Analysis of differential GPS performance for marine users during solar maximum

Authors


Abstract

[1] GPS signals are refracted by the dispersive ionosphere, resulting in ranging errors dependent on both the given signal frequency and ionospheric total electron content. Such range errors translate into a degradation of positioning accuracies. While it is possible to mitigate the impact of ionospheric effects on GPS positioning applications through ionosphere modeling and/or differential techniques (DGPS), residual errors may persist in regions where steep gradients or localized irregularities in electron density exist, particularly during periods of high geomagnetic activity. Such effects are an issue for the reliable implementation of safety-critical GPS systems. A solar maximum was observed in mid 2000 with associated degradations in GPS positioning accuracies. In this paper the impact of solar maximum on DGPS horizontal positioning applications is investigated. Analyses focus on determining limitations in horizontal positioning accuracies for operational marine DGPS systems. Long-term analyses are conducted using data from permanent GPS reference networks in Canada, Brazil, and the United States. Several million observations are processed in this study during the years 1998–2000. Studies focus on large ionospheric gradients near the equatorial anomaly and at subauroral latitudes (associated with the main trough and storm-enhanced densities). Results indicate that DGPS horizontal positioning accuracies are degraded by a factor of 2–5 relative to average values.

1. Introduction

[2] In differential GPS (DGPS), range errors are calculated at a reference site with known coordinates and transmitted to remote users. The errors remaining after DGPS processing are the atmospheric effects (both tropospheric and ionospheric errors), multipath, as well as orbital errors to a lesser extent. Multipath can be mitigated through proper antenna selection and placement. Atmospheric errors, however, can be rather large depending on the weather conditions (in the case of the troposphere) and activity of the ionosphere. The ionospheric range error depends on both the frequency of the signal and the electron density along the signal path:

equation image

(in meters) where the total electron content (TEC) is integrated along the signal path (in el/m2), f is the signal frequency (in Hz), and + (−) denotes the group delay (phase advance). The ionospheric range error can dominate the DGPS error budget under high levels of ionospheric activity. Additional effects of ionospheric scintillation can cause degradation of GPS receiver tracking performance, and in extreme cases, loss of navigation capabilities entirely [Knight et al., 1999].

[3] Marine users worldwide rely on DGPS systems for safety of navigation, hydrographic surveying applications, and exploration/exploitation of marine resources. Marine horizontal position accuracy requirements are 2–5 m (95%) and 8–20 m (95%) for safety of navigation in inland waterways and harbor entrances/approaches, respectively; horizontal position accuracies of 1–100 m (95%) are required for benefits of resource exploration in coastal regions [U.S. Department of Defense/Department of Transportation, 2001]. Operational systems such as the U.S. and Canadian Coast Guard DGPS services [Fisheries and Oceans Canada, 2001a, 2001b] specify minimum accuracy requirements of 10 m (95%). Marine DGPS is currently used for a diverse range of government, industrial, and military applications; these include hydrographic surveying, assistance to vessel traffic management services, search and rescue operations, environmental assessment and cleanup, and underwater mine detection and disposal.

[4] Under normal operating conditions, DGPS horizontal positioning accuracies on the order of several meters are achieved; correlated ionospheric range errors are compensated to a large extent through the horizontal geometry of the range observations. In the mid 1990s, marine users regularly observed horizontal positioning accuracies well within stated system tolerance. Under high levels of ionospheric activity, however, significant azimuthal gradients in ionospheric TEC can exist, and degradations in DGPS positioning accuracies can occur. In the fall of 1998, offshore surveying applications were interrupted in west Africa and South America [cf. Vigen, 2000] owing to increased ionospheric effects near the equatorial anomaly. The analyses presented here focus on limitations in horizontal differential positioning accuracies in the low-latitude and subauroral regions, where some of the largest TEC gradients in Earth's ionosphere may be observed. A brief discussion of relevant ionospheric effects follows.

2. Ionospheric Effects

[5] The largest global TEC values are generally observed in the equatorial region as a result of stronger incident solar radiation and therefore enhanced ionization. A feature of the equatorial ionosphere is the equatorial, or Appleton, anomaly [Appleton, 1946]. This anomaly consists of two maxima in electron density located approximately 10–15° north and south of the magnetic equator. The daily equatorial anomaly generally begins to develop around 0900–1000 LT, reaching its maximum development at 1400–1500 [Huang and Cheng, 1991]. In periods of solar maximum, however, the anomaly may peak at ≈2100 LT, and gradients in TEC are considerably larger at this secondary diurnal maximum. During the previous solar maximum, Wanninger [1993] observed north-south TEC gradients as large as 30 TEC units (TECU) per 100 km (4.8 m/100 km for L1 ionosphere range delay) in the postsunset anomaly region. Note that 1.0 TECU equals 1016 el/m2 and is roughly equivalent to 0.16 m of range delay at the L1 frequency. Enhancements of the secondary diurnal peak are observed during the equinoctial months in the South American sector [Aarons, 1982].

[6] Enhanced electric fields are present near the equatorward auroral boundary during geomagnetically disturbed periods, which can lead to depletions and enhancements of electron density at subauroral latitudes. The resulting north-south gradients in TEC can cause large differential ionospheric range errors, leading to a degradation of DGPS positioning accuracies. Such large-scale gradients exist at the edges of an ionospheric trough below the equatorward boundary of the auroral oval, at subauroral latitudes of 45°–50° geographic (North American sector), and local times postnoon into dusk. Gradients in this region can persist for several hours, with magnitudes of 10 TECU/degree (15 ppm for L1 ionospheric range delay) [Foster, 2000]. Regions of storm-enhanced electron density (SED) can also occur during more global magnetic storm events, with ionosphere gradients as large as 50 TECU/degree at latitudes near 45° geographic [Foster, 2000]. This effect can also persist for several hours.

[7] The magnitude of subauroral TEC gradients has been shown to be well-correlated with geomagnetic indices [Vo and Foster, 2001]. Such indices are derived using measured variations in magnetic field strength at ground-based magnetometer stations. The Kp three-hourly global index [Mayaud, 1980] is derived from observations at globally distributed subauroral (and auroral) stations. Local three-hourly K indices can also be derived for a given magnetometer station, such that the level of local activity may be quantified in a given region. K indices range from 0 to 9, with 9 representing the highest level of ionospheric activity. In this paper, geomagnetic activity indices are used to quantify DGPS positioning accuracies at subauroral latitudes as a function of ionospheric activity.

3. DGPS Processing

[8] In order to investigate the impact of enhanced ionospheric gradients on DGPS positioning accuracies, two primary analyses were conducted:

3.1. Low-Latitude Region

[9] Horizontal DGPS position estimates were computed using data from two reference stations (UEPP and PARA; see Figure 1) in the Brazilian Rede de Monitoramento Contínuo do Sistema GPS (RBMC) geodetic network, for the period 1999 to May 2000. The 430 km baseline between UEPP and PARA is aligned approximately north-south in the magnetic reference frame and is located 15–20 degrees south of the magnetic equator, near the southern equatorial anomaly peak (evening sector). Daily observation and broadcast ephemeris files were available in receiver independent exchange (RINEX) format with an observation sample interval of 15 s.

Figure 1.

Permanent reference stations in the RBMC geodetic network. The magnetic equator is plotted for reference.

3.2. Subauroral Region

[10] Horizontal DGPS position estimates were computed using two International GPS Service (IGS) reference stations, ALBH and WILL, in western Canada (Figure 2). These two stations are located primarily in the subauroral region. The 438 km baseline between ALBH and WILL is directed approximately north-south in the magnetic reference frame such that this baseline is ideal for evaluating the effects of north-south subauroral ionospheric gradients. Daily observation and broadcast ephemeris files were available in RINEX format, with an observation sample interval of 30 s. Data from 3 full years (1998–2000) during solar maximum were processed. Computed horizontal position errors were matched with the corresponding local K indices from Fredericksburg, Virginia (1998), and Boulder, Colorado (1999–2000), to quantify the level of ionospheric activity. Ideally, K indices from higher-latitude stations closer to western Canada should be used. No such indices were available for this analysis however.

Figure 2.

IGS reference stations Williams Lake (WILL) and Albert Head (ALBH), baseline 438 km. The equatorward boundary of the auroral oval during a moderate substorm event is plotted for reference (line).

[11] Additional analysis of an intense storm event is also conducted in section 5. The DGPS postprocessing for all baselines was conducted using L1 code observations and a modified version of the C3NAV™ software [Cannon et al., 1995]. Horizontal DGPS position estimates were computed for each epoch and 95th percentile positioning error statistics were generated. An horizontal dilution of precision (HDOP) threshold of 2.0 was applied to ensure adequate satellite geometry. An elevation cutoff angle of 10 degrees was used, and troposphere corrections, derived from theoretical models [Saastamoinen, 1973] and mapping functions [Herring, 1992; Niell, 2000], were applied to observations at all stations. Standard atmospheric parameters were assumed. A priori ionospheric corrections from the broadcast ionosphere model [Klobuchar, 1986] were applied. The differential corrections and position estimates were derived using a least squares adjustment, in which observations are weighted as a function of elevation angle, through appropriate modeling of a priori covariance information [e.g., Martin, 1980].

4. Analysis and Results

4.1. Low-Latitude Region

[12] Figure 3 shows a comparison of DGPS horizontal positioning accuracies at reference station UEPP for each hour of local time in March 2000 and June 1999. Note that the average sunspot number was approximately 140 for both of these months. These results were derived by binning all 15-s position estimates for a given month into 1-hour local time intervals. The 95th percentile statistics were then computed for all available data in each bin. More than 7000 position estimates are used to derive each hourly statistic in Figure 3. In June, overall TEC values are lower and large gradients do not exist, such that DGPS horizontal positioning errors are on the order of 1–5 m (95%). In contrast, positioning errors greater than 20 m (95%) are observed for the local time sector 2000–2400 during March 2000. These are consistent with horizontal positioning accuracies observed by Vigen [2000] in March 2000 for a 526 km baseline in western Africa. Such horizontal accuracies exceed marine DGPS error thresholds required for several hydrographic surveying applications [International Hydrographic Organization, 1998].

Figure 3.

Horizontal DGPS positioning accuracies for GPS reference station UEPP, as computed for June 1999 and March 2000 using the UEPP-PARA baseline.

[13] Seasonal variations in the DGPS horizontal position errors are observed in Figure 4, where 30-min 95th percentile horizontal positioning accuracies are plotted for each day of the period 1999 to May 2000, local time sector 2000–2400. While a 24-day data gap exists during July 1999, the seasonal variations are still evident with consistently larger position errors during the winter months. An overall increase in horizontal position error is also observed for early 2000 versus early 1999, evidence of dependence on the solar cycle.

Figure 4.

Horizontal DGPS positioning accuracies for the evening local time sector (2000–2400) at GPS reference station UEPP as computed for the UEPP-PARA baseline.

[14] The HDOP threshold of 2.0 was applied to compute positioning statistics, such that degraded positioning accuracies are attributed to enhanced differential ionospheric range errors as opposed to degraded satellite geometry. It is important to note that only a fraction of 1% of the positioning solutions exceeded the HDOP threshold and were rejected for March 2000. This is consistent with the percentage of rejected solutions for June 1999. The availability of L1 pseudorange data was not significantly compromised in March 2000, a period of high scintillation. Less than 1% of the L1 pseudorange observations were observed to be corrupt for March 2000. However, significant degradations in tracking of L2 code and phase observations using semicodeless receivers are commonly observed during the equinoctial months [Knight et al., 1999].

4.2. Subauroral Region

[15] Figure 5 shows three-hourly local K indices during 1997–2001, where K values of 5–6 indicate a moderate storm event, and K values greater than 6 reflect major intense storm activity. These K indices were derived using magnetometer data from Boulder, Colorado, and are therefore a reflection of subauroral geomagnetic activity in the North American sector. Moderate storm events have occurred relatively frequently since 1997, while only 15 periods with K values greater than 6 have been observed during this solar cycle. Note that significant storm activity occurred during 1998, several years before solar maximum. The frequency and magnitude of geomagnetic storm events tends to peak several years before and after solar maximum; storm events are expected to occur once every few months during 2002–2003 [Kunches, 1997].

Figure 5.

Local K indices for Fredericksburg, Virginia (38.2°N, 77.4°W), during 1997–1998 and Boulder, Colorado (40.0°N, 105.3°W), during 1999–2001. K indices greater than 6 (circles) represent major intense storm activity. Values before (after) the dashed vertical line are for Fredericksburg (Boulder).

[16] Figure 6 shows horizontal positioning accuracies versus local time for the ALBH-WILL baseline (Figure 2) for each level of ionospheric activity as a function of K index. These statistics were generated by classifying all 30-s DGPS horizontal position estimates for the ALBH-WILL baseline according to K value (Figure 5) and then by binning the position estimates in 1-hourly local time intervals. The 95th percentile statistics were then derived for each 1-hour interval for the given value of K index.

Figure 6.

ALBH-WILL DGPS horizontal positioning accuracies (95th percentile) as a function of local time and K index.

[17] In general, larger 95th percentile values are observed for the larger K indices. Diurnal variations in positioning accuracy are also observed, reflecting the nature of ionospheric phenomena in various local time sectors. In particular, maximum horizontal positioning errors for a quiet ionosphere (K < 3) are found in the dayside local time sector with a peak during the local times 1200–1400 and a minimum at local midnight. This is consistent with the diurnal variation of TEC, where larger ionospheric range errors and gradients are observed on the dayside. For enhanced levels of ionospheric activity, a similar diurnal variation is observed, with maximum positioning errors in the dayside local time sector.

[18] The larger positioning errors for K values greater than 4, versus statistics for a quiet ionosphere (K < 3), may be attributed to an increase in the background level of TEC during geomagnetically disturbed periods (ionospheric storms) and/or an enhancement of north-south TEC gradients. These large-scale gradients are associated with the trough and SED phenomena. The presence of such gradients was observed by Vo and Foster [2001] for Kp values greater than 4 using data from the Millstone Hill incoherent scatter radar. In general, marine DGPS users may experience degradations in positioning accuracy by a factor of 2–4 at subauroral latitudes for K values of 7 or more. Such levels of ionospheric activity are associated with major intense geomagnetic storm events, however, and are observed relatively infrequently. It must be noted that only 15 separate three-hourly periods of K > 6 were available to generate the statistics in Figure 6, such that these results are representative of a limited data set. It is possible to monitor ionospheric activity in the auroral and subauroral regions, using a network of GPS receivers, and to quantify the potential impact on GPS users [El-Gizawy and Skone, 2002].

5. Storm Event

[19] One of the largest geomagnetic storms of the current solar cycle occurred 14–16 July 2000. This event began with a solar flare on 14 July, which was accompanied by a coronal mass ejection and enhancement of the solar wind. The wave of solar particles was four times more intense than any other event since 1989. Initial impact on Earth's ionosphere was observed at approximately 1430 UT on 15 July. Kp values of 9 were recorded for the period 1500–2400 UT on 15 July and ionospheric effects continued into 16 July. Aurora were observed over the United States during this event, and midlatitude gradients in TEC were enhanced significantly. Local K indices at Fredericksburg, Virginia (Figure 7), reached values of 9 for the period 1800–2400 UT on 15 July, indicating the presence of severe storm effects in North America.

Figure 7.

Local K indices for Fredericksburg, Virginia, on 15–16 July 2000 (days 197–198).

[20] A map of the TEC over North America at 2225 UT 15 July is shown in Figure 8. Observations from 45 GPS reference stations in both the IGS and Continuously Operating Reference Stations (CORS) networks were used to derive this TEC map, using a wide area ionosphere modeling approach based on the dual frequency GPS observations [Mannucci et al., 1998; Skone, 2000a]. The spatial distribution of vertical TEC was derived using a standard commercial software package, TECANALYS™, in multiple reference station mode [Skone, 2000b]. A localized enhancement of TEC is observed over the Caribbean. This “hot spot” likely corresponds to the northern peak of an enhanced equatorial anomaly. Larger values of TEC expand northward and westward from the Caribbean peak, forming a patch of SED up to geographic latitudes of 37° over the United States. TEC variations during this event have been studied in detail by Coster et al. [2001]. Figure 9 shows the gradients associated with this TEC distribution as a function of latitude. Large gradients on the order of 25–50 TECU/degree are observed near latitudes of 28–30° N. This translates into gradients of 3.6–7.2 m/100 km (L1 range delay).

Figure 8.

Distribution of vertical TEC over North America at 2225 UT on 15 July 2000. Locations of two CORS GPS reference stations are shown: Cape Canaveral (CCV3) and the Atlantic Oceanographic and Meteorological Lab (AOML).

Figure 9.

Vertical TEC variations at longitude 80°W and associated gradients at 2225 UT on 15 July 2000.

[21] In order to assess the impact of these gradients on DGPS horizontal positioning accuracies, DGPS processing was conducted using data from two stations in the CORS network (CCV3 and AOML; see Figure 8) with a baseline of 304 km and a data sample interval of 30 s. The ionospheric range errors exhibit a strong azimuthal dependence near these stations, and larger degradations in positioning accuracies are observed. Figure 10 shows DGPS horizontal positioning accuracies for station AOML. These results were derived as 95th percentile values for the 30-s position estimates in each 30-min interval. An initial increase in position error is observed at approximately 1800 UT on 15 July (day 197), with position errors continuing to increase until approximately 2230 UT on 15 July. Horizontal positioning accuracies of 20–40 m (95%) are observed for several hours during the storm event. Such accuracies far exceed the error thresholds for several hydrographic surveying applications. The larger positioning errors are positively correlated with the local K indices in North America (Figure 7).

Figure 10.

DGPS horizontal positioning accuracies at AOML, as derived using the CCV3-AOML baseline. The dashed line shows the marine DGPS positioning accuracy requirement.

6. Conclusion

[22] Large ionospheric gradients have been observed in a localized low-latitude region during a period of solar maximum, with associated degradations in DGPS horizontal positioning accuracies. Large position errors were observed consistently near the equatorial anomaly during the equinoctial months, with magnitudes of 20–30 m in the local time sector 2000–2400. These errors are approximately a factor of 5 times larger than those observed during the summer months. Such errors arise from the presence of large-scale gradients in TEC near the secondary peak of the equatorial anomaly.

[23] DGPS horizontal positioning accuracies were also investigated in the subauroral region, where large-scale gradients in TEC exist during periods of increased ionospheric activity. Such gradients are not strongly dependent on season or sunspot number, although larger gradients do tend to be observed during periods of solar maximum. Periods of enhanced ionospheric activity in the subauroral region were identified using local K indices, and it was determined that DGPS horizontal positioning accuracies may be degraded by a factor of 2–4 for the higher levels of ionospheric activity.

[24] A region of storm-enhanced density was also observed in the midlatitudes during an intense storm event in July 2000. Large ionospheric gradients, on the order of 30 ppm (L1 range delay), were observed in the southern United States for an extended period. DGPS horizontal positioning errors exceeded 20 m (95%) for several hours during this storm event. Such events are not common at midlatitudes, but study of this event demonstrates the potential of having degraded positioning accuracies in midlatitude regions.

[25] Marine DGPS accuracies of better than 20 m (95%) are required for several hydrographic surveying applications [International Hydrographic Organization, 1998]. Operational DGPS systems, such as the Canadian and U.S. Coast Guard DGPS services, guarantee DGPS horizontal positioning accuracies of 10 m (95%) for marine users. Typical DGPS horizontal positioning accuracies are on the order of several meters, well within specified service thresholds. Results of this paper demonstrate, however, that DGPS positioning accuracies may be degraded in subauroral regions and may exceed error thresholds at low and middle latitudes. This is a significant issue for commercial users relying on DGPS in a marine environment.

[26] In this paper, we have focused on quantifying DGPS horizontal positioning accuracies in various latitude regions. We have identified limitations in the single reference station DGPS approach for marine positioning. It must be noted, however, that the baselines processed here are in the range 300–440 km. These results are therefore representative of expected accuracies at the limits of marine DGPS services. For users located closer to reference sites the results would generally be improved with decreased baseline length (where this relationship would depend on level and nature of ionospheric activity). In order to significantly improve horizontal positioning accuracies, users may consider upgrading to a survey-grade dual frequency receiver or subscribing to a commercial wide area DGPS service. These options are costly but potentially effective. We are currently investigating and developing regional multiple reference station DGPS solutions for marine users.

Acknowledgments

[27] The authors acknowledge the CORS network, the IGS network, and the IBGE, Department of Geodesy, for providing GPS data.

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