Radio Science

Modeling the effects of ionospheric scintillation on GPS/Satellite-Based Augmentation System availability

Authors


Abstract

[1] Ionospheric scintillation is a rapid change in the phase and/or amplitude of a radio signal as it passes through small-scale plasma density irregularities in the ionosphere. These scintillations not only can reduce the accuracy of GPS/Satellite-Based Augmentation System (SBAS) receiver pseudorange and carrier phase measurements but also can result in a complete loss of lock on a satellite. In a worst case scenario, loss of lock on enough satellites could result in lost positioning service. Scintillation has not had a major effect on midlatitude regions (e.g., the continental United States) since most severe scintillation occurs in a band approximately 20° on either side of the magnetic equator and to a lesser extent in the polar and auroral regions. Most scintillation occurs for a few hours after sunset during the peak years of the solar cycle. Typical delay locked loop/phase locked loop designs of GPS/SBAS receivers enable them to handle moderate amounts of scintillation. Consequently, any attempt to determine the effects of scintillation on GPS/SBAS must consider both predictions of scintillation activity in the ionosphere and the residual effect of this activity after processing by a receiver. This paper estimates the effects of scintillation on the availability of GPS and SBAS for L1 C/A and L2 semicodeless receivers. These effects are described in terms of loss of lock and degradation of accuracy and are related to different times, ionospheric conditions, and positions on the Earth. Sample results are presented using WAAS in the western hemisphere.

1. Introduction

[2] Ionospheric scintillation is a rapid change in the phase and/or amplitude of a radio signal as it passes through small-scale plasma density irregularities in the ionosphere. These scintillations both reduce the accuracy of GPS/Satellite-Based Augmentation System (SBAS) receiver pseudorange and carrier phase measurements, and can result in a complete loss of lock on a satellite. SBAS is an augmentation system to GPS and will be used for navigation and precision approach. It consists mainly of three systems: (1) the U.S. Wide-Area Augmentation System (WAAS), (2) the European Geostationary Navigation Overlay System (EGNOS), and (3) the Japanese MTSAT (Multifunctional Transport SATellite) Satellite-Based Augmentation System (MSAS). Information on these systems and technical descriptions of the GPS signals are given by Walter and El-Arini [1999] and Parkinson and Spilker [1996].

[3] Typical delay locked loop (DLL)/phase locked loop (PLL) designs of GPS/SBAS receivers enable them to handle moderate amounts of scintillation. Scintillation has not been seen to have a major effect on midlatitude regions, however, for operations in a band 20 deg on either side of the magnetic equator, scintillation effects on GPS/SBAS receiver performance must be determined.

[4] Previous work in this area [Hegarty et al., 1999; Pullen et al., 1998] defined a statistical model of scintillation signal coupled with a model of receiver processing for L1 (1575.42 MHz) GPS and SBAS carrier and code tracking loops as well as semicodeless L2 (1227.6 MHz) carrier and Y-code tracking capabilities [Woo, 2000]. Also, an impressive research effort was described by Knight and Finn [1998] in their work to model carrier phase tracking errors and code phase errors in terms of scintillation parameters produced by the well-known wide-band scintillation model WBMOD [Secan et al., 1997] (WBMOD was developed by researchers at Northwest Research Associates, Inc. (NWRA), and funded by several government agencies). This research created an ability to determine the effects of scintillation on GPS receivers. A hardware bench testing for scintillation is being conducted by Morrissey et al. [2000] for GPS/SBAS receivers.

[5] The purpose of this paper is to describe the status of research on modeling scintillation effects on GPS/SBAS reference and user receivers' performance. This is summarized as follows: (1) Develop a receiver model that includes the effects of scintillation on tracking performance, (2) estimate the effects of scintillation on navigation service availability, (3) estimate the degree that ionospheric scintillation presents a problem for the operation of the GPS in general and SBAS in particular, and (4) develop an ionospheric scintillation prediction capability for GPS/SBAS availability models [Poor et al., 1999].

2. Background and Approach

2.1. Scintillation Propagation Model

[6] The propagation model implemented in WBMOD is described by Secan et al. [1997]. Scintillation estimates are given in terms of a power spectral density (PSD) of phase scintillation of the form equation image where f is frequency (Hz) (greater than or equal to a cutoff frequency), T is a strength parameter (rad2/Hz) corresponding to the PSD value at 1 Hz, and p is a unitless slope. Also produced are intensity-scintillation parameters R95% and S4, which are, respectively the 95th percentile fade depth (dB) and the dimensionless standard deviation of the signal power normalized to the average received power. R95% and S4 and are related as shown in Figure 1. This relationship is established through the Nakagami-m distribution [Nakagami, 1960].

Figure 1.

Relationship between S4 and R95%.

[7] Scintillation in the ionosphere varies according to Sunspot Number (SSN), geomagnetic index (0 ≤ Kp ≤ 9), time of year, time of day, and geographical position. A receiver's ability to cope with scintillation will be affected by these factors, and the azimuth and elevation of the observed satellite which indicate what part and how much of the ionosphere a radio signal must pass through. It is not possible to show the effects of all of these parameters in one plot, but in order to get a general understanding of the extent of scintillation, a plot has been constructed depicting S4, a widely used representation of amplitude fading. Figure 2 (produced by WBMOD) depicts S4 globally with no geomagnetic storms (i.e., Kp = 1) for an ionosphere with SSN = 150, about the peak of the solar cycle. Thus, this figure shows a nominal level ionospheric scintillation undisturbed by storms. The day of the year is September 15 with local time 9:00 P.M. everywhere on the planet. This unusual representation is chosen since scintillation tends to peak after sunset. Consequently, Figure 2 tends to show the maximum effects of S4 for this day and these ionospheric conditions. Clearly shown is the multimodal distribution of severe scintillation around the magnetic equator, light scintillation in the midlatitude regions and moderate scintillation in the polar and auroral regions. A value of 0 for S4 indicates no scintillation while a value of 1 indicates severe scintillation.

Figure 2.

S4 scintillation parameter for September 15 (95 percentile) (SSN = 150; Kp = 1; local time = 9pm everywhere).

2.2. Approach

[8] The approach of this study is to generate estimates of ionospheric scintillation related to different ionospheric conditions, times and locations and determine what effect would be seen by a user receiver after receiver processing. The approach is summarized as follows: (1) Use the WBMOD to obtain the scintillation parameters as a function of ionospheric conditions, day of year, and time of day, (2) develop a GPS/SBAS receiver model sensitive to amplitude and phase scintillation, (3) calculate the output of the DLL and PLL of the receiver as a function of the receiver parameters as well as the scintillation signal parameters, and (4) use these results in a GPS/SBAS availability model [Poor et al., 1999] to examine the impact on service availability for different phases of flight.

2.3. GPS/SBAS Receiver Description

[9] A block diagram of a typical GPS C/A-code receiver is shown in Figure 3 [Ward, 1994; Hegarty et al., 2001]. The RF signal is received by an L-band antenna. This signal is filtered and then amplified by a low-noise amplifier (LNA). Next, the signal is down-converted to a convenient intermediate frequency (IF) and converted from analog to digital (A/D). The digital signal is then passed to a bank of N channels (see Figure 4 [Ward, 1994]) that form complex sums of the correlation between the input signal and C/A code replicas. One channel is needed for each satellite to be tracked. The complex correlation sums are used by a processing unit to track the code and carrier of the received signals so that pseudoranges to each satellite can be estimated. The correlation sums are also used by the processor to demodulate the data.

Figure 3.

GPS receiver overview.

Figure 4.

Receiver channel.

[10] In this paper, we model L1 GPS/SBAS C/A code processing and semicodeless GPS L1 and L2 Y-code processing using a baseband model [Van Dierendonck et al., 1992; Van Dierendonck, 1996] that starts with the complex correlation sums produced by the generic receiver channel shown in Figure 3. For C/A code processing, the integration periods of 20 ms for GPS and 2 ms for SBAS are used. For semicodeless Y-code processing, the received signals on L1 and L2 are correlated with the P-code over an integration period of 1.96 μs (the deduced period of the underlying encryption code [Hatch et al., 1992]).

[11] The WBMOD generated parameters T, p, and S4 will be used in a GPS/SBAS receiver model to calculate the code and carrier tracking errors. Specifically, the following will be determined: (1) standard deviation of carrier phase tracking errors for a third-order PLL for L1 GPS and SBAS (to indicate loss of lock), (2) standard deviation of carrier phase errors for a second-order PLL for L2 GPS semicodeless carrier tracking aided by L1 (to indicate loss of lock), (3) standard deviation of code tracking errors from a first-order DLL for L1 GPS and SBAS C/A code (to indicate degradation of accuracy), and (4) standard deviation of code tracking errors from a first-order DLL for L2 GPS semicodeless carrier aided by L1 (to indicate degradation of accuracy).

3. Receiver Modeling

3.1. Computing Signal-to-Noise Ratio

[12] GPS/SBAS receivers can tolerate moderate amounts of ionospheric scintillation. Consequently, a model of receiver processing must be constructed in order to calculate the residual effects on signal amplitude and phase after receiver processing and in the presence of scintillation. An L1 C/A code signal can be received by the user from either an SBAS Geostationary Earth Orbiting (GEO) satellite or a GPS satellite. The received power from these sources at a point on or near the earth's surface is specified in references [U.S. Air Force, 1993; RTCA, Inc., 2001, p. A-3] and is shown in Figure 5. The first step in determining signal-to-noise ratio is to linearly estimate the user received signal, C in dBW, from these curves.

Figure 5.

User received minimum signal levels.

[13] The minimum signal levels are those required at the end of a satellite's projected lifetime. The Block II/IIA satellites have exceeded the specified levels, in average, by 3.3 dB for L1-C/A, 6.3 dB for L1P, and 5.4 dB for L2P [Fisher and Ghassemi, 1999]. (For future Block IIF satellites, the signal level of L2P is projected to be even higher.) We have chosen to add a conservative 3 dB to the minimum signal levels across the entire elevation angle spectrum (5 to 90 deg). Antenna gain, Ga (dBic), is linearly estimated from values in the curve shown in Figure 6. This curve was constructed from the minimum antenna gain values specified in the RTCA GPS Antenna Minimum Operational Performance Standards (MOPS) [RTCA, Inc., 1995]. Actual L1 and L2 antenna gain patterns for a typical, commercial antenna are shown in reference [Van Dierendonck, 1996].

Figure 6.

Minimum antenna gain.

[14] The signal-to-noise density ratios for L1-C/A, L1 P-code, and L2 P-code expressed in dB-Hz are respectively [Conker et al., 2000]:

equation image

where CL1-C/A, CL1P, CL2P is the minimum required signal power (dBW) at receiver for L1-C/A, L1P, and L2P; B is the difference between typical observed signal strength and minimum specified strength (3 dB); Ga is the antenna gain (dBic); L is the receiver loss (dB), equal to −2.5 dB; N0 is the noise density, equal to −201.5 dBW-Hz; I is the interference level, equal to 0 dB; and (c/n0)L1-C/A, (c/n0)L1P, (c/n0)L2P is the fractional forms of signal-to-noise ratio for L1-C/A, L1P, and L2P.

[15] As a point of interest, receivers may in general achieve even higher signal levels than 3 dB above minimum due to the difference between typical antenna gains and the minimum specified by RTCA, Inc. [1995]. Two hours of data for (C/N0)L1-C/A and (C/N0)L2P were recently extracted from the Millennium WAAS receiver. Figures 7 and 8 show respectively the values for (C/N0) achieved for different elevation angles. Plotted against these measured values are the C/N0 levels corresponding to the minimum received power levels and the modeled C/N0 levels with 3 dB added.

Figure 7.

(C/N0)L1-C/A for Millennium WAAS receiver.

Figure 8.

(C/N0)L2P for Millennium WAAS receiver.

[16] The scintillation parameter for L1, S4(L1), is part of the output of WBMOD. The equivalent parameter for L2 could be determined by executing WBMOD for L2. Instead it is easier to determine S4(L2) from S4(L1) by the relationship [Hegarty et al., 1999] based on the frequencies of L1 and L2:

equation image

The receiver can lose lock because of a large phase tracking error. The next two sections will present models for calculating these phase errors for two types of PLLs: a third-order L1 GPS and SBAS carrier PLL, and a second-order L2 semicodeless carrier aided by L1 PLL.

3.2. Determining Tracking Error Variance at Output of PLL for L1 GPS and SBAS Carrier

[17] Assuming no correlation between amplitude and phase scintillation, tracking error variance at the output of the PLL can be computed as follows [Knight and Finn, 1998; Hegarty, 1997]:

equation image

where σϕS2, σϕT2 and σϕ,osc2 are respectively the phase scintillation, thermal noise, and the receiver/satellite oscillator noise components of the tracking error variance (σϕ,OSC is assumed to be equal to 0.1 rad (5.7 deg)) [Hegarty, 1997]. For simplicity, we neglect phase variance due to other error sources, e.g., multipath. Thermal noise and oscillator noise constitute a lower bound on carrier phase tracking error since, if there is no scintillation, σϕS2 = 0. Thermal noise tracking error in the presence of scintillation is derived by Conker et al. [2000] and is given as follows:

equation image

where

Bn

L1 third-order PLL one-sided bandwidth, equal to 10 Hz;

(c/n0)L1-C/A

fractional form of C/A code signal-to-noise density ratio, equal to 100.1(C/N0)L1−C/A

η

predetection integration time, equal to 0.02 s for GPS and 0.002 s for WAAS;

S4(L1)<

0.707.

When there is no scintillation S4(L1) = 0, and the above equation becomes the standard thermal noise tracking error for the PLL [Hegarty et al., 1999]:

equation image

From Rino [1979] we see that the PSD of phase scintillation can be represented as:

equation image

where f0 is the frequency corresponding to the maximum irregularity size in the ionosphere, T is the spectral strength at 1 Hz, and p is the slope of the PSD for ff0. The phase error at the input of the PLL is given by Rino [1979]:

equation image

where τc is a system parameter relating to the phase stability time of the receiver. The phase variance of the carrier phase tracking error is given by Knight and Finn [1998]:

equation image

where

equation image

represents common closed loop transfer functions of the PLL with k, the loop order, equal to 1, 2, or 3 and fn the loop natural frequency (Hz). Therefore,

equation image

Both Rino [1979] and Knight and Finn [1998] considered the case where ff0, in which case an approximation can be made by substituting 0 for f0, obtaining

equation image

The phase variance at the input of the receiver PLL is then approximately

equation image

Further substituting into equation (3):

equation image

which is legitimate as long as 2kp > 0 and p > 1. Considering that p is generally in the range between 1 and 4, the requirement is met for both third- and second-order loops. For a third-order loop, k = 3 and fn = 1.91 Hz [Van Dierendonck, 1996]. Knight and Finn [1998] maintain that this approximation is fairly accurate.

[18] Finally, from (1), (2), and (4), the phase tracking error variance (rad2) including scintillation and thermal noise becomes (1 < p < 2k):

equation image

Figure 9 shows the standard deviation of the tracking jitter for L1 carrier using equation (5) for both GPS and WAAS.

Figure 9.

Standard deviation of the tracking jitter for L1 carrier (GPS and WAAS).

3.3. Receiver PLL Threshold

[19] An important carrier loop performance measure for many GPS applications is the mean time between cycle slips (called the mean time to lose lock). The mean time between cycle slips, equation image, for a first-order Costas loop is given by the following equation for the unstressed loop case [Hegarty, 1997; Holmes, 1982]:

equation image

where Bn is the loop bandwidth (10 Hz), and I0 (•) is the modified Bessel function (order zero) of the first kind. Figure 10 shows the relationship between equation image and σϕε for a first-order loop. Higher-order loops, used for dynamic platforms, typically exhibit much smaller (two to three orders of magnitude) values of equation image versus σϕε [Stephens and Thomas, 1995].

Figure 10.

Mean time to lose lock versus total RMS tracking jitter.

[20] The second column of Table 1 contains the results of evaluating equation (6) for jitter values of 9 through 12 deg. These values are representative of a first-order PLL. The third column is two orders of magnitude smaller and represents the equivalent values for a third-order PLL based on simulation results from Stephens and Thomas [1995].

Table 1. Mean Time to Lose Lock for Selected RMS Tracking Jitter Values
σϕε, degequation image (First-Order PLL), hoursequation image (Third-Order PLL), hours
914,149.57141.50
10303.023.03
1117.680.18
122.040.02

[21] From Table 1, it seems reasonable to select a threshold value of 10 deg since that will represent a mean time to lose lock of about 3 hours. Consequently, a long flight through CONUS might expect no more than one loss of lock over the duration of the flight in areas where loss of lock was not predicted. Therefore, if equation image, the receiver is considered to have lost lock on L1-C/A due to carrier phase error.

3.4. Determining PLL Variance for Semicodeless L2 Receiver Aided by L1

[22] An exact determination of phase variance error for this case cannot be determined; however, minimum and maximum bounds can be determined based on whether there is respectively full correlation or no correlation between L1 and L2. This relationship is derived by Conker et al. [2000]. The process is shown in Figure 11 where λ1, λ2, = L1, L2 wavelenghts (m) and ϕ1, ϕ2 = L1, L2 carrier phases (radians).

Figure 11.

Semicodeless PLL.

[23] As before, the phase tracking error variance is the sum of the phase scintillation variance with respect to L2 plus the thermal noise and receiver oscillator noise or:

equation image

However, for this case the thermal noise component is dependent on L1 and L2 as derived by Conker et al. [2000]:

equation image

where

Bn

second-order PLL bandwidth, equal to 0.25 Hz;

(c/n0)L1P

= 0.1(C/N0)L1P;

(c/n0)L2P

= 0.1(C/N0)L2P;

ηY

GPS predetection time for Y code on L2, equal to 1.96 × 10−6 s;

S4(L1)

<0.687.

Again in the case of no scintillation, S4(L1) = S4(L2) = 0 and (8) reduces to the standard representation for thermal noise [Hegarty et al., 1999]:

equation image

The phase scintillation variance for L2 is:

equation image

A representation for equation image, the PSD of equation image, with respect to equation image, the PSD of equation image1, is needed and is derived by Conker et al. [2000]. It is as follows:

equation image

where

equation image

Combining (7)(10) and the approximation Sϕ1(f) ≅ Tfp, we have:

equation image

where: case A = ϕ1 and ϕ2 are uncorrelated, case B = ϕ1 and ϕ2 are fully correlated, and k = 2 and fn = .075 Hz [Van Dierendonck, 1996]. As before, if σϕε2 (rad) · (180/π) > tP = 10 deg, the receiver is considered to have lost lock due to phase variance error.

[24] Figure 12 shows the standard deviation of the tracking jitter for L2 semicodeless aided by L1 carrier using equation (11) for GPS.

Figure 12.

Standard deviation of the tracking jitter for L2 semicodeless aided by L1 carrier (GPS).

3.5. Determining DLL Variance For L1 GPS and SBAS C/A Code

[25] Civilian GPS users are typically not interested in tracking code phase once carrier tracking is lost, since navigation data parity checking is used as a robust lock detector. However, if carrier tracking is not lost from amplitude or phase scintillation, the question becomes to what degree are code tracking errors (and therefore pseudorange errors) increased. Phase scintillations are ignored since they have little effect on code tracking errors. We need only concern ourselves with code tracking errors caused by thermal noise, interference, and amplitude scintillations.

[26] In the absence of scintillation, the tracking variance for a DLL, in C/A code chips squared, may be expressed as [Hegarty et al., 1999]:

equation image

where Bn is the one-sided noise bandwidth, equal to 0.1 Hz (typical), and d is the correlator spacing in C/A chips, equal to 1 to 0.1 (typical).

[27] In the presence of scintillation, the thermal noise jitter variance, in C/A code chips squared, is:

equation image

This is derived in a manner completely analogous to the derivation of the thermal noise jitter variance for a PLL by Conker et al. [2000], by representing the jitter variance in terms of the scintillation amplitude and distributing the variance over the Nakagami-m distribution. Note that for the case of no scintillation, S4(L1) = 0, and equation (13) becomes equation (12).

[28] The standard deviation of the DLL tracking jitter in meters is:

equation image

where WCA is the chip length for L1-C/A, equal to 293.0523 m.

[29] Figures 13 and 14 show respectively the results of L1-C/A code tracking for d = 1 and 0.1 for GPS receivers. Displayed are the values of equation image with respect to (C/N0)L1-C/A for different levels of ionospheric scintillation. The curve for S4(L1) = 0.705 begins to diverge upward. This value was chosen since it is just below 0.707, and from equation (13) is not valid for S4(L1) ≥ 0.707. Of course, this does not present a problem, since according to our model, loss of lock occurs above this level in which case range errors are irrelevant.

Figure 13.

L1-C/A code tracking error (d = 1).

Figure 14.

L1-C/A code tracking error (d = 0.1).

3.6. Determining DLL Variance for L2 Semicodeless

[30] With no scintillation, the DLL jitter variance due to noise or wideband interference, in chips squared, for a semicodeless receiver is [Hegarty et al., 1999]

equation image

where Bn is the one-sided bandwith, equal to 0.3 Hz. Once again in a manner analogous to that of Conker et al. [2000], we express the variance in terms of the scintillation amplitude for L1P and L2P and distribute this over the 2-D Nakagami-m distribution, which produces (in chips squared):

equation image

If scintillation is not present, S4(L1) = S4(L2) = 0, and equation (15) becomes equation (14). The standard deviation of the DLL tracking jitter in meters is:

equation image

where Wp is the chip length for P code, equal to 29.30523 m. The semicodeless code tracking results are shown in Figure 15, which depicts the standard deviation of the DLL tracking jitter against C/N0 of L1-C/A in order to form a comparison with Figures 13 and 14. The ionospheric scintillation is expressed in terms of S4(L1). To construct this chart, the following relationships were used:

equation image

The curve for S4(L1) = 0.685 is shown deviating from the other curves since 0.685 is just below the point at which the equation is not defined. From Conker et al. [2000], this calculation is shown to be valid only for S4(L1) < 0.687. Recall, however, that this is a threshold above which the model will determine that there is a loss of lock making range errors irrelevant.

Figure 15.

L2 semicodeless code tracking error.

4. Analysis of Peak Solar Cycle Scintillation in the Western Hemisphere

[31] Figure 1619 represent the results of applying the above equations for phase angle error to L1 and L2 in the western hemisphere. The UTC time is 0400, which translates to a local time of 11:00 PM EST and 8:00 PM PST. These after sunset times represent a period when scintillation is at its maximum. The day chosen is February 21 with SSN = 150 and Kp = 1 representing the peak of the solar cycle but without the complication of an ionospheric storm.

Figure 16.

Number of satellites visible broadcasting L1-CA (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; UTC = 0400).

Figure 17.

Maximum number of satellites not locked broadcasting L1-CA (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; SSN = 150; Kp = 1; UTC = 0400).

Figure 18.

Number of satellites visible broadcasting L2 (27 GPS satellites; 5-deg mask angle; UTC = 0400).

Figure 19.

Maximum number of satellites not locked broadcasting L2 (27 GPS satellites; 5-deg mask angle; SSN = 150; Kp = 1; UTC = 0400).

[32] The first two charts depict the effects of scintillation on L1. Loss of lock is considered to have occurred at any time the phase angle threshold of 10 deg or the S4(L1) index of 0.707 is exceeded. The first chart, Figure 16, gives at each 5-deg grid increment the number of satellites that broadcast L1 and could be seen at that time and place. These totals include the two GEOs stationed at 54W and 178E. In Figure 17, the maximum number of satellites not locked is given. Subtracting the number of satellites in Figure 17 from the number of satellites of Figure 16 for the same position, the minimum number of satellites still in lock is obtained. The minimum availability of en route through nonprecision approach (NPA) service is obtained by assuming all satellites with large scintillation (ones whose phase errors exceed the 10-deg threshold or which exceed the S4(L1) of 0.707) will result in loss of lock. In practice, the probability of losing lock on all satellites in any one location with large scintillation is very small.

[33] The second group of charts (Figures 1819) are the same as the first two except that the totals apply to L2. The L2 signal received by the SBAS reference receiver is used to correct the pseudoranges caused by the delay through the ionosphere for precision approach applications. Both L1 and L2 must be tracked by a reference receiver for its measurement to be used by the SBAS master station. Loss of lock is considered to have occurred at any time the phase angle threshold of 10 deg or the S4(L1) index of 0.687 is exceeded. SBAS receiver lock is calculated for the fully correlated case and not for the uncorrelated case. The number of satellites maintaining lock tends to be smaller than that for L1. This is due to several factors: First, ionospheric scintillation has a more pronounced effect on lower frequencies than higher frequencies. As shown previously, for the same ionospheric conditions, S4(L2) is about 45% larger than S4(L1) because of the frequency difference. Second, the strength of L2 is lower than the strength of L1 as shown in Figure 5. The weaker signal is less able to accommodate scintillation. Third, the SBAS reference receiver is tracking L2 with semicodeless techniques that suffer SNR degradation. Finally, L2 is not broadcast on GEOs. Consequently, the total number of satellites visible and locked in Figure 18 contain only the GPS satellites and not the GEOs.

[34] Conker et al. [2000] generated charts for number of satellites locked for L1-C/A and L2 with the buffer B above the specified power set to 0 dB instead of 3 dB. This generates a worst case in terms of signal strength. Conker et al. [2000] show that even in this worst case situation, there is no problem with scintillation for L1-C/A in the CONUS.

5. An Example of the Effect of Scintillation on the Instantaneous Availability for En Route and Nonprecision Approach

[35] An example of the effect of scintillation on the instantaneous availability for en route and NPA is given in this section. This availability is calculated by the Global Navigation Satellite System (GNSS) Air Traffic Operations Model (GATOM) as described by Poor et al. [1999]. GATOM is a detailed, Markov-process model that estimates the availability of navigation accuracy and integrity for GPS and its augmentation systems. Scintillation-induced loss of lock information on L1 and L2 is produced for specific satellites, times, and user locations such as shown in Figures 17 and 19. This information is input to the GATOM model. The assumptions used in this example are as follows. (1) A 27 GPS constellation as of 02/21/1999 with two Inmarsat3 GEOs at 54W, and 178E. (2) SA is turned off. (3) There were 45 WAAS Reference Stations (WRSs) assumed for the western hemisphere in this analysis. Of those, 25 WRSs are located in the United States, and the others are proposed sites in Canada, Mexico, and South America. These sites are shown in Figure 20. (4) Effects of interference are not taken into account. (5) A satellite's ranging function is monitored only if the satellite is in simultaneous view of 2 or more WRSs. (6) The Horizontal Alert Limit (HAL) is equal to 2 nmi for en route and 0.3 nmi for NPA. (7) SBAS avionics comply with the minimum requirements of the SBAS Minimum Operational Performance Standards [RTCA, Inc. 2001].

Figure 20.

WAAS phase I WRSs in addition to 20 proposed WRSs in Canada, Mexico, and South America.

[36] It should be noted that the results of this availability prediction are overly pessimistic since WBMOD produces conservative results. Research reported by Knight et al. [2000] indicates that scintillation regions tend to be spatially sporadic and probability of loss of lock on a particular satellite in the impacted area is less than 0.5 even for high scintillation.

[37] Figures 21 and 22 show the minimum en route availability at 0400 UTC without and with scintillation, respectively, and Figures 23 and 24 show the minimum availability of NPA at 0400 UTC without and with scintillation, respectively. The definition of availability used is the probability (equivalent to the expected fraction of time) that SBAS user avionics can compute a position that meets integrity requirements and supports a given phase of flight (en route to NPA). This definition of availability is consistent with International Civil Aviation Organization (ICAO) Annex 10. The effect of scintillation is obvious in the equatorial region. It should be noted that this availability is calculated at one snapshot (0400 UTC) and the results are somewhat pessimistic as mentioned above. By increasing (or decreasing) the time, the red area with no or very low availability in the equatorial region will move westward (or eastward).

Figure 21.

Instantaneous availability for en route without scintillation for L1 (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; UTC = 0400).

Figure 22.

Minimum instantaneous availability for en route with scintillation for L1 (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; SSN = 150; Kp = 1; UTC = 0400).

Figure 23.

Instantaneous availability for NPA without scintillation for L1 (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; UTC = 0400).

Figure 24.

Minimum instantaneous availability for NPA with scintillation for L1 (27 GPS satellites; 2 Inmarsat GEOs; 5-deg mask angle; SSN = 150; Kp = 1; UTC = 0400)

6. Summary and Conclusions

[38] Models have been developed to determine the effects of ionospheric scintillation on the phase-locked loops and delay-locked loops of GPS/SBAS receivers. The phase-locked loop models, when combined with the well-known wide-band scintillation model WBMOD, have enabled estimates to be made on the potential loss of lock of a GPS/SBAS signal due to ionospheric scintillation given specific times and ionospheric conditions. The delay-locked loop models have produced estimates of code tracking jitter related to ionospheric conditions.

[39] For the L1-C/A PLLs and DLLs, the models are limited to S4(L1) < 0.707. For the semicodeless PLLs and DLLs, the models are limited to S4(L1) < 0.687. Above these limits, the receiver is considered to have lost lock. Also a threshold of 10 deg for the standard deviation of the carrier phase tracking errors for the PLLs is employed, above which the receivers are considered to have lost lock.

[40] A study of loss of lock for the carrier phase PLL was performed with minimal signal levels plus 3 dB, SSN = 150, Kp = 1, and time of day = 0400 UTC. These conditions represent high solar activity (solar cycle peak, but no ionospheric storm) during a part of the day where scintillation is at a maximum.

[41] This analysis suggests that loss of lock should be rare for L1-C/A in the CONUS, Alaska, and Canada. However, in the equatorial region and Hawaii in the worst case there could be a significant number of satellites lost (up to 7) due to the effects of scintillation during high solar activity periods (such as solar cycle peaks). Even during these outage periods, a sufficient number of satellites remain to provide users with GPS position solutions and (usually) RAIM integrity (as a backup to SBAS integrity information).

[42] For semicodeless receivers with L2 aided by L1 (such as those located at SBAS reference stations), almost all of CONUS and Alaska suffer no loss of lock. However, the far-northern reaches of Canada, the equatorial regions, and Hawaii could suffer loss of lock for a significant number of satellites. A more realistic estimate is needed of the probability of simultaneously losing multiple satellites in the scintillation region.

[43] The models described in this paper are used to identify areas where scintillation effects can degrade the operational service provided by GPS and SBAS. Service providers need to determine operational strategies for dealing with ionospheric scintillation. Service providers are encouraged to validate the models preferably during the peak of solar cycle (e.g., 2000–2001). Further research is needed to determine the probability of encountering scintillation of multiple satellites for the same location.

Acknowledgments

[44] The authors would like to acknowledge the FAA GPS Product Team (AND-730) for sponsoring this work and the U.S. Air Force Research Laboratory (AFRL) and Northwest Research Associates (NWRA) for providing the WBMOD computer software used in this analysis. Thanks are also given to James K. Reagan and Melvin J. Zeltser of MITRE for their reviews and helpful comments and Swen Ericson for producing the availability maps. This paper reflects the views of the authors. Neither the Federal Aviation Administration nor the Department of Transportation makes any warranty or guarantee, or promise, expressed or implied, concerning the content or accuracy of the views expressed herein. This work was produced for the U.S. Government under contract DTFA01-93-C-00001 and is subject to Federal Acquisition Regulation Clause 52.227-14, Rights in Data-General, Alt. III (June 1987) and Alt. IV (June 1987).

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