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[1] It is well known that ionospheric scintillation has the potential to affect all types of GPS receivers, even dual-frequency military precise-positioning service versions. In a previous effort the degree of degradation to Wide Area Augmentation System (WAAS) operation caused by scintillation, on the basis of simulated data input to an actual WAAS reference receiver under carefully controlled laboratory conditions at Space and Naval Warfare Systems Center, was analyzed and reported [Morrissey et al., 2000]. This degradation is manifested in increased errors for carrier phase and code range measurements and in a higher probability of loss of GPS signal track. However, the results supported the assessment that scintillation should not be a problem for WAAS receivers in the conterminous United States, except perhaps during the very rare occurrence of a “severe geomagnetic storm.” The previous work was briefed in a number of fora, and a detailed report was widely distributed throughout the ionospheric community along with a request for identification of any “gaps” in the results that could be addressed with further testing. From the feedback received, the following tests were conducted: (1) tests with long-duration deep amplitude nulls, corresponding to the GPS signal moving with the ionospheric disturbance; (2) tests with phase scintillation waveforms derived from 50 Hz ionospheric scintillation monitor (ISM) data previously collected by the U.S. Air Force (Philips Laboratory) at Antofagosta, Chile; (3) tests of a modified military single-frequency receiver (Enhanced Miniaturized Airborne GPS Receiver (EMAGR)) side-by-side with the WAAS receiver, with emphasis on maintaining lock at L1; and (4) tests at values of input carrier-to-noise ratio (CNR) lower (i.e., down to 36 dB Hz) than those used in the original tests. The tests with deep amplitude nulls were reported by Morrissey et al. [2002], and the tests with realistic input phase scintillation waveforms were reported at the Ionospheric Effects Symposium (IES) 2002. The current paper is based upon the IES 2002 results as modified by recent testing. Both these amplitude and phase results include EMAGR and low CNR performance.

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[2] GPS single-frequency receivers augmented by the Wide Area Augmentation System (WAAS) can potentially provide the integrity, accuracy, and availability required for a primary-means navigation system for all phases of flight up to category I precision approach in the National Air Space [Loh et al., 1995]. However, a major source of residual error for single-frequency GPS receivers is imperfect modeling of L1 ionospheric delays, the inaccuracy of which can be magnified by ionospheric scintillation [Pullen et al., 1998]. Although simulations have been performed on the effects of scintillation on dual-frequency receivers using phase and amplitude scintillation waveforms generated by Mitre [Hegarty et al., 1999a, 1999b, 2001; Zeta Associates, 2000], there is little actual data with which to quantify the effects of scintillation on WAAS reference station (WRS) dual-frequency receivers and to validate the results of these previous simulations. The purpose of this and previous such investigations has been to collect and analyze data sufficient to quantify such effects.

[3] In this phase of the ongoing effort to characterize WAAS performance, actual dual-frequency WRS and single-frequency Enhanced Miniaturized Airborne GPS Receiver (EMAGR) receivers were tested under carefully controlled conditions at the Space and Naval Warfare Systems Center (SPAWAR) with simulated GPS signals and input scintillation data sets. The control variables were the average input phase scintillation strength (σ_{ϕ}) at L1, the correlation (ρ) between the phase scintillation inputs at L1 and L2, and the input carrier-to-noise ratio (CNR) at L1-C/A. In response to an informal request made by members of the RTCA WAAS and Local Area Augmentation System (LAAS) working groups, an EMAGR receiver was tested concurrently.

2. SPAWAR Test Configuration

[4] The overall methodology and scintillation test setup at SPAWAR has been previously documented [Morrissey et al., 2000; Zeta Associates, 2000; Van Dierendonck et al., 1999] and is only briefly summarized here. The scintillation phase and amplitude perturbations, either simulated or data-derived, are transformed into Doppler profile and power commands, respectively, which in turn drive an STel model 7200 series GPS signal simulator, thus providing an RF simulation of a GPS signal with ionospheric scintillation. These RF signals are input at L1 and L2 into a GPS (similarly did EMAGR at L1) receiver, and data logs are collected for subsequent processing and analysis.

[5] The WAAS reference station receiver has been designed to provide GPS signal measurements for the ground installations in the WAAS network. This receiver unit is actually composed of three integrated NovAtel receivers: two dual-frequency L1/L2 GPSCards (OEM3) and a multipath estimation and delay (MEDLL) receiver (OEM2) [Shallberg et al., 1998]. The three receivers share a common RF feed from the antenna and are phase-locked to the same cesium frequency standard. After clock synchronization of the three receivers at startup, each receiver operates autonomously and provides independent GPS measurements. The two dual-frequency L1/L2 receivers utilize NovAtel's P-Code semicodeless correlation technology, which has been designed to provide robust tracking of the L2 P(Y) signal in the presence of antispoofing.

[6] For the tests reported here, data were collected from the dual-frequency L1/L2 receivers under the following configurations: semicodeless operation; 3, 5, 10 and 15 Hz L1 carrier loop bandwidths (though primary interest was performance at the planned L1 bandwidth of 3 Hz for WAAS); 0.2 Hz L2 carrier loop bandwidth; 0.1 chip spacing (Narrow) for each receiver at L1; code delay lock loop bandwidths of 0.01 Hz for both L1 and L2; and with the firmware (S33) that was recently designed to tolerate deeper amplitude fades by lowering the strict L2 lock detector thresholds.

[7] The L1 RF signal output from the STel 7200 satellite signal simulator was also input to a GSV4004 GPS Ionospheric Scintillation and TEC Monitor (GISTM), which generated independent, real-time estimates of the phase and amplitude scintillation parameters (σ_{ϕ} and S_{4}) and of CNR. The GISTM, developed by GPS Silicon Valley using NovAtel's OEM4 technology, contains the major components of a GPS signal monitor and is specifically configured to measure amplitude and phase scintillation from the L1 frequency GPS signal [Van Dierendonck et al., 1993, 1996].

3. Phase Scintillation Waveform Generation

[8] For the data-derived waveforms the phase scintillation command profiles input to the SPAWAR simulator were based on two contiguous 900 s segments of 50 samples per second ISM data collected from PRN 19 by the Air Force at Antofagosta, Chile, on 11 November 1998. These waveforms, which are denoted here as A(t) and B(t), correspond to 273500-274400 and 272600-273500 seconds GPS time, respectively.

[9] Each of the two waveforms was first high-pass filtered with a sixth-order Butterworth filter with cutoff at 0.1 Hz [Van Dierendonck et al., 1993, 1996], low-pass filtered with a first-order Butterworth filter with cutoff at 2 Hz to reduce the effects of receiver noise, and then resampled at 40 samples per second for input to the SPAWAR simulator. The filtered waveforms A(t) and B(t) are shown as the L1 (lower) waveforms in Figures 1 and 2, respectively, and their corresponding standard deviations over the 900 s intervals are σ_{A} = 0.455 and σ_{B} = 0.38 radians.

[10] The above 2 Hz low-pass filtering was an attempt to separate the scintillation variations from the ISM receiver measurement noise. In theory [Knight and Finn, 1998; Conker et al., 2000], the logarithm of a phase scintillation power spectral density (PSD) function is related to the logarithm of frequency by a straight line. However, in the absence of any low-pass filtering, the PSDs associated with the above data began leveling off around 2-3 Hz owing to the more dominant receiver noise floor, a typical observation at the GPS L1 frequency. Several low-pass filtering techniques were investigated and the first-order Butterworth with 2 Hz cutoff was found to result in an approximate straight line PSD decrease with frequency up to the 20 Hz Nyquist limit. The corresponding slopes were equal to −3.1 and −2.3, respectively, for waveforms A(t) and B(t) and to −2.4 for the simulated data at L1 (see below).

[11] Four test waveform sets were derived from the (filtered) A(t) and B(t) scintillation waveforms as follows (units in radians): The first such set, denoted P1_10, was formed as

and has σ_{ϕ} (at L1) = σ_{A} = 0.455 and a correlation coefficient of ρ = 1.0 between its L1 and L2 components. The second waveform set, denoted P2_10, was formed as

and has σ_{ϕ} = σ_{B} = 0.38 (at L1) and a correlation coefficient ρ = 1.0 between its L1 and L2 components. In order to form waveform sets with ρ = 0.9, the A(t) and B(t) waveforms were linearly combined as follows.

Note that the standard deviation at L1 is equal to σ_{ϕ} = σ_{A} = 0.455, the standard deviation at L2 is equal to σ_{A}, and the correlation coefficient between the L1 and L2 components is ρ. The final waveform set was then formed as

where the standard deviation at L1 is equal to σ_{ϕ} = σ_{B} = 0.38, the standard deviation at L2 is equal to σ_{B}, and the correlation coefficient between the L1 and L2 components is ρ. Note that 77/60 in the equations above is the ratio of the L1 and L2 GPS frequencies and that the A(t) and B(t) waveforms, which were formed from nonoverlapping segments of actual data, are uncorrelated.

[12] Simulated scintillation waveforms generated by Mitre for a previous phase of this effort [Morrissey et al., 2000], corresponding to σ_{ϕ} = 0.5 and ρ = 0.9, were also used in these tests. In addition, the L1 component was scaled by a factor of 77/60 to create an L2 component corresponding to ρ = 1.0.

[13] The L1 and L2 waveforms for P1, for P2, and for the simulated data are shown in Figures 1, 2, and 3, respectively, all for ρ = 0.9. It should be noted that biases were added to the L2 waveforms in these figures for visualization purposes. L2 waveforms for the ρ = 1.0 case are not plotted since these are simply scaled versions of their respective L1 waveforms. In addition, corresponding 60 s σ_{ϕ} values (calculated over the previous 60 s) for L1 and L2 are plotted in Figures 4–6.

[14] The simulated waveforms of Figure 3 appear different than the data-derived waveforms of Figures 1 and 2. The former were simulated as Gaussian random processes, whereas probability distributions for the latter differ from Gaussians in that (1) somewhat more probability mass is concentrated between their plus and minus one sigma values than with a Gaussian, and (2) they decrease somewhat less rapidly in their tail regions than do Gaussian distributions with the same sigmas. This non-Gaussian behavior could be due to nontextbook phase scintillation and/or to residual measurement noise from the data collection. The real and simulated input waveforms described above were also linearly scaled (see first column of Tables 1–6) to simulate similar waveforms but with different phase scintillation levels.

Table 1. Simulated Data Summary, ρ = 0.9

σ_{ϕ}

CNR

49

41

38

36

0.6

6 FIT21 HPF

3 FIT18 HPF

5 FIT19 HPF

12 FIT25 HPF

0.5

6 HPF

2 FIT5 HPF

1 FIT9 HPF

6 FIT8 HPF

0.4

0

0

2 HPF

2 FIT3 HPF

0.3

0

0

0

0

Table 2. Simulated Data Summary, ρ = 1.0

σ_{ϕ}

CNR

49

41

38

36

0.6

13 HPF

15 HPF

16 HPF

2 FIT18 HPF

0.5

5 HPF

6 HPF

6 HPF

7 HPF

0.4

0

1 HPF

0

3 FIT3 HPF

0.3

0

0

0

0

Table 3. P1 Data Summary, ρ = 0.9

σ_{ϕ}

CNR

49

41

38

36

0.59

1 CS11 HPF

1 CS9 HPF

1 CS2 FIT7 HPF

1 CS3 FIT5 HPF

0.50

1 CS3 FIT11 HPF

1 CS2 FIT9 HPF

1 CS1 FIT9 HPF

1 CS5 FIT8 HPF

0.46

1 CS11 HPF

1 CS2 FIT9 HPF

1 CS1 FIT9 HPF

1 CS3 FIT8 HPF

0.41

1 CS9 HPF

1 CS1 FIT8 HPF

1 CS9 HPF

1 CS3 FIT8 HPF

Table 4. P1 Data Summary, ρ = 1.0

σ_{ϕ}

CNR

49

41

38

36

0.59

1 CS2 FIT11 HPF

1 CS2 FIT13 HPF

1 CS4 FIT8 HPF

1 CS5 FIT11 HPF

0.50

1 CS11 HPF

1 CS9 HPF

1 CS2 FIT7 HPF

1 CS3 FIT5 HPF

0.46

1 CS9 HPF

1 CS8 HPF

1 CS2 FIT8 HPF

1 CS2 FIT8 HPF

0.41

1 CS9 HPF

1 CS1 FIT8 HPF

1 CS9 HPF

2 CS3 FIT8 HPF

Table 5. P2 Data Summary, ρ = 0.9

σ_{ϕ}

CNR

49

41

38

36

0.61

3 FIT2 HPF

5 FIT2 HPF

10 FIT3 HPF

12 FIT3 HPF

0.49

1 FIT

2 FIT

3 FIT

4 FIT2 HPF

0.38

0

1 FIT

1 FIT

3 FIT

0.30

0

0

0

0

Table 6. P2 Data Summary, ρ = 1.0

σ_{ϕ}

CNR

49

41

38

36

0.70

10 FIT5 HPF

8 FIT7 HPF

13 FIT5 HPF

21 FIT9 HPF

0.61

2 FIT

2 FIT1 HPF

5 FIT2 HPF

7 FIT3 HPF

0.49

0

0

1 FIT

0

0.38

0

0

0

0

4. WAAS Cycle Slip Detection Algorithms

[15] To provide a realistic assessment of the impact of different scintillation waveforms on WAAS operations, receiver test data were processed using WAAS cycle slip detection algorithms [Zeta Associates, 2001]. WRS processing depends on dual frequency carrier phase processing and therefore requires a robust cycle slip detection capability. Cycle slip detection in WAAS is accomplished using two algorithms: one (FIT) that operates on L1–L2 phase difference and the second (HPF) that operates on L2 phase only. The L1–L2 detector performs a linear fit using the previous five samples and then extrapolates this fit for comparison with the current L1–L2 phase difference. If the magnitude of this residual exceeds 0.055 m, a cycle slip is declared. (This stringent detection threshold is required so that L1 cycles slips are reliably detected.) The fit algorithm also performs an RMS check on the initial fit to ensure the algorithm starts properly.

[16] This linear fit algorithm is very robust at detecting cycle slips but does have a weakness detecting conspiring L1 and L2 slips (i.e., slips at both L1 and L2 that cancel in the “L1–L2” phase difference calculation). The purpose of the L2 phase detector is to protect against these occurrences. This second detector uses a 5-point high-pass filter to account for signal dynamics up to and including a parabolic type input, and if the filter residual exceeds 0.3 m, an L2 cycle slip is declared. The 0.3 m threshold for this algorithm is not as stringent as for the linear fit algorithm because conspiring slips of a few L1 and L2 cycles do not cause significant errors in WAAS processing, and the a priori probability of conspiring slips is relatively low. Both the linear fit algorithm and high-pass filter algorithm accommodate data gaps of less than 4 s by essentially “fly-wheeling” through the missing data periods. Data gaps in WAAS receiver data, however, generally are indicative of the receiver losing lock.

5. WRS Results

[17]Tables 1–6 provide a summary of receiver tracking performance over the 900 s test interval as functions of input CNR, σ_{ϕ}, and ρ for the input waveforms described above and their scaled versions. In the tables, cycle slip (CS) denotes a visually detected change in output carrier phase by more than cycle, FIT and HPF denote cycle slip detections by the WAAS linear fit and high-pass filter algorithms, respectively, and “0” denotes that cycle slips were detected neither visually nor by the WAAS detection algorithms. The linear fit algorithm preceded the high-pass filter algorithm in this analysis and therefore the high-pass filter algorithm would only indicate a cycle slip if the 0.3 m threshold was exceeded and the linear fit detector passed. Note that most of the detected cycle slips (i.e., FIT and HPF) are false alarms in that they are not associated with a visually detected CS. This reflects the conservatism in tuning of detector performance driven by WAAS integrity considerations. Loss of lock (LOL), denoting a receiver dropout greater than or equal to the 4 s coast interval described above, did not occur for any of the conditions depicted in the tables.

[18] There were inconsistencies in the results reported at the May IES-2002, particularly for the lower (36 and 38 dB-Hz) CNR cases. After significant testing and analysis, however, it was determined that the major cause of these inconsistencies was the interaction of WRS semicodeless processing with a reference signal at L2 injected during testing to ease Doppler extraction. This reference signal was eliminated from the test procedure and selected cases were rerun in August 2002 and incorporated into the final results shown in Tables 1–6. Minor inconsistencies remain, however, such as the general decrease in number of HPF detections with decreasing CNR for the P1 data, as shown in Tables 3 and 4. This observation may well be the result of how the cycle slip detection algorithms are ordered in the analysis tool as was mentioned above.

[19]Figures 7–10 provide plots of the behavior of the FIT and HPF cycle slip detection algorithms for simulated data inputs, for ρ = 0.9 and 1.0 and for CNR inputs of 49, 41, and 38 dB Hz. The horizontal lines denote the algorithm thresholds for FIT (+0.055 m) and for HPF (+0.3 m). Similar plots are shown in Figures 11–14 and 15–18 for the input P1 and P2 waveforms, respectively. Note that the plots in Figures 7–18 are biased for the purpose of visualization.

[20] In Figures 7–18, FIT behavior is a strong function of ρ but HPF behavior is not. That is, the FIT algorithm is formulated directly in terms of the successive L2–L1 phase differences, and such differences are greater on the average for a phase correlation of 0.9 than for 1.0. (Ideally, for an L1 phase variance of σ_{1}^{2} and an L2 phase variance of σ_{2}^{2} , the variance of the L2–L1 phase difference is σ_{1}^{2} + σ_{2}^{2} − 2ρσ_{1} σ_{2}, where ρ is the L1/L2 phase correlation.) However, the HPF algorithm behavior depends only upon the higher frequency receiver L2 phase fluctuations, and so it is relatively insensitive to the L1/L2 phase correlation.

[21] Note that the 60 s σ_{ϕ} values plotted in Figures 4–6 are reasonable, though not perfect, indicators of where the WAAS algorithms might detect cycle slips. For example, the HPF threshold crossings around 250 and 284 s in Figure 14 are caused by the rapid scintillation phase variations at the same times shown in Figure 1. Although these crossings correspond to a reasonably high σ_{ϕ} values (at 250 s) in Figure 4, there are higher values of σ_{ϕ} throughout the 900 s interval (e.g., around 600 s) for which HPF threshold crossings did not occur.

[22] All of the visually detected cycle slips reported here occurred for the P1 data (see Tables 3 and 4) at a time of approximately 284 s, and all such slips occurred at both L1 and L2. The slips at L1 are somewhat surprising since the L1 C/A signal is 6 dB stronger than the L2 signal and since L1 performance is not limited by semicodeless technology. Moreover, this differs from previously reported results with simulated data only [Morrissey et al., 2000] for which, for appropriately stressful scenarios, L2 cycle slips occurred but L1 tracking remained robust. Nevertheless, conditions were sufficiently bad for the P1 waveform around 284 s for L1 to slip cycles as well. As a practical matter, since WAAS needs both L1 and L2 data, it matters little whether the L1 carrier loop is still maintaining lock if L2 lock is lost.

6. EMAGR and GSV4004 Results

[23] No cycle slips or losses of lock occurred with either the EMAGR or the GSV4004. This is not surprising since it is well known that tolerance to phase scintillation increases with increasing carrier loop bandwidth [Morrissey et al., 2000; Knight and Finn, 1998; Conker et al., 2000]. The L1 carrier loop bandwidths of the EMAGR and GSV4004 are 15 and 10 Hz, respectively, as compared to the 3 Hz WRS L1 carrier loop bandwidth. The latter bandwidth, though chosen primarily for RFI reduction purposes, provides a good compromise between tolerance to phase scintillation and tolerance to amplitude scintillation, which decreases with increasing carrier loop bandwidth [Morrissey et al., 2000; Knight and Finn, 1998; Conker et al., 2000].

7. Estimation of Phase Scintillation at L1 (σ_{ϕ})from L2 Carrier Phase Error Standard Deviation

[24] In a related effort [Shallberg, 2001] an analysis was performed of the correlation between phase scintillation strength σ_{ϕ} and L2 carrier phase standard deviation for WAAS measurement data. Specifically, the following relationship was developed:

where σ_{ϕ} is the phase scintillation strength at L1 in radians, σ_{L2} is the smoothed receiver estimated L2 carrier phase error standard deviation in meters, and the scale factor relating the two has the value of 42. σ_{L2} is computed by the receiver as the low-pass filtered output (approximate 1 s time constant) of the PLL error signal squared. If proven to be accurate, such a relationship would be extremely valuable in estimating phase scintillation values associated with previously collected and stored WAAS receiver data.

[25] The above relationship is purely empirical. However, it is not surprising that a strong correlation should exist between σ_{ϕ} at L1 and σ_{L2} since (1) the phase scintillation at L1 and that at L2 are highly correlated (correlation coefficient assumed to be between 0.9 and 1.0 in this paper), and (2) the component of σ_{L2} due to scintillation is linearly related to (square root of) any scale factor applied to the L2 phase scintillation PSD.

[26] Plots are illustrated of the above relationship in Figures 19, 20, and 21 for ρ = 0.9, where σ_{ϕ} has been smoothed over 60 s (e.g., as in Figures 4–6) and σ_{L2} has been smoothed over 30 s. Note that the correlation between L1 and L2 is good on the average but not at specific times. The correlation is much better for the case of ρ = 1.0, as shown in Figure 22, though the scale factor 42 has been replaced by the value of 49. Of course, in the absence of dual frequency phase data, the value of ρ is generally unknown.

[27]Figure 23 is a plot from Shallberg [2001] comparing σ_{ϕ} estimates from an ISM at Fairbanks to biased and scaled (see equation above) σ_{L2} values from a WAAS receiver at Anchorage. To limit the effects of any multipath, only estimates associated with elevation angles greater than 30° were used. Note that the comparison is quite good on the average, indicating the relationship is accurate.

[28] It should be noted that a very useful closed form expression is provided by Conker and El-Arini [2002] relating the variance of the tracking error at the output of a phase lock loop (PLL) to the input phase scintillation signal PSD, the amplitude scintillation signal strength S_{4}, and to the PLL parameters.

8. Summary/Conclusion

[29] The following conclusions can be drawn from these tests:

[30] 1. Every visually detected WRS cycle slip was also detected by the WAAS cycle slip detection algorithm, though there were numerous cases of false alarms. These results corroborate the design of the WAAS cycle slip detection algorithm as being quite conservative.

[31] 2. FIT behavior is a strong function of ρ, but HPF behavior is not.

[32] 3. Sixty second σ_{ϕ} values are reasonable, though not perfect, indicators of where the WAAS algorithms might detect cycle slips.

[33] 4. Even for average values of σ_{ϕ} as low as 0.4 radians and for CNR = 49 dB Hz, cycle slip detections are possible with the WAAS HPF algorithm, though these are likely to be false alarms. (See Tables 3 and 4.)

[34] 5. The comparison between phase scintillation strength and scaled receiver estimated carrier phase standard deviation is quite good on the average but not necessarily at specific times.

9. Recommendations

[35] 1. Perform similar tests with input scintillation waveforms derived from dual-frequency (L1/L2) data collected by receivers processing coded L2 signals. (In the tests reported here the phase scintillation command profiles input to the SPAWAR simulator at L1 were based on ISM data collected at Antofagosta, Chile. The corresponding L2 command profiles were synthesized from segments of this L1 data under the assumption of either a 0.9 or a 1.0 correlation coefficient between the L1/L2 phase scintillation waveforms. However, with scintillation data collected at both L1 and L2, more realistic tests could be performed.)

[36] 2. Obtain feedback from the ionospheric community on the results of this paper and recommendations for any additional test scenarios.

Acknowledgments

[37] The authors want to acknowledge that this effort was sponsored by the FAA Satellite Navigation Program Office.