Surveys in Geophysics

, Volume 33, Issue 5, pp 1107–1131

Analysis of the Characteristics of Low-Latitude GPS Amplitude Scintillation Measured During Solar Maximum Conditions and Implications for Receiver Performance

Authors

    • Instituto Tecnológico de Aeronáutica (ITA)
  • Fabiano da Silveira Rodrigues
    • Atmospheric & Space Technology Research Associates (ASTRA)
  • Waldecir João Perrella
    • Instituto Tecnológico de Aeronáutica (ITA)
  • Eurico Rodrigues de Paula
    • Instituto Nacional de Pesquisas Espaciais (INPE)
Article

DOI: 10.1007/s10712-011-9161-z

Cite this article as:
de Oliveira Moraes, A., da Silveira Rodrigues, F., Perrella, W.J. et al. Surv Geophys (2012) 33: 1107. doi:10.1007/s10712-011-9161-z

Abstract

Ionospheric scintillations are fluctuations in the phase and/or amplitude of trans-ionospheric radio signals caused by electron density irregularities in the ionosphere. A better understanding of the scintillation pattern is important to make a better assessment of GPS receiver performance, for instance. Additionally, scintillation can be used as a tool for remote sensing of ionospheric irregularities. Therefore, the study of ionospheric scintillation has both scientific as well as technological implications. In the past few years, there has been a significant advance in the methods for analysis of scintillation and in our understanding of the impact of scintillation on GPS receiver performance. In this work, we revisit some of the existing methods of analysis of scintillation, propose an alternative approach, and apply these techniques in a comprehensive study of the characteristics of amplitude scintillation. This comprehensive study made use of 32 days of high-rate (50 Hz) measurements made by a GPS-based scintillation monitor located in São José dos Campos, Brazil (23.2°S, 45.9°W, −17.5° dip latitude) near the Equatorial Anomaly during high solar flux conditions. The variability of the decorrelation time (τ0) of scintillation patterns is presented as a function of scintillation severity index (S4). We found that the values of τ0 tend to decrease with the increase of S4, confirming the results of previous studies. In addition, we found that, at least for the measurements made during this campaign, averaged values of τ0 (for fixed S4 index values) did not vary much as a function of local time. Our results also indicate a significant impact of τ0 in the GPS carrier loop performance for S4 ≥ 0.7. An alternative way to compute the probability of cycle slip that takes into account the fading duration time is also presented. The results of this approach show a 38% probability of cycle slips during strong scintillation scenarios (S4 close to 1 and τ0 near 0.2 s). Finally, we present results of an analysis of the individual amplitude fades observed in our set of measurements. This analysis suggests that users operating GPS receivers with C/N0 thresholds around 30 dB-Hz and above can be affected significantly by low-latitude scintillation.

Keywords

IonosphereGPSScintillationReceiver performanceSolar maximum

1 Introduction

The ionosphere is known to have two types of detrimental effects on radio signals used for satellite-based navigation systems such as the Global Positioning System (GPS). The first effect is the additional delay in the signals used for estimation of pseudo-ranges and pseudo-phases (Klobuchar 1987). The second effect is the fluctuation in the amplitude or phase of the transmitted signals, commonly referred to as ionospheric scintillation (e.g., Fremouw et al. 1978; Yeh and Liu 1982). Ionospheric scintillation can cause excessive stress in GPS signal tracking, which can lead to loss of phase or code lock and, consequently, poor navigation performance. The effects of the ionospheric delay can be mitigated, in most part, using an estimate of the phase difference between two signals with closely spaced frequencies (Klobuchar 1996). This is the approach used by dual-frequency GPS receivers. Single-frequency receivers, however, must rely on independent estimates of the ionospheric delay for corrections in their position estimates. The effects of scintillation are more difficult to mitigate and require the application of specialized signal processing techniques so that the receiver does not lose track of the signal carrier and code. Therefore, it is useful to know the main characteristics of the scintillating signals in order to adequately design the receiver.

Scintillation is caused by electron density fluctuations in the ionosphere across the path traveled by the radio signal from the satellite to the receiver. The fluctuations in electron density cause perturbations in the index of refraction (n) of the medium (the ionosphere), which in turn cause diffraction of the radio waves. Multiple diffracted wavefronts, with different phases, reach the antenna receiver at the same time. Because the ionospheric irregularities causing the diffraction as well as the GPS satellites are moving, the receiver experiences alternating periods of constructive/destructive signal interference, and fluctuations in the phase and amplitude of the received signal develop. Ionospheric scintillation is known to affect the performance of GPS receivers at various levels (Aquino et al. 2005; Beniguel et al. 2004; Conker et al. 2003).

Recently, a number of different research efforts have focused on the characteristics of the GPS signal under scintillation conditions and investigation of GPS receiver performance under those conditions (e.g., Knight and Finn 1998; Knight et al. 2000; Groves et al. 2000, Hegarty et al. 2001; Conker et al. 2003; Beniguel et al. 2004; Ganguly et al. 2004; Morrissey et al. 2004; Humphreys et al. 2005, 2009, 2010; Kintner et al. 2005; Dubey et al. 2006; Hinks et al. 2008; Seo et al. 2009; Zhang and Morton 2009; Yang et al. 2011). Conker et al. (2003) and Beniguel et al. (2004), for instance, considered the occurrence of loss of phase lock when the carrier phase error, \( \sigma_{\phi \varepsilon }^{2} \), exceeded a threshold. In this approach, \( \sigma_{\phi \varepsilon }^{2} \) is estimated using the amplitude scintillation index S4 as an input and assuming a linear model for the phase locked loop (PLL). The assumption is useful for moderate scintillation scenarios, but fails to realistically predict the performance of the PLL during strong scintillation (Humphreys et al. 2010). This is, among other things, because these models do not take into account the decorrelation time (τ0) of the amplitude scintillation patterns. The decorrelation time is an important parameter since signal tracking is particularly difficult during fast (small τ0 values) and deep fading events (Humphreys et al. 2010). Recently, a model that incorporates τ0 and estimates the bit error and the cycle slips for GPS carrier tracking loop during amplitude scintillation events has been presented by Humphreys et al. (2010).

Humphreys et al. (2009) developed a statistical model that is capable of producing synthetic time series of amplitude and phase scintillation. The time series generated by this model reproduce fading patterns with the characteristics that were observed on equatorial scintillation. More importantly, the model generates the signal phase that is consistent with what has been observed during measurements made by GPS receivers at low latitudes. Of particular importance are the sudden ½ cycle phase changes accompanying deep power fades that could be mainly responsible for loss of carrier phase in GPS receivers. Supposedly, realistic complex signal patterns can now be easily generated with this model and used to adequately test the performance of GPS scintillation receivers under conditions of severe scintillation. The model, however, requires two basic inputs: (1) the scintillation index (S4), which is an estimate of the severity of the amplitude fading; and (2) the decorrelation time (τ0), which indicates the rapidity of the signal fading. We must point out that the model was developed based on a limited set of high-rate scintillation measurements (33 measurement sets with durations ranging from 50 to 300 s) and further studies of the model accuracy would prove to be useful.

In this study, we revisit various recent studies that propose alternative ways to characterize scintillating signals and different methodologies for estimation of the scintillation impact on GPS receiver performance. As we review these methodologies, we also make original assessments by analyzing a large set of high-rate (50 Hz) measurements of GPS L1 (1.575 GHz) amplitude scintillation made during the previous maximum of the solar cycle. The measurements and results are representative of the scintillation conditions experienced by a static receiver located near the Equatorial Anomaly peak, a region characterized by a high occurrence of strong scintillation. Finally, using both theoretical and empirical approaches, we investigate the impact that amplitude scintillation can have on GPS receiver performance.

The presentation of our study is organized as follows: Details about the GPS L1 measurements used in this investigation are given in Sect. 2. In Sect. 3, we describe how we processed the observations and carried out our analyses. The results of our analyses are presented and discussed in Sect. 4. Final remarks and plans for future work are given in Sect. 5.

2 Measurements

2.1 Experimental Setup

Amplitude scintillation measurements used in this study were made by a scintillation monitor developed by Cornell University (Beach and Kintner 2001) and deployed in Brazil as a part of the ionospheric scintillation network of the Instituto Nacional de Pesquisas Espacias—INPE. The Cornell Scintillation Monitor (CSM or SCINTMON) was built using a GEC-Plessey GPS card with special firmware. The CSM was developed to maintain lock during most scintillation conditions. Therefore, it can measure the amplitude of the GPS signal when most standard GPS receivers would have lost lock. This CSM has a 12-channel correlator that allows the tracking of signals from up to 11 GPS satellites, simultaneously. One channel is dedicated to noise estimation.

For this study, only data from GPS satellites with elevation greater than 30° were considered. This elevation mask is applied to minimize the use of measurements that could have been affected by non-geophysical sources such as multipath. The CSM provides measurements of both the L1 (1.575 GHz) wide band power and wide band noise at a 50 Hz sampling rate. The CSM does not provide carrier phase measurements.

2.2 Observation Period and Geophysical Conditions

The measurements of the GPS L1 amplitude used in this study were made by a CSM installed at INPE’s headquarters in São José dos Campos, Brazil (Geographic coordinates: 23.20435°S, 45.86075°W, −17.5° dip latitude), a site located near the peak of the Equatorial Anomaly. We focused our analysis on measurements made between December 14, 2001 and January 14, 2002. This was a period of high solar activity during the previous solar cycle. The strongest amplitude scintillations are known to occur near the Equatorial Anomaly peak during periods of high solar flux conditions (Aarons et al. 1981; Aarons 1982, 1985; de Paula et al. 2003; Whalen 2009).

Figure 1 shows the variability of the sunspot numbers and 10.7 cm solar flux index (F10.7) over the past three solar cycles. These indices are widely used to characterize the conditions of the solar activity. The vertical dashed lines indicate the period when the measurements used in this study were made. The average sunspot number for the period of analysis was 126, while the average F10.7 for the period was 176 × 10−22 W/m2/Hz. Therefore, the observation period can be classified as of high solar flux conditions. Strong scintillations are known to occur frequently during high solar flux conditions (e.g., Aarons 1985; Basu et al. 1988; Kintner et al. 2007).
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig1_HTML.gif
Fig. 1

The top and bottompanels show the variability in sunspot number and in the solar flux index (F10.7), respectively, for the past three solar cycles. The observations analyzed in this study were collected during the last solar maximum, in the period indicated by the vertical dashed lines (Dec. 14, 2001–Jan. 14, 2002). The solar indices were obtained from the National Geophysical Data Center (NGDC), Space Physics Interactive Data Resource (SPIDR)

Figure 2 shows a global map of the ionospheric peak density (NmF2) as predicted by the International Reference Ionosphere—IRI (e.g., Bilitza et al. 1993; Bilitza 2003; Bilitza and Reinisch 2008), a semi-empirical model of the ionosphere, for December 30, 2000 at 20:00 LT. The map shows the enhancements in NmF2 that are commonly observed at low-latitudes. These density enhancements are caused by ionospheric plasma that is moved away from the equator to low latitudes by the action of ionospheric electric fields, neutral winds, gravity, and pressure (Klobuchar et al. 1991; Balan and Bailey 1995, 1996). They are also known as the Appleton Anomaly peaks (e.g., Kelley 1989; Schunk and Nagy 2000). The map also indicates the location of the observing site (São José dos Campos–SJC). As mentioned earlier, the site is located near the Southern anomaly peak, where the strongest scintillations are known to occur. Additionally, the measurements were made in the middle of the equatorial spread F season in Brazil, which starts around September and lasts until April under high solar flux conditions (e.g., Sobral et al. 2002; Abdu et al. 2003). The geophysical conditions under which these measurements were made allow the study of a broad range of scintillation levels.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig2_HTML.gif
Fig. 2

Global map of the modeled ionospheric peak density (NmF2) for 20:00 LT for December 30, 2001. The map was generated using the International Reference Ionosphere (IRI) model. The location of the observing site (SJC) is indicated. Note that NmF2 is given in electrons/m3; 1012 electrons/m3 is shown as 12 on the scale at the right

Scintillation observations started every day at 18:00 LT and continued until the next day at 06:00 LT. Scintillations at GHz frequencies are normally observed between sunset hours and local midnight, but cases of post-midnight scintillation have also been observed. Post-midnight scintillations are usually associated with spread F triggered by storm-time disturbance electric fields (Aarons 1991; Martinis et al. 2005). From our set of observations (32 days), we found about 172 h of GPS L1 amplitude measurements with S4 ≥ 0.3, considering only satellites with an elevation greater than 30°. Scintillations were observed virtually every night, mostly between sunset and midnight, during the period of observation considered here.

Figure 3 shows an example of observations made in São José dos Campos on December 14, 2001. Panel (a) shows the C/N0 of the L1 signal received from satellite PRN 28. Panel (c) shows the azimuth and elevation angle of the PRN 28. Panels (b) and (d) show the decorrelation times (τ0) and S4 indices, respectively, computed for the signal shown in panel (a) for every minute. More details about the S4 and τ0 indices are given in the following sections. Values of τ0 are not computed for S4 < 0.1. This example illustrates the data we used in our analysis and the variability in S4 and τ0 we have observed. Very large scintillation intensities are seen between 20:30 and 21:05 LT, with S4 exceeding 1 at times. We point out that, in this example, the scintillation intensity decreases and the decorrelation time increases as time progresses. We investigate and discuss this variability throughout this article.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig3_HTML.gif
Fig. 3

Example of observations made in São José dos Campos on December 14, 2001, for PRN 28. a Detrended C/N0 measurements with varying levels of scintillation. b The S4 index estimated from the measurements. c The azimuth and elevation of PRN 28 during the measurements. Finally, d The decorrelation time (τ0) estimated from the measurements. Note that τ0 is only computed and shown for S4 > 0.1

3 Analysis

The CSM generates two types of files: one is a low-rate (1-min) summary file and the other one is a high sampling rate (50 Hz) data file. The summary file contains information about the satellites being tracked and signals being monitored. The summary file has satellite/signal information for every minute of the observations. The high-rate data file contains 50 Hz measurements of the Wide Band Power (P) of all (up to 11) satellites being tracked and measurements of the Noise Wide Band Power (N) channel.

We used the information in the summary files to identify periods when measurements were adequate for our analysis. For instance, we only used observations made when the GPS satellite had an elevation above 30° and when the receiver did not lose lock. Once we selected periods of observations that were adequate for our study, we used the high sampling rate data to compute 1-min (3,000 samples) values of the amplitude scintillation index (S4) and decorrelation time (τ0).

3.1 Scintillation Indices

The S4 index indicates the severity of amplitude scintillation, and it is defined as the normalized variance of the received signal intensity, given by Briggs and Parkin (1963).
$$ S_{4}^{{}} = \sqrt {\frac{{\left\langle {I^{2} } \right\rangle - \left\langle I \right\rangle^{2} }}{{\left\langle I \right\rangle^{2} }}} $$
(1)
where I = |A|2 is the intensity, and A is the amplitude of the received signal; the angle brackets denote an ensemble average (in practice, time average is used). The S4 index is computed using measurements of Wide Band Power P, Noise Wide Band Power N, and their low-pass filtered versions \( \left\langle {\text{P}} \right\rangle \) and \( \left\langle {\text{N}} \right\rangle \), respectively. The filtered versions are obtained using a 6th order low-pass Butterworth filter with a cutoff frequency of 0.1 Hz. The filter removes the high-frequency component of the fluctuations caused by ionospheric irregularities. The cutoff frequency value of 0.1 Hz is based on Beach (1998) and Van Dierendonck et al. (1993) and is considered an acceptable value for low-latitude scintillation. Forte and Radicella (2002), however, pointed out that the optimal cutoff frequency for detrending scintillation data might vary somewhat with geophysical conditions. At high-latitudes, for instance, this value (0.1 Hz) might not be suitable (Forte 2005).
The series of P and \( \left\langle {\text{P}} \right\rangle \) are then used to estimate the real signal strength variance over a 1-min period following the approach described by Beach (1998):
$$ \hat{\sigma }^{2} = \frac{1}{M}\sum\limits_{k = 1}^{M} {\left( {P_{k} - \left\langle P \right\rangle_{k} } \right)\left( {P_{k - 1} - \left\langle P \right\rangle_{k - 1} } \right)} $$
(2)
where M = 3000 is the total number of samples during 1 min. The mean signal power (\( \hat{S} \)) for the same period is given by:
$$ \hat{S} = \frac{1}{M}\sum\limits_{k = 1}^{M} {\left( {\left\langle P \right\rangle_{k} - \left\langle N \right\rangle_{k} } \right)} $$
(3)
Therefore, the computed S4 index is given by
$$ S_{4} = \frac{{\hat{\sigma }^{2} }}{{\hat{S}}} $$
(4)
and the normalized signal amplitude scintillation (AN) is:
$$ A_{\text{N}} = \sqrt {\frac{P}{\left\langle P \right\rangle - \left\langle N \right\rangle }} $$
(5)
We also computed the decorrelation time τ0 of the signal amplitude. The autocorrelation function of the normalized signal amplitude scintillation RA(τ) is given by
$$ R_{\text{A}} \left( \tau \right) = \frac{1}{2}E\left[ {A_{\text{N}} (t)A_{\text{N}} (t + \tau )} \right] $$
(6)
where E[] denotes the expected value operator. The τ0 value is defined as the time lag at which the autocorrelation function falls off by e−1 from its maximum (zero lag) value:
$$ \frac{{R_{\text{A}} \left( {\tau_{0} } \right)}}{{R_{\text{A}} \left( 0 \right)}} = e^{ - 1} $$
(7)
while the S4 index is an indicator of the depth (or magnitude) of amplitude fading, and the decorrelation time (τ0) is an indicator of the rapidity of the fades.
Figure 4 shows four examples illustrating the variability in the decorrelation time computed from GPS L1 amplitude measurements made during the campaign of observations used in this study. In all cases, the time series of measured signal amplitude have approximately the same S4 (~0.9), but very distinct τ0 values: 0.94, 0.68, 0.43, and 0.18 s. This figure serves to exemplify the variability of amplitude scintillation patterns.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig4_HTML.gif
Fig. 4

Examples of scintillation observations with S4 = 0.9 but with different decorrelation times τ0

3.2 Mean Time Between Cycle Slips

Humphreys et al. (2010) proposed a statistical model to estimate the mean time between cycle slips (TS) based on a differential detect bit error probability (Pe). In this model, amplitude scintillation is described by a Rician fading channel, and the S4 and τ0 are parameters used in the TS estimation. Here, we briefly describe this model. We applied this model to analyze our set of measurements, and the results are presented in the following section. The bit error probability is estimated assuming a model for the autocorrelation (RA(τ)) function of the amplitude scintillation pattern. In this case, the model is based on a 2nd order Butterworth-type power spectrum (Mason 1987).

The model for RA(τ) is described by Humphreys et al. (2010):
$$ R_{\text{A}} (\tau ) = \sigma_{\text{A}}^{2} {\text{e}}^{{({{ - \beta \left| \tau \right|} \mathord{\left/ {\vphantom {{ - \beta \left| \tau \right|} {\tau_{0} }}} \right. \kern-\nulldelimiterspace} {\tau_{0} }})}} \left[ {\cos ({{\beta \tau } \mathord{\left/ {\vphantom {{\beta \tau } {\tau_{0} }}} \right. \kern-\nulldelimiterspace} {\tau_{0} }}) + \sin ({{\beta \left| \tau \right|} \mathord{\left/ {\vphantom {{\beta \left| \tau \right|} {\tau_{0} }}} \right. \kern-\nulldelimiterspace} {\tau_{0} }})} \right] $$
(8)
where β = 1.2396464; σA2 is given by σA2 = 1/2(1 + K), where K is the parameter of Rice distribution and it is related to the S4 index though \( K = {{\sqrt {m^{2} - m} } \mathord{\left/ {\vphantom {{\sqrt {m^{2} - m} } {m - \sqrt {m^{2} - m} }}} \right. \kern-\nulldelimiterspace} {m - \sqrt {m^{2} - m} }} \), where m = 1/S42.
The bit error probability, Pe, is then given by Simon and Alouini (2006):
$$ P_{\text{e}} = \frac{1}{2}\left[ {\frac{{1 + K + \overline{\gamma } \left( {1 - \rho } \right)}}{{1 + K + \overline{\gamma } }}} \right]{\text{e}}^{{{{ - K\overline{\gamma } } \mathord{\left/ {\vphantom {{ - K\overline{\gamma } } {1 + K + \overline{\gamma } }}} \right. \kern-\nulldelimiterspace} {1 + K + \overline{\gamma } }}}} $$
(9)
where \( \overline{\gamma } = \Upomega T_{\text{b}} {C \mathord{\left/ {\vphantom {C {N_{0} }}} \right. \kern-\nulldelimiterspace} {N_{0} }} \) is the average signal-to-noise ratio per bit, Tb is the bit period, C/N0 is the carrier-to-noise power density ratio, and \( \Upomega \equiv E\left[ {A_{\text{N}}^{2} (t)} \right] \). ρ is the fading correlation coefficient, which depends on the fast-fading channel model assumed, in this case, a 2nd order Butterworth-type filter (Humphreys et al. 2010). The fading correlation coefficient represents the degrading effect of bit-to-bit fluctuation on DSPK detection due to scintillation. ρ can be estimated from Humphreys et al. (2010):
$$ \rho = \frac{{({{\sigma_{\text{A}}^{2} } \mathord{\left/ {\vphantom {{\sigma_{\text{A}}^{2} } {2q^{2} }}} \right. \kern-\nulldelimiterspace} {2q^{2} }})[f(2q) - 2f(q) + 1]}}{{({{\sigma_{\text{A}}^{2} } \mathord{\left/ {\vphantom {{\sigma_{\text{A}}^{2} } {q^{2} }}} \right. \kern-\nulldelimiterspace} {q^{2} }})[2q + f(q) - 1]}} $$
(10)
where \( f(q) = {\text{e}}^{ - q} (\cos q - \sin q) \) and q = βTb0.
Finally, the mean time between cycle slips (TS) is given by the ratio between the bit period (Tb) and the bit error probability (Pe):
$$ T_{\text{S}} = T_{\text{b}} /P_{\text{e}} . $$
(11)
The cycle slip rate is the inverse of TS, and its distribution can be modeled using a Poisson distribution function. Therefore, the probability that a cycle slip will occur within ν seconds (PCS) is given by (Holmes 1982):
$$ P_{\text{CS}} = 1 - {\text{e}}^{{ - \nu /T_{\text{S}} }} $$
(12)

3.3 Fading Depth and Duration

As mentioned earlier, the S4 index is widely used as an indicator of amplitude scintillation. The S4 index, however, does not provide information about the temporal characteristics of the fading. Information about the temporal characteristics of the fading is provided by the decorrelation time (τ0). It quantifies the rapidity of the amplitude fluctuations. Figure 4, for instance, illustrates that scintillation events with similar S4 values can have significantly different fading rates.

In the previous section, we showed how S4 and τ0 can be related to the probability of cycle slips (PCS). In this section, we describe an alternative approach used to investigate the effects of measured scintillation patterns on GPS receiver performance. First, we introduce the relationship between fading duration and the probability of cycle slips. The time it takes for the signal intensity to reach its initial value, after a fading event, is defined as the fading duration time (fd). It can be computed from the time series of normalized signal amplitude squared (AN2 defined in Eq. 5). Here, we also define fading depth (df). It is the minimum intensity reached by the signal during a fading event. The definitions of fading depth and fading duration are illustrated in Fig. 5. It is worth mentioning that the methodology for obtaining AN follows the procedure outlined in Sect. 3.1.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig5_HTML.gif
Fig. 5

Illustration of how the fading duration and depth are defined and determined from Wide Band Power (WBP) measurements

We can use estimates of fading duration times to determine the probability of cycle slips to occur during fading events. To do so, we rewrite Eq. 12 as:
$$ P_{\text{FS}} = 1 - {\text{e}}^{{ - {\text{fd}}/T_{\text{S}} }} $$
(13)

Equation (13) now establishes a relationship between S4, τ0, cycle slip rate (TS) and fading duration.

3.4 Carrier-to-Noise Density (C/N0) Estimation

Finally, we revisit the work of Seo et al. (2009) and we use the deep fading concept to evaluate the impact of amplitude scintillation on the performance of GPS receivers using our extensive set of measurements. A deep power fade is defined by Seo et al. (2009) as the fading event in which the received power drops below the minimum operational value of the receiver. In such an event, the low C/N0 condition stresses the receiver’s PLL causing loss of lock. The minimum C/N0 value is receiver dependent.

According to Beach (1998), C/N0 can be estimated using the measurements of the Wide Band Power (P) and Noise Band Power (N). Beach (1998) recommends the use of averages of \( \left\langle {\text{P}} \right\rangle \) and \( \left\langle {\text{N}} \right\rangle \). In this work, \( \left\langle {\text{P}} \right\rangle_{60} \) and \( \left\langle {\text{N}} \right\rangle_{60} \) were obtained by averaging \( \left\langle {\text{P}} \right\rangle \) and \( \left\langle {\text{N}} \right\rangle \), respectively, over 60-s intervals. Then, we used these averages to estimate C/N0:
$$ \mathop {{C \mathord{\left/ {\vphantom {C {N_{0} }}} \right. \kern-\nulldelimiterspace} {N_{0} }}}\limits^{ \wedge } = E\left[ {10\log_{10} \left( {\frac{1}{{T_{\text{C}} }}\frac{{\left\langle {\text{P}} \right\rangle_{60} - \left\langle {\text{N}} \right\rangle_{60} }}{{\left\langle {\text{N}} \right\rangle_{60} }}} \right)} \right] $$
(14)
where TC is the C/A (Coarse/Acquisition) code period of approximately 1 ms. For the 172 h of data used in this work, the mean value of C/N0 is 45.33 dB-Hz. Figure 6 shows the distribution of the C/N0 estimates for various scintillation levels, from S4 = 0.3 ± 0.025 up to S4 = 1.0 ± 0.025.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig6_HTML.gif
Fig. 6

Distribution of C/N0 for various levels of scintillation severity (S4) observed during our observations campaign. The histograms included data within ±0.025 of the indicated S4 value

4 Results and Discussion

In this section, we present and discuss the main results of the application of the methodologies reviewed in the previous section to the extensive set of low-latitude scintillation measurements described in Sect. 2.

4.1 Decorrelation Time Versus Amplitude Scintillation Intensity

This section presents the results of our analysis of the measured decorrelation times (τ0) for different levels of scintillation activity. All the high-rate (50 Hz) measurements (from GPS satellites with elevation >30°) made during our campaign of observations were used to compute S4 indices. Weak scintillation (S4 value below 0.3) is not believed to cause tracking problems in GPS receivers. Therefore, only observations with S4 ≥ 0.3 were considered in this analysis. Once all the S4 values were computed, they were grouped into S4 intervals varying from 0.3 to 1.0 in steps of 0.1. Each interval was 0.05 wide (±0.025 from central S4). These S4 intervals and widths were chosen to maintain a manageable number of data points in our analysis while keeping the values very close to the mean S4. Even with this limitation in our data set, we have over 3,570 scintillation cases (almost 60 h worth of data) for analysis.

Figure 7 shows a histogram describing the overall distribution of the measured decorrelation times. The histogram was computed for the S4 intervals described above and for τ0 intervals that were 0.1 s wide. An important feature of Fig. 7 is that most of the fast scintillation cases (small τ0) are associated with strong amplitude scintillation, i.e., high S4. When S4 is greater than 0.7, the decorrelation time is generally less than 0.3 s. Figure 8 now shows histograms of the distribution of τ0 values for all the S4 intervals. The histograms show that, both the variability/spread of τ0 values as well as the mean value of τ0 tend to decrease as scintillation intensity (S4) increases. Table 1 summarizes the results shown in Fig. 8. It also shows the mean and standard deviation values of τ0 as well as the number of observations (in minutes) available for each S4 interval. Table 1 shows that the mean decorrelation time tends to decrease as the scintillation magnitude increases. This inverse relationship between S4 and τ0 is in good agreement with other recent experimental results (Carrano and Groves 2010). The values in Table 1 are then used to create the plot shown in Fig. 9, which shows the inverse, quasi-linear relationship between the S4 and τ0 values measured in our study.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig7_HTML.gif
Fig. 7

Distribution of amplitude scintillation index (S4) values as a function of decorrelation times (τ0) measured during our campaign of observations (from Dec. 14, 2001 to Jan. 14, 2002)

https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig8_HTML.gif
Fig. 8

Histograms of decorrelation times (τ0) for different levels of scintillation activity

Table 1

Average decorrelation time (τ0) versus scintillation intensity (S4)

S4

Average τ0

(s)

SD τ0 (s)

Number of observations

0.3

0.7800

0.2356

1,423

0.4

0.7325

0.2343

742

0.5

0.6578

0.2072

526

0.6

0.5617

0.1623

338

0.7

0.5168

0.1702

243

0.8

0.4487

0.1600

161

0.9

0.3685

0.1067

117

1.0

0.3223

0.0762

44

SD standard deviation

https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig9_HTML.gif
Fig. 9

Relationship between the mean amplitude scintillation index (S4) and the mean decorrelation time (τ0) for the scintillation events measured during the observation campaign. The error bars represent the standard deviations (SDs) of the τ0 values

Figure 10 shows two time series of S4 and τ0 estimated from measurements made during our campaign. They show the behavior indicated by the histograms presented in the previous section, indicating a tendency of longer decorrelation times as scintillation becomes weaker, and vice versa. These observations were made during the passes of GPS satellites PRN 28 on the night of December 14, 2001, and PRN 7 on the night of January 7, 2002.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig10_HTML.gif
Fig. 10

Examples of scintillation intensities (S4) and decorrelation times (τ0) for two different GPS signals: PRN 28 on the night of December 14, 2001, and PRN 7 on the night of January 7, 2002. In both cases, it is possible to notice the tendency of longer decorrelation times as scintillation becomes weaker. We also point out that, for cases where S4 < 0.1, we did not compute τ0

4.2 Variability of Decorrelation Times and Scintillation Intensity Versus Local Time

Figure 11 shows the results of an analysis of the measured τ0 values as a function of S4 and local time. It shows the average τ0 and its variability (error bars) from about 1930 LT until local midnight. Again, the analysis was carried out for various levels of scintillation intensity. Data are grouped into 1-h bins (±30 min around each full hour) and then averaged. Figure 11 shows the averages and error bars (standard deviation of the points) plotted for each local time bin. The most interesting result of this analysis is that the mean decorrelation values (for a given S4 value) do not seem to vary much with local time. Except for S4 = 0.3, we did not find a clear trend (increase or decrease) on the average τ0 as a function of local time. Note that the analysis here is for a fixed S4. The mean decorrelation time does not vary more than 0.2 s throughout the night for all S4 indices studied here. We also did not observe strong scintillation with S4 ≥ 0.8 after 23:30 LT. This is because of the decay of the ionospheric irregularities with scale sizes responsible for scintillation and because of the reduced background ionospheric density during that time (e.g., Basu et al. 1978; Rodrigues et al. 2004).
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig11_HTML.gif
Fig. 11

Variation of mean decorrelation times as a function of local time and S4

4.3 Estimation of TS and Pcs Based on Realistic Values of S4 and τ0

In general, a cycle slip is an indication that the receiver PLL briefly lost the lock of the carrier phase. The PLL, however, can lock the phase again and continue to track the signal until another cycle slip occurs. To better evaluate the impact of amplitude scintillation, it is important to determine the mean time between cycle slips for different conditions of τ0 and S4.

Employing the theoretical approach proposed by Humphreys et al. (2010) and summarized in the previous section, we investigated the mean time between cycle slips that a user might expect under various levels of amplitude scintillation. The measurements made during our one-month observation campaign provide a large database of realistic and self-consistent values of τ0 and S4 index. Figure 12 shows the variability of the mean time between cycle slips as a function of measured τ0, S4, and C/N0. For S4 < 0.7, TS values are high, usually greater than 100 s. However, TS values reduce to a few seconds for S4 values greater than 0.8, especially during cases of fast scintillation (short decorrelation times). Small TS values might be a serious issue, for instance, on aviation applications (de Rezende et al. 2007; So et al. 2009). The influence of τ0 on TS is more clearly observed for S4 > 0.7.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig12_HTML.gif
Fig. 12

Mean time between cycle slips (TS) versus τ0 for different values of S4. The left panel shows results for scintillation scenarios where S4 is less than 0.7. In general, TS values are greater than 100 s. The right panel shows the results for S4 ≥ 0.7. Ts values now vary between a few s and 100 s. The effect of τ0 on TS is more noticeable as well

Using the computed values of TS and applying them into Eq. 12, it is possible to estimate the probability of cycle slip (PCS). Figure 13 shows the computed PCS values as a function of S4 and τ0 for S4 greater than 0.6. For S4 ≤ 0.6, typical values of PCS do not exceed 1%. The probability of cycle slips was computed for ν = 1 s. For S4 = 0.7, PCS values vary between 2.4 and 4.8%. For S4 values between 0.8 and 1.0, PCS values can vary from 3.5 to 32%, indicating a significant likelihood of difficulties for the tracking loop.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig13_HTML.gif
Fig. 13

The influence of τ0 on the probability of cycle slips (PCS). Note that the decorrelation time plays an important role, particularly for cases where S4 ≥ 0.8

It is also possible to observe in Fig. 13 that, for S4 = 0.7, τ0 does not seem to play a major role on the variability of PCS. For S4 ≥ 0.9, however, τ0 seems to cause significant changes in PCS. For instance, for S4 = 0.9 and decorrelation times around 0.5 s, PCS is about 5%. For S4 = 0.9 and decorrelation times around 0.2 s, PCS can exceed 15%.

4.4 Fading Characteristics and Cycle Slips

In the previous sections, we reported values of S4 and τ0 that a static receiver located under the Equatorial Anomaly measured during high solar flux and typical equatorial spread F conditions. The observed values of S4 and τ0 were then used to make a quantitative assessment of the impact of ionospheric scintillation on GPS PLL cycle slips, using the modeling approach of Humphreys et al. (2010). In this section, we investigate the depth and duration of the measured fading events and use these parameters to determine the probability of cycle slips. Following the approach proposed by Seo et al. (2009), we also analyze the rate of deep fades per minute. In this analysis, any fading event in which the intensity of the received signal dropped by 6 dB, or more, was considered. For each fading event considered here, we determined its duration (fd) and depth (df), according with the definitions described in Sect. 3.3.

Figure 14 shows the distribution of fading cases as a function of fading duration and τ0 for different ranges of fading depth and values of S4. On the left hand side panels, the distribution of fading depth values for three different ranges are shown (note the different ranges of fading depth in the horizontal axes). The central and right hand side panels show distributions of fading duration and τ0, respectively, corresponding to each range of fading depth indicated in the left hand side panels. Table 2 provides the values shown in Fig. 14. We must point out that the duration of a fading event depends on the velocity of the ionospheric piercing point with respect to the geomagnetic field and to the velocity of the ionospheric irregularities (Aarons et al. 1980; Aarons 1982; Kintner et al. 2001, 2004). Therefore, a non-static receiver, for instance, moving in the geomagnetic eastward direction is more likely to observe more signal fades with longer durations than those measured by our static receiver. This is because post-sunset irregularities causing ionospheric scintillation usually move in the eastward direction during geomagnetically quiet periods (Kelley 1989). The irregularities contributing the most to GPS scintillation are located near the main F-region peak (say ~ 350 km altitude), have horizontal scale sizes (fresnel scale) of about a few hundreds of meters, and are aligned with the geomagnetic field line (e.g. Kintner et al. 2007). The velocity of the GPS signal piercing point with respect to the velocity of the irregularities dictates the rapidity of the scintillations.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig14_HTML.gif
Fig. 14

Left handsidepanels distribution of fading depths for different S4 values. Note that each panel is for different range of fading depth. Middle panels: distribution of fading duration for different fading depth ranges (see left hand side panels) and different S4 values. Right hand side panels: distribution of the decorrelation times for different fading depth ranges (see left hand side panels) and S4 values

Table 2

Estimates of fading duration (fd) and τ0 as a function of S4 and fading depth (fd)

df

−7 < df ≤−6

−8 < df ≤−7

−9 < df ≤−8

−10 < df ≤−9

−11 < df ≤−10

−12 < df ≤−11

S4

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

0.3

2.408

0.782

2.567

0.874

2.853

0.911

2.485

0.941

1.988

0.986

0.600

0.702

0.4

2.300

0.704

2.359

0.740

2.285

0.724

2.524

0.811

1.919

0.645

2.494

0.796

0.5

2.134

0.636

2.170

0.634

2.187

0.637

2.210

0.658

2.390

0.707

2.343

0.682

0.6

1.946

0.535

1.898

0.522

2.021

0.530

1.946

0.534

2.047

0.551

2.000

0.545

0.7

1.742

0.479

1.750

0.469

1.786

0.482

1.952

0.497

1.761

0.496

1.894

0.485

0.8

1.452

0.420

1.535

0.409

1.671

0.417

1.573

0.423

1.678

0.412

1.609

0.406

0.9

1.072

0.350

1.223

0.344

1.313

0.363

1.428

0.346

1.319

0.340

1.351

0.348

1.0

0.803

0.313

1.040

0.309

0.974

0.309

1.005

0.306

1.153

0.322

1.289

0.318

df

−13 < df ≤−12

−14 < df ≤−13

−15 < df ≤−14

−16 < df ≤−15

−17 < df ≤−16

−18 < df ≤−17

S4

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

0.3

0.317

0.640

0.590

0.780

1.800

0.710

2.402

0.900

4.800

1.300

2.060

0.550

0.4

2.195

0.856

1.888

0.842

2.237

0.784

2.428

0.954

3.010

0.880

2.730

0.930

0.5

2.435

0.733

2.281

0.669

2.171

0.704

1.995

0.677

2.753

0.746

2.233

0.715

0.6

1.971

0.551

1.900

0.549

1.954

0.528

2.039

0.574

1.855

0.530

2.386

0.604

0.7

1.855

0.473

1.855

0.510

1.832

0.481

2.078

0.480

2.076

0.496

1.983

0.571

0.8

1.625

0.413

1.554

0.404

1.678

0.405

1.812

0.422

1.782

0.423

1.659

0.445

0.9

1.438

0.349

1.456

0.339

1.518

0.342

1.584

0.343

1.517

0.346

1.635

0.363

1.0

1.324

0.310

1.298

0.294

1.280

0.304

1.481

0.306

1.590

0.301

1.791

0.305

df

−19 < df ≤−18

−20 < df ≤−19

−21 < df ≤−20

−22 < df ≤−21

−23 < df ≤−22

df ≤−23

S4

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

E[fd]

E0]

0.3

3.360

1.260

0.4

0.740

0.400

0.5

2.270

0.600

3.155

0.755

2.550

0.780

5.560

0.820

0.6

1.798

0.526

1.664

0.602

1.140

0.630

1.520

0.680

0.060

0.420

0.7

1.718

0.520

2.041

0.481

2.326

0.586

0.160

0.440

2.820

0.740

0.168

0.620

0.8

1.455

0.367

1.552

0.545

1.623

0.486

2.320

0.680

0.440

0.560

0.146

0.366

0.9

1.577

0.354

1.744

0.336

1.017

0.320

0.460

0.240

0.160

0.220

0.140

0.300

1.0

1.658

0.322

1.366

0.343

1.833

0.366

0.12

0.320

0.120

0.280

2.020

0.380

We can now use the average values of fading duration (fd), shown in Table 2, and Eq. 13 to estimate the probability of cycle slips (PFS) during fading events. The mean time between cycle slips (TS) is obtained as described in Sect. 3.2. The results of this analysis are presented in Fig. 15, which shows the probability of cycle slips as a function of τ0 for four different values of S4. Only strong scintillation (S4 ≥ 0.7) cases are considered in this analysis. Figure 15 also shows the values of PCS for comparison purposes. We remind the reader that the difference between PCS and PFS is the fact that PCS is the probability of cycle slips normalized over one second while PFS takes the average fading duration into consideration. The results show that, when considering the fading duration time, the probability of cycle slip (PFS) is significantly increased compared with PCS. This is a consequence of the fact that the average fading duration is longer than 1 s for the cases investigated here.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig15_HTML.gif
Fig. 15

Comparison of the computed probability of cycle slips with (PFS) and without (PCS) taking into account the fading duration. The values of PFS were calculated using an average value of the fading duration for each scintillation index S4. The average value of the fading duration (E[fd] in seconds) is indicated in each panel

4.5 An Assessment of the Loss-of-Lock Conditions

Seo et al. (2009) investigated the effects of “deep power fades” (see Sect. 3.4) in the performance of aviation GPS receivers. They used an empirical C/N0 threshold value of 20 dB-Hz based on measurements made by a NordNav receiver to determine the occurrence of loss of lock. Based on measurements, they found that loss of lock would occur, most of the time, when the C/N0 dropped below this threshold value. They pointed out, however, that the C/N0 threshold is receiver dependent and suggested that other C/N0 values should be also considered when analyzing deep power fades. Therefore, for a more comprehensive analysis, we considered deep power fade events where C/N0 dropped below three different thresholds: 20, 25, and 30 dB-Hz.

Figure 16 shows the results of our analyses of the occurrence of deep fades for the 172 h of scintillation observations (with S4 > 0.3 and elevation >30°) available for this study. It shows a scatter plot of S4 versus τ0 of the individual deep power fades for the three C/N0 threshold values considered in our analysis. It is possible to observe that most of the deep fades occurred during times when S4 is greater than 0.7 and τ0 is less than 0.6 s. These results also reinforce that the decorrelation time tends to decrease with the increase of S4 as mentioned in Sect. 4.1. The results of Fig. 16 agree quite well with those reported by Carrano and Groves (2010) in March 2002, based on measurements made in Ascension Island.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig16_HTML.gif
Fig. 16

Scatter plots of S4 versus τ0 for our estimates of the occurrence of loss of lock due to deep power fades for three different C/N0 thresholds (20, 25, and 30 dB-Hz). Most of the deep fades occur when S4 is greater than 0.7 and τ0 is less than 0.6 s

Table 3 shows the number of cases of loss-of-lock occurrences based on Seo et al. (2009) analysis approach for the three different C/N0 threshold values. It also shows the average τ0 (E0]) and the mean time deep fade duration (E[fd]) for the loss-of-lock occurrences. Table 3 indicates that the number of loss-of-lock occurrences caused by deep fades is relatively low when a threshold value of C/N0 = 20 dB-Hz is considered. GPS receivers that require a C/N0 of 25 dB-Hz or more, however, might suffer a significant number of loss-of-lock occurrences, particularly when S4 is close to 1. Deep fades could be a potential issue for GPS receivers operating with a minimum C/N0 around 30 dB-Hz as pointed out by Kintner et al. (2007). We found a total of 2,269 deep fades when we considered S4 values ranging from 0.6 to 1.
Table 3

Loss-of-lock occurrences based on deep fading events for GPS receivers with three different thresholds of minimum operation power

S4

C/N0 = 20 dB-Hz

C/N0 = 25 dB-Hz

C/N0 = 30 dB-Hz

E0]

E[fd]

Cases

E0]

E[fd]

Cases

E0]

E[fd]

Cases

0.3 > S4 ≥ 0.4

1

0.900

2.372

19

0.4 > S4 ≥ 0.5

0.430

0.390

2

0.566

1.156

10

0.735

2.142

57

0.5 > S4 ≥ 0.6

1

0.783

1.906

6

0.657

2.149

201

0.6 > S4 ≥ 0.7

0.660

1.340

2

0.768

1.942

9

0.577

2.003

349

0.7 > S4 ≥ 0.8

0.463

0.103

6

0.484

0.542

17

0.446

1.744

600

0.8 > S4 ≥ 0.9

0.285

0.155

4

0.346

0.686

15

0.394

1.649

638

0.9 > S4 ≥ 1.0

0.346

0.740

3

0.294

1.096

11

0.338

1.494

682

We must point out that, despite the large set of measurements available for this study, we only found a few cases where deep fades reached C/N0 below 20 dB-Hz. This limited number of cases might be a result of a limitation of the scintillation monitor. Despite the robustness of the CSM compared with typical GPS receivers, it might still be susceptible to loss-of-lock occurrences caused by strong scintillation. In our selection of the data, we chose not use the entire minute of observations if it had any data gaps. Data gaps are indication of loss of lock by the receiver. Therefore, we might have missed cases when there was a deep fade and the CSM lost lock.

One might also consider the time it takes for the receiver to reacquire signal lock as pointed out by Seo et al. (2011). The work of Carrano and Groves (2010) showed an interesting analysis about the time the GPS receiver takes to reacquire the signal after losing lock due to scintillation. Their analysis suggests that the acquisition takes longer during scintillation scenarios with short decorrelation times (small τ0). Table 3 shows the values of E0] for the observed deep fading events. Based on the results of Carrano and Groves (2010), a receiver in this scenario could take several minutes to reacquire signal lock.

Our set of measurements also allows us to compute the average number of deep fades per minute. Figure 17 shows the results of our estimate of deep fades per minute considering different C/N0 thresholds and S4 values. We found that the worst-case scenario occurs when S4 is near 1. In that case, we found that, on average, a 20 dB-Hz fade occurred every 33 min and a 25 dB-Hz occurred every 10 min. Considering a 30 dB-Hz threshold, however, we found an average of 6 deep fades per minute for S4 ~ 1.
https://static-content.springer.com/image/art%3A10.1007%2Fs10712-011-9161-z/MediaObjects/10712_2011_9161_Fig17_HTML.gif
Fig. 17

Average number of deep fade occurrences per minute for different S4 values and C/N0 thresholds

If we combine these results with the reacquisition time analysis of Carrano and Groves (2010), we find that, depending on the C/N0 threshold, the operation of GPS receivers can be seriously affected during strong scintillation scenarios, since it might take several minutes for a receiver to reacquire signal after losing lock due to deep fades. Another interesting point raised by Seo et al. (2011) was the importance of investigating deep power fades occurring on multiple satellite signals simultaneously. We plan to carry out such an investigation as a follow-up study taking into account different C/N0 thresholds.

5 Conclusions and Final Remarks

In this work, we revisited recently proposed techniques for the analyses of ionospheric scintillation methodologies to evaluate the impact of scintillation on GPS performance. This review was followed by the application of these methodologies to a new, extensive set of high-rate measurements of GPS L1 amplitude made during high solar flux and strong spread F conditions. The measurements were made by a Cornell Scintillation Monitor (CSM) near the peak of the Equatorial Anomaly between December 14, 2001 and January 14, 2002.

The variability of the decorrelation time (τ0) was presented as a function of scintillation severity (S4 index). We showed that the values of τ0 tend to decrease as S4 increases. This result is in good agreement with what was found in previous studies. The variability of mean τ0 as a function of local time was also investigated. The results show that values of average τ0, for a fixed S4 value, do not vary much with local time. We must point out, however, that S4 tends to decrease with local time, with cases of strong scintillation occurring very rarely near midnight.

The impact of the scintillation decorrelation time in the cycle slip process was analyzed in order to better evaluate the performance of the GPS receiver under different scintillation scenarios seen during our observation campaign. Our results indicate a significant impact of fast scintillations in the GPS receiver performance, especially for S4 ≥ 0.7. Typical values for the probability of cycle slips for τ0 ~ 0.2 s varied from 2.4% for S4 = 0.7 to 32% for S4 = 1.0. We also proposed an alternative way to compute the probability of cycle slips that takes into account the average duration a fading event. Average fading durations were obtained from our set of measurements. The results show an increase in the probability of cycle slips, with values reaching 38% for S4 ~ 1 and τ0 ~ 0.2 s, for instance.

Finally, we presented results of an analysis of the individual fades observed in our set of measurements. This analysis was carried out in order to investigate the occurrence of breaks in the carrier loop operation due to fades with C/N0 below the minimum required by the receiver for proper operation. The results of this analysis suggest that GPS receivers with C/N0 thresholds below 25 dB-Hz can be significantly less affected by amplitude scintillation than GPS receivers operating with higher operational thresholds, say 30 dB-Hz. Our analysis indicates that GPS receivers with C/N0 thresholds around or over 30 dB-Hz could be seriously affected by deep fading events particularly when the reacquisition time is taken into consideration.

Future work will include a follow-up analysis using a larger number of measurements under strong/fast scintillation scenarios (S4 ≥ 0.9 and τ0 ≤ 0.2 s) in an attempt to obtain results with even better statistics for these conditions. We will also investigate the simultaneous occurrence of deep fades in different GPS signals.

Acknowledgments

The authors are grateful to INPE technical staff for maintaining the continuous operation of the scintillation monitor in São José dos Campos. FSR would like to thank the support from NSF through Award AGS-1024849, which allowed this collaborative work with INPE and ITA. AOM wishes to thank the Brazilian Institute of Aeronautics and Space (IAE), where he works as a research engineer, for supporting his doctoral studies at ITA.

Copyright information

© Springer Science+Business Media B.V. 2011