standard deviation of the detrended carrier phase measurements in 60 s, given by (Van Dierendonck, 1999) where φ det is the detrended carrier phase. The detrending of the carrier phase measurements is realized by passing the high frequency carrier phase measurements through a sixth-order high pass Butterworth filter with a cut-off frequency of 0.1 Hz (Van Dierendonck et al., 1993; and reference therein).
Power spectral density (PSD) of the detrended carrier phase measurements in 1 min is calculated to characterize phase scintillation in the frequency domain. The temporal power spectrum of the detrended carrier phase is given by (Rino, 1979) where f 0 is the frequency corresponding to the outer scale size of irregularities. p is the opposite of the slope of the line, that is fitted to the PSD in log-log axes over 0.1 to 25 Hz. T is the energy spectral  Space Weather density at 1 Hz, called spectral strength. When f ≫ f 0 , which is usually the practical case, S φ (f) ≈ Tf −p . More details regarding the spectrum analysis of scintillation can be found in Yeh and Liu (1982) and Strangeways (2009).
According to Rino (1979), the carrier phase variance is estimated by integrating Equation 6 over all the frequencies. Thus, in the practical case, the phase variance is calculated by (Aquino et al., 2007;Conker et al., 2003;Rino, 1979) Performing Equation 7, the following equation is obtained (Aquino et al., 2007): where r = 1 − p. Equation 8 presents the relationship among σ φ , p, and T. If the PSD is calculated using 1-min detrended carrier measurements, σ φ becomes the approximate of Phi60.

PLL Tracking Loop Models and Tracking Jitter Under Scintillation
The PLL tracking loop is implemented in coherent GNSS receivers to match the local replica of the received signal and to provide carrier phase measurements. A simplified linear PLL tracking loop model is demonstrated in Figure 1 (Gardner, 2005;Razavi et al., 2008;Van Dierendonck, 1996). The discriminator measures the tracking error Δφ, which is the difference between the incoming phase φ i and the receiver locally duplicated phase φ o . The output of the discriminator, denoted as δ φ , is filtered by the loop filter F(s). The output of F(s) is then input to Number Controlled Oscillator to provide an updated φ o , which feeds back to the tracking loop and matches with the incoming phase again (Braasch & Van Dierendonck, 1999;Kaplan & Hegarty, 2017).
The performance of the tracking loop is indicated by the tracking jitter, i.e., the standard deviation of the tracking error Δφ. The PLL tracking jitter under scintillation is given by (Conker et al., 2003;Knight & Finn, 1998) where σ 2 T is the thermal noise component taking the amplitude scintillation into consideration. σ pha is the phase scintillation induced tracking jitter. θ A is the tacking jitter due to oscillator noise. Under amplitude scintillation, the thermal noise is enhanced in the tracking loop in relation to S4 levels. According to Conker et al. (2003), the tracking jitter thermal noise component under scintillation is evaluated as where B n and η are the PLL bandwidth and coherent integration time, which are essential parameters selected by the designer of the receiver tracking loop. The selection of B n and η can affect the stability and sensitivity of the PLL in response to noise (Gardner, 2005). Equation 10 shows that σ 2 T is a function of S4 and C/N0, as well as PLL B n and η. It should be noted that the C/N0 here is the 60-s averaged value

10.1029/2019SW002362
Space Weather corresponding to the interval in which the scintillation index is calculated. When S4 is 0, Equation 10 becomes the standard thermal noise tracking error for carrier phase tracking, given by (Kaplan & Hegarty, 2017) The phase scintillation induced tracking jitter can be calculated through (Knight & Finn, 1998) ; 1 <p<2k; where k is the PLL loop order. f n is the loop natural frequency.
θ A is due to the instability of the oscillator in both the receiver and satellite clocks. As the GNSS satellites use a stable atomic clock, the satellite oscillator noise is ignorable. The receiver oscillator noise is constant for an individual receiver. According to Irsigler and Eissfeller (2002), for a third-order PLL, θ 2 A is calculated by where f L is the carrier frequency. h −2 , h −1 , and h 0 are clock parameters determined by the type of oscillator. The ISMR used in this study is implemented with an oven-controlled crystal oscillator. According to the clock parameters given by Irsigler and Eissfeller (2002), θ A is calculated as a function of B n on GPS L1 band, as Figure 2 shows. θ A is seen to be much higher when B n = 5 Hz compared with 10 and 15 Hz.
Equation 9 has been used in previous studies to evaluate the effect of scintillation on receiver tracking loops (Aquino et al., 2009;Sreeja et al., 2011;Strangeways et al., 2011;Vani et al., 2019). From Equations 9, 10, and 12, it can be known that the rate of scintillation indices determines the rate of the estimated tracking jitters.
The ISMR used in this analysis applies an arctangent discriminator. Thus, the PLL discriminator output is calculated as (Kaplan & Hegarty, 2017) and the standard deviation of discriminator output noise is given by On the other hand, according to Razavi et al. (2008), the discriminator output noise is considered as the sum of thermal noise σ 2 w and correlated noise σ 2 c , given by In this study, σ 2 c is mainly due to the oscillator noise and scintillation effects. From Equation 16, σ c is calculated by

Space Weather
It should be noted that the thermal noise in Equation 16 is the noise in the output of the discriminator, which is propagated through the closed-loop noise time-update function to the thermal noise in the tracking error variances, given by (Groves, 2013;Van Dierendonck et al., 1992) With Equations 16, 17, and 18, the tracking error can be estimated using the discriminator output by Equation 19 offers an alternative way to estimate the PLL carrier phase tracking jitter. It can help to validate the values of the tracking jitter estimated using Equation 9.

Experimental Setup and Data Processing Flow
The experimental setup to generate scintillation data and data processing flow is described in this section. As Figure 3 shows, a Spirent GNSS signal simulator-GSS8000-available at the University of Nottingham is used to generate GPS L1 signals. A user command file (.ucd file) is activated in the simulation to superimpose scintillation effects on the signals. The .ucd file used in this study was generated from a 2-hr real life scintillation data set collected at Presidente Prudente, a low latitude scintillation monitoring station near the geomagnetic equator in Brazil. A Septentrio PolaRxS Pro receiver is connected to the GSS8000 simulator to record the simulated GPS L1 data. The PolaRxS receiver is a multifrequency multiconstellation receiver dedicated to ionospheric monitoring (www.septentrio.com/en/support/polarx/polarxs). The receiver can output 50 Hz I corr and Q corr measurements and carrier phase data. The tracking loop bandwidth and the coherent integration time of the receiver can be configured by the user through a friendly graphical user interface. In this

10.1029/2019SW002362
Space Weather analysis, a total number of five simulations is carried out by configuring different B n and η. The configurations of the tracking loop for each case are summarized in Table 1. It is worth mentioning that Case 3 has the same parameters as the default receiver configuration. Clean data are also generated in Case 5 for comparison. Additionally, when the .ucd file is activated in the simulation, the same scintillation scenario is applied to all the visible satellites. Therefore, only one satellite is selected for the analysis in this study.
The 50 Hz I corr and Q corr measurements logged by the receiver in each case are used to calculate the signal intensity, which is then detrended to calculate S4 in the analysis. The 50 Hz carrier phase measurements are detrended directly and Phi60, p, T are calculated thereafter. The PLL tracking jitter is finally estimated, and comparisons are made for different tracking loop parameters. It should be noted that the C/N0 values logged by the receiver are used to carry out the analysis in this work.

Scintillation Index Calculation With Receiver Tuning
The calculated amplitude and phase scintillation indices under different tracking loop bandwidths and coherent integration times are initially presented in this section. Figure 4 shows the variation of S4 and Phi60 in relation to time. From the figure, both S4 and Phi60 are seen to increase between the 5th and 20th minute and the 40th and 60th minute. The strongest amplitude scintillation occurs at the 50th minute when S4 is around 0.62, while the largest Phi60 is observed at the 14th minute, with a value of around 0.50 rad. Additionally, the S4 indices calculated with different B n and η have few differences, which indicates that both loop bandwidth and integration time have almost no effect on S4 calculation. This agrees with the conclusions in Rougerie et al. (2016). Meanwhile, there are slight differences in Phi60 when B n and η are different, especially when Phi60 is higher than 0.2 rad. In Case 5 when scintillation effects are not added in the signal simulation, both S4 and Phi60 show extremely low levels.
The phase scintillation spectral slope p is then calculated for different tracking loop bandwidths and integration times, as shown in Figure 5. When the signal is affected by scintillation, the values of p are generally higher than 2. Increases in p values can be seen with the increase in scintillation levels between the 40th and 60th minute. When η is configured to 10 ms, the p values of tracking loop with B n of 5, 10, and 15 Hz are close, which means that the tracking loop bandwidth has low impacts on the p value estimation. By contrast, when integration time is increased to 20 ms, obvious higher values are seen, especially when scintillation levels are not strong between the 70th and 115th minute. Besides, p values are lower than 2 throughout in Case 5, which further suggests that the presence of scintillation can increase the p value. The averaged p values for each case are also summarized in Table 2. The effect of scintillation on the shape of the PSD curves and the calculation of p values will be explained in detail next.
To further understand the effects of ionospheric scintillation and receiver tuning on signal carrier phase spectrum characteristics, the PSD of the detrended carrier phase measurements is studied. Figure 6 gives an example of the calculated PSD curves of two different minutes with receiver default settings, i.e., B n = 15 Hz and η = 10 ms. The linear fitting functions of the PSD curves over 0.1 to 25 Hz in log-log axes are also included in the figure. As the figure shows, when there is no scintillation on the 116th minute, the phase power density curve, in pink, is relatively flat between 0.1 and 5 Hz. A large part of spectral energy is at high frequency. By contrast, when phase scintillation is present, as on the 14th minute, the PSD curve (in blue) obviously shifts upward resulting in an increased spectral energy. The spectral energy between 0.1 and 5 Hz also increases significantly, thus the curve has a steeper slope and a larger p value. It

Space Weather
should be noted that for both curves, the energy of the phase spectrum remains at a low level when the frequency is lower than 0.1 Hz. This is due to the effect of the high pass filter, which uses a cut-off frequency of 0.1 Hz. Figure 5 shows that the p values are not significantly influenced by the change in PLL bandwidth. However, the increase in integration time can correspondingly increase the values of p. To analyze the impact of η on the calculation of p, the PSD curves on the 116th minute, when Phi60 is around 0.02 rad, and on the 14th minute, with Phi60 around 0.50 rad, are calculated with B n set to 15 Hz and η set to 10 and 20 ms, respectively, as shown in Figure 7. When the scintillation effect is minor in the left panel, the PSD curves of both cases at low frequency are quite similar, while at high frequency, the spectrum energy is reduced by increasing the integration time from 10 to 20 ms. This results in a steeper slope of the fitted line between 0.1 and 25 Hz. However, on the right panel, the PSD curves of different integration times present similar patterns over all the frequency range, thus the slopes are close.

C/N0 Variation Under Scintillation
C/N0 is a crucial indicator of the signal strength and quality. According to Equation 11, the decrease in C/N0 can increase the thermal noise induced tracking jitter. In the presence of scintillation, particularly amplitude scintillation, C/N0 is attenuated to different extents due to the signal intensity fading (Seo et al., 2009), which further increases the tracking jitter. In this section, the C/N0 variation under scintillation with receiver tracking loop tuning is studied. Figure 8 presents the receiver output C/N0 in relation to time with different tracking loop bandwidths and integration times. In the case of clean data, the C/N0 values, marked by magenta pentagrams, increase gradually as a function of time, which is due to the increase in satellite elevation, while when scintillation is present, downward tendencies are seen during scintillation occurrence. Thus, it can be concluded that amplitude scintillation can decrease the signal C/N0 levels to different extents. Additionally, C/N0 values in the figure are quite close to each other when the PLL is configured with different B n and η, which means that receiver tuning has minor effects on signal C/N0 computation. It should be noted that the C/N0 values used here are the 1-min averaged value logged by the receiver.

C/N0 deviation between Case 3 and 5 can be calculated by
In these two cases, both tracking loops refer to receiver default configurations, so that the difference in C/N0 is mainly caused by scintillation effects. Figure 9 shows the C/N0 deviations as a function of S4. It can be seen that when the scintillation level is weak, i.e., S4 < 0.3, the deviations are distributed near 0. However, with the increase in S4, the C/N0 deviation tends to increase, which further indicates the attenuation effects of amplitude scintillation on C/N0. A statistical model can be established to describe the relationship between CN0 decreases and S4 levels if there are enough samples. This will be part of future study.
As the 1-s C/N0 values are also available from the PolaRxS receiver outputs, the variation of C/N0 within 60 s, i.e., one scintillation event period, is analyzed. Figure 10 presents an example of the 1-s C/N0 output in the 51st minute, when strong scintillation occurs, with S4 reaching 0.63. As the figure shows, the C/N0 values of different tracking loop parameters under scintillation effects are quite similar, which again confirms that receiver tracking loop tuning would not significantly influence C/N0 calculation under scintillation. C/N0 values of the scintillation affected signals fluctuate dramatically within 1 min. The highest C/N0 is more than 50 dBHz, which is

10.1029/2019SW002362
Space Weather much higher than the average value which is around 46 dBHz. Meanwhile, the C/N0 can be as low as almost 35 dBHz, which is far lower than the nominal values and will probably cause serious receiver tracking problems. On the contrary, in the case when clean data is simulated, the C/N0 remains relative stable around 46 dBHz over the whole minute. Thus, it can be seen that using 1-min averaged C/N0 to represent the signal strength and quality under scintillation is not accurate enough. The signal intensity may change significantly within 1 min.

Estimated PLL Tracking Jitters
The previous sections analyzed how the receiver tracking loop tuning affects scintillation indices calculation. In this section, the estimation of the PLL tracking jitter using Equation 9 with different tracking loop bandwidths and integration times is presented. It should be noted that, as θ A is considered to be constant once the tracking loop bandwidth is defined, only the analyses of σ pha and σ T are presented in this section.
The evaluated PLL σ pha and σ T under scintillation are shown in Figure 11. For comparison, the tracking jitter of clean signals (Case 5) is also included. It can be seen from the figure that σ pha is generally at low levels in all cases, except for one epoch at the 14th minute when Phi60 suddenly jumps to 0.5 rad and σ pha exceeds 0.06 rad in the first four cases. Thus, it might be concluded that phase scintillation will not cause serious tracking problems for most PLL settings when Phi60 < 0.4 rad. A sudden increase of Phi60 may cause extremely large tracking errors. This conclusion needs to be further verified by carrying out more experiments with stronger phase scintillation events. Additionally, when the receiver PLL bandwidth increases from 5 to 15 Hz, σ pha decreases gradually, although the difference is slight. The tracking loop when B n is set to 5 Hz has the largest σ pha . This indicates that the tracking loop with lower bandwidth is more susceptible to phase scintillation, which is in agreement with the conclusions by Knight and Finn (1998). Furthermore, it can be seen from the figure that in general, the increase in tracking loop integration time can slightly decrease the phase induced tracking jitter, as the σ pha in Case 4 is slightly lower than that of Case 3 where η is set to 10 ms.
The estimated σ T in each case is shown in Figure 12. With different loop bandwidths, the thermal noise jitter is generally at different levels, but following similar patterns. Obvious increases in σ T can be seen when scintillation becomes stronger. The PLL with B n of 5 Hz presents the smallest jitter over the whole period, even

10.1029/2019SW002362
Space Weather lower than that of the clean data of Case 5, while the largest values are seen on the tracking loop with B n = 15 Hz. This is reasonable as σ T is proportional to B n , as defined in Equation 11. Additionally, it can be seen that the values of σ T in Cases 3 and 4 are quite close, which means that the integration time has a minor effect on the tracking loop jitter.
As a result, a smaller B n will decrease the value of σ T . But this has an opposite effect for phase scintillation induced tracking jitter and oscillator noise, because both will increase with the decrease in B n . Therefore, there is a trade-off when selecting the PLL bandwidth in order to maximize the receiver performance in the presence of scintillation.

PLL Tracking Jitter Validation Using the Discriminator Output
High frequency I corr and Q corr measurements are not output by most commercial and generic receivers. Therefore, Equation 9 is commonly used to estimate the effect of scintillation on the PLL tracking performance. Equation 19 offers an alternative way to estimate the PLL carrier phase tracking jitter. In this study, the ISMR is capable of outputting 50 Hz I corr and Q corr data in the predetection integration process, which makes it possible to verify the values of tracking jitter estimated by Equation 9 using discriminator output errors. Figure 13 first presents the variation of σ δφ calculated using Equation 15 in relation to time. As the figure shows, σ δφ increases to different extents in each case during the scintillation period. The largest value is seen on the 14th minute when both S4 and Phi60 are at high levels. Additionally, σ δφ in Case 1 is generally higher when scintillation occurs, followed by that in Cases 2 and 3, which means the increase in B n can decrease the total discriminator output noise variance and improve the receiver tracking performance in the presence of scintillation. Furthermore, σ δφ in Case 4 is slightly higher than that in Case 3, indicating that a larger η may decrease the tracking loop jitter. This needs to be further verified with more scintillation events.
To validate the estimated tracking jitter using Equation 9, σ Δφ_discri is calculated using the discriminator output noise. Figure 14 shows the variation of σ Δφ and σ Δφ_discri with receiver tuning. The correlation coefficients along with the Root-Mean-Square (RMS) of the difference between σ Δφ and σ Δφ_discri are calculated and summarized in Table 3. It can be seen that for all the four cases, σ Δφ follows the pattern of σ Δφ_discri , although there are slight biases between σ Δφ and σ Δφ_discri . The total estimated tracking jitters σ Δφ in Cases 1, 2, and 3 are generally higher than σ Δφ_discri over the whole period, except in Case 1 when σ Δφ_discri overtakes σ Δφ during the scintillation occurrence. The RMSs of the differences for Cases 2 and 3 are less than 0.01 rad. In Case 4, σ Δφ is seen lower than σ Δφ_discri during all the period. The RMS of the difference is 0.0142 rad in this case, indicating that the increase in PLL integration time could result in underestimating the tracking jitter using Equation 9. Additionally, σ Δφ and σ Δφ_discri are seen to be highly correlated for these four cases. Obvious increases are seen during the scintillation occurrence. This means both of σ Δφ and σ Δφ_discri are sensitive to scintillation effects. Moreover, the estimated tracking jitter σ Δφ is seen to be more stable than σ Δφ_discri in all the cases. The explanation may be that when estimating the tracking jitter, Equation 10 uses the 1-min averaged C/N0, therefore not accounting for the C/N0 fluctuations within 1 min in the calculation, while, for the calculation of σ Δφ_discri based on I corr and Q corr , every measurement is taken into account. The variation of C/N0 within 1 min is thus reflected.
In order to further verify the relationship between σ Δφ and σ Δφ_discri at a rate of 1 s, the 1-s tracking jitter and discriminator noise are calculated. The 1-s σ δφ is easy to obtain by using Equation 15 at 1 s intervals, whereas, to estimate tracking jitter σ Δφ using Equation 9 at a

10.1029/2019SW002362
Space Weather rate of 1 s, 1-s scintillation indices are required. Therefore, the following approaches are proposed in this study to calculate the 1-s scintillation indices: 1. The 1-s amplitude scintillation index, denoted as S4 − , is calculated using the same data processing method for the calculation of S4, except that the normalization is performed within 1 s. Then, σ T is computed using Equation 10 with the S4 − and 1-s C/N0 output by the receiver. 2. With 50 Hz carrier phase measurements, there are not enough number of samples to calculate the phase PSD in 1 s, thus the p and T indices for phase scintillation cannot be evaluated according to the approaches described in section 2. According to Aquino et al. (2007), the 1-hr averaged spectral slope p can lead to values of T in close agreement with those estimated by 1-min discrete of p. Additionally, the 1-s σ φ can be estimated using 50 Hz detrended carrier measurements. Thus, with the hourly averaged p, 1-s T can be estimated using Equation 8. The 1-s σ pha is consequently calculated using the estimated p and T at a rate of 1 s. Figure 15 shows the 1-s amplitude scintillation index in the 51st minute of Case 3. It can be seen from the top panel that the signal intensity and C/N0 fluctuate significantly within the minute. The difference between the maximum and minimum C/N0 can be as large as 15 dBHz, indicating the severe effects of amplitude scintillation on signal quality. The 1-s amplitude scintillation index S4 − in the bottom panel shows the levels of signal fluctuations in each second. When the signal intensity suffers from dramatic variations, e.g., on the 33rd, 35th, 51st second, S4 − increases correspondingly. The largest S4 − and minimum C/N0 both occur on the 51st second with S4 − = 0.62 and C/N0 = 35.5 dBHz. Figure 16 shows the histograms of 1-s S4 − samples as a function of 1-m S4 when it equals to 0.3, 0.4, 0.5, and 0.6 in Case 3. It can be seen that for all these four levels of S4, the 1-s amplitude scintillation index with S4 − = 0.1 has the largest frequency. When S4 is 0.5 or 0.6, most values of S4 − are less than 0.4, which indicates that even when S4 shows the moderate levels of scintillation, there are large parts of weak scintillation within the S4 calculation period.
The 1-s phase scintillation σ φ and T as well as the variation of the detrended carrier phase measurements in the 51st minute of Case 3 are presented in Figure 17. The detrended carrier phase in the top

Space Weather
panel is seen to vary rapidly, leading to the increases in both 1-s σ φ and T indices. σ φ and T present good correlation within this minute. The largest σ φ and T indices are both seen on the 54th second. The 1-s scintillation indices are used to further calculate the 1-s tracking jitters, which is shown thereafter.
The variations of the 1-s σ Δφ and σ Δφ_discri in the 51st minute of Case 3 are shown in Figure 18. As it can be seen from the figure, tracking jitter shows more fluctuations compared with Figure 14-this is because that using 1-s scintillation indices and C/N0 to calculate the tracking jitters can reflect more details of the signal fluctuations under scintillation. The values of σ Δφ and σ Δφ_discri are seen to be closer and to follow similar patterns. In Case 4, when B n is 15 Hz and η is 20 ms, σ Δφ is seen to be less than σ Δφ_discri over the corresponding period of time, which is in agreement with the results shown in Figure 14. The increases in σ Δφ and σ Δφ_discri are directly related to the increase of signal fluctuation, which is also represented by the scintillation indices in Figures 15 and 17. In Cases 2, 3, and 4, the largest σ Δφ and σ Δφ_discri is seen on the 51st second, when exactly the largest S4 − and minimum C/N0 occurs. However, in Case 1, the largest σ Δφ and σ Δφ_discri is seen on the 54th second, when strong phase scintillation occurs. This further verifies that tracking loop with lower bandwidth is more susceptible to phase scintillation.
The RMS of the difference and correlation coefficients between σ Δφ and σ Δφ_discri for each case shown in Figure 18 are summarized in Table 4. The theoretical tracking jitter σ Δφ in Cases 2 and 3 presents the relatively close values to σ Δφ_discri , with RMS of the difference less than 0.01 rad. Additionally, σ Δφ is seen to highly correlate with σ Δφ_discri for all the cases, which means that both σ Δφ and σ Δφ_discri are sensitive to the tracking errors caused by scintillation. Thus, it can be concluded that when high frequency post-correlation I corr and Q corr measurements are available, the value of σ Δφ_discri can be used to verify the values of tracking jitters estimated using Equation 9 under scintillation. Moreover, the 1-s scintillation indices and tracking jitters can successfully represent the signal fluctuation under scintillation and tracking loop performance. More details of the signal distortion caused by scintillation can be reflected compared with the tracking jitter calculated every 1 min. However, there are still differences between σ Δφ and σ Δφ_discri , especially when PLL bandwidth is set to 5 Hz. Therefore, more advanced models need to be  Space Weather developed to better account for scintillation effects on the GNSS receiver tracking loops. This will be the focus of the future work.

Conclusions and Remarks
This work analyzes the effects of receiver tracking loop tuning on ionospheric scintillation monitoring and PLL tracking jitter estimation. A hardware signal simulator is used to generate GPS scintillation data, which is recorded by a Septentrio ISMR. The following conclusions can be drawn based on the analysis: 1. By investigating the effects of receiver tuning on scintillation monitoring, it is found that S4 is less affected by both loop bandwidth and integration time, while for Phi60, very slight differences are seen with different loop configurations. When scintillation effects are minor, a large part of the spectral power is at high frequency, while, in the presence of scintillation, the spectral energy between 0.1 and 5 Hz increases significantly. Therefore, the phase PSD curve has a steeper slope. Additionally, the results show that p values are not related to the PLL bandwidth. However, the increase in PLL tracking loop integration time can correspondingly increase the values of p. 2. In the study of C/N0 variation under scintillation, C/N0 present quite similar values when PLL is configured with different tracking loop parameters, which leads to conclude that receiver tuning has minor effects on signal C/N0 computation under scintillation. By comparing the C/N0 differences between scintillation affected and clean signals, it is found that C/N0 deviation tends to increase with the increase in S4. A model can be established to describe the relationship between C/N0 and S4 levels with more scintillation data samples. This will be part of future study. The variation of 1-s C/N0 within 60 s is analyzed under strong amplitude scintillation. C/N0 values are seen to fluctuate dramatically. Thus, the conclusion can be drawn that using 1-min averaged C/N0 to represent the signal strength and quality under scintillation is not accurate enough as the signal may change significantly within 1 min. 3. By studying the estimated tracking jitter with receiver tracking loop tuning, it is found that the increase in PLL bandwidth can decrease the levels of σ pha . This indicates that the tracking loop with lower bandwidth is more susceptible to phase scintillation. However, σ T increases with the increase in B n . Therefore, there is a trade-off when selecting the tracking loop bandwidth in order to maximize the receiver performance in the presence of scintillation. 4. By comparing the 1-min theoretically estimated tracking jitter σ Δφ and the tracking jitter σ Δφ_discri estimated using the discriminator output noise, it is seen that σ Δφ is approximately close to σ Δφ_discri although there are slight biases. In order to calculate tracking jitter at a rate of 1 s, new approaches are proposed to estimate the tracking jitter at 1-s intervals. The results show that 1-s scintillation indices and tracking jitters can successfully represent the signal fluctuation under scintillation and tracking loop performance. More details of the signal distortion caused by scintillation can be reflected compared with the tracking jitter calculated every 1 min. Additionally, the values of 1-s σ Δφ are seen to approximately match σ Δφ_discri , except when B n = 5 Hz. This may be due to the fact that the theoretical equations in Conker et al. (2003) are not performing well with low loop bandwidth. More advanced models need to be developed to better account for scintillation effects on the GNSS receiver tracking loops. This will be the focus of the future work.