Limitations in DGPS positioning accuracies at low latitudes during solar maximum



[1] While it is possible to mitigate the impact of ionospheric effects on Global Positioning System (GPS) positioning applications through differential techniques, residual errors may persist in regions of steep TEC gradients. An enhancement of absolute TEC and large-scale gradients is observed at low latitudes near the equatorial anomaly. This effect is significant in the equinoctial months during periods of solar maximum. In this paper, differential GPS (DGPS) positioning accuracies in the anomaly region are investigated during the period of solar maximum 1999–2000, using as data the L1 pseudoranges. TEC gradients of 30 TECU per 100 km are observed during March 2000, with corresponding horizontal and vertical position errors of approximately 25–30 m (95% confidence level) for single baseline processing. Positioning accuracies are improved by a factor of 5 for a wide area DGPS approach.

1. Introduction

[2] The ionosphere is a dispersive medium, in which RF signals are refracted by an amount dependent on the given signal frequency and the electron density, resulting in a range error:

equation image

where TEC denotes the total electron content integrated along the signal path (in el/m2), f is the signal frequency (in Hz), and + (−) denotes the group delay (phase advance). GPS signals are transmitted on two frequencies, 1575.42 MHz (herein referred to as L1) and 1227.60 MHz (herein referred to as L2), and the dispersive nature of the ionosphere allows direct calculation of the absolute TEC using a dual frequency GPS receiver. The TEC is generally expressed in units of TECU, where 1 TECU translates to a 0.16 m propagation delay in the L1 observable. Regional or wide area TEC models can be derived using observations from multiple dual frequency GPS reference stations. A common technique is to estimate parameters describing the vertical TEC (or electron density distribution) and hardware biases simultaneously, in a solar-geomagnetic reference frame using a Kalman filter formulation [Mannucci et al., 1998; Juan et al., 1997; Skone, 2000a].

[3] Single frequency GPS users must employ differential GPS techniques to reduce spatially correlated ranging errors. The ionospheric range error can dominate the DGPS error budget under high levels of ionospheric activity. The largest global TEC values are observed at low latitudes in the equatorial anomaly. This region is also characterized by strong north-south gradients in TEC. Irregularities in electron density cause scintillation of the RF signals and degraded receiver tracking performance, particularly for the L2 signal [Knight et al., 1999]. Ionospheric effects in the anomaly region are a function of local time, season and solar cycle. In this paper we focus on DGPS positioning accuracies in the anomaly region.

2. Equatorial Anomaly

[4] The equatorial, or Appleton, anomaly [Appleton, 1946] consists of two maxima in electron density, located approximately 10–15 degrees north and south of the magnetic equator. This feature is controlled by an E-region dynamo that is driven by global tidal winds, resulting in a zonal electric field at the magnetic equator. In the dayside to postsunset local time sector, this electric field is directed eastward, creating an E × B drift velocity that is directed upwards and away from the magnetic equator (the “fountain effect”) [Balan and Bailey, 1995]. In the post-midnight sector, the equatorial electric field is generally directed westward, resulting in the opposite effect—a lowering of ionospheric plasma towards the magnetic equator.

[5] The daily equatorial anomaly generally begins to develop around 0900–1000 local time, reaching its maximum development at 1400–1500 [cf. Huang and Cheng, 1991]. In periods of solar maximum, however, the anomaly may peak at ≈2100 local time, 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 TECU per 100 km (48 ppm for L1 ionosphere range delay if any model is applied) in the postsunset anomaly region. Seasonal peaks in equatorial TEC are observed during the equinoctial months. Seasonal enhancements in scintillations are also observed during equinoctial months near the anomaly peaks—South American sector [Aarons, 1982].

3. TEC Estimates

[6] The current solar cycle reached a peak in mid-2000. In order to analyse the various trends in low latitude TEC during the period of solar maximum, dual frequency data from the period 1999–2000 were processed for GPS reference station UEPP of the Rede de Monitoramento Conti´nuo do Sistema GPS (RBMC) geodetic network in Brazil (Figure 1). Observation and broadcast ephemeris files were available in RINEX format [Gurtner et al., 1989; Gurtner and Mader, 1990], with an observation sample interval of 15 s. The dual frequency observations were processed using a standard commercial software package (TECANALYS™) to derive vertical TEC estimates [Skone, 2000b]. Accuracies of vertical TEC estimates were in the range 1–5 TECU.

Figure 1.

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

[7] Figure 2 shows a comparison of diurnal variations in TEC for summer (June 3, 1999) versus the equinox (March 23, 2000) at UEPP. Dayside TEC values are a factor of approximately 2 larger for March versus June. Daily peak values of TEC are observed at approximately 1400 local time. Diurnal values vary by approximately 20 percent with respect to monthly mean values. An enhancement of the secondary diurnal peak is observed at approximately 2200 local time during March 2000. This secondary peak is particularly enhanced during the period of solar maximum and associated gradients can be very large in the north-south direction.

Figure 2.

Vertical TEC values observed during the summer (June 3, 1999) and equinoctial (March 23, 2000) months for GPS reference station UEPP.

[8] In order to investigate the magnitude of TEC gradients at low latitudes, data from reference stations in the Brazilian RBMC geodetic network (Figure 1) were used to compute regional maps of the vertical TEC. The spatial distribution of vertical TEC was derived using TECANALYS™ software in multiple reference station mode employing a grid approach [Skone, 2000a]. The two-dimensional TEC maps are defined in geomagnetic latitude and local time. A further conversion to magnetic coordinates allowed extraction of TEC gradients in the north-south (magnetic) direction over Brazil.

[9] Figure 3 shows the TEC gradients computed for March 2000. Enhancement of the secondary anomaly peak is observed in the local time sector 2000–2400, where gradients as large as 20–30 TECU per 100 km (32–48 ppm for L1 ionospheric range delay) exist. Figure 3 also shows the average latitude of the southern anomaly peak for each hour of local time. The largest gradients are observed near this peak, which is located at approximately 15° south magnetic latitude in the evening local time sector. Note that the magnitude of west-east gradients rarely exceeded 10 TECU per 100 km.

Figure 3.

North-south vertical TEC gradients near the equatorial anomaly during March 2000, and magnetic latitude of the southern anomaly peak (line).

4. DGPS Positioning Accuracies

[10] In order to investigate the impact of such low latitude gradients on DGPS positioning accuracies, data from two reference stations, UEPP and PARA (Figure 1), in the Brazilian RBMC geodetic network were processed for the period 1999–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 anomaly peak (evening sector). Daily observation and broadcast ephemeris files were available in RINEX format, with an observation sample interval of 15 s.

4.1. Baseline Processing

[11] Post-processing was conducted using L1 code observations and a modified version of the C3NAV™ software [Cannon et al., 1995]. Differential corrections were generated for the reference station PARA, and these corrections were then applied to observations at the reference station UEPP. Position estimates were computed for UEPP and 95th-percentile positioning error statistics were computed for every 30-minute interval. A PDOP threshold of 3.0 was applied to ensure adequate satellite geometry. An elevation cutoff angle of 10 degrees was used and troposphere corrections, derived from theoretical models, were applied to observations at both UEPP and PARA. 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.

[12] Figure 4 shows a comparison of DGPS positioning accuracies at reference station UEPP for each hour of local time in March 2000 and June 1999. In June, overall TEC values are lower and large gradients do not exist—such that DGPS horizontal and vertical positioning errors are on the order of 1–5 m (95%). In contrast, positioning errors greater than 20 m (95%) are observed in both vertical and horizontal components for the local time sector 2000–2400 during March 2000. Such horizontal accuracies exceed marine DGPS error bounds of 10 m (95%), as required for several hydrographic surveying applications [International Hydrographic Organization, 1998].

Figure 4.

Vertical and 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 5, where 30-minute horizontal positioning accuracies are plotted for each day of the period 1999–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 5.

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 PDOP threshold of 3.0 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 percent of the positioning solutions exceeded the PDOP 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. Significant degradations in tracking of L2 code and phase observations are commonly observed during the equinoctial months, however [Knight et al., 1999].

4.2. Wide Area DGPS

[15] In the previous section, a priori ionospheric corrections were applied using the broadcast Klobuchar ionosphere model. This model is a function of local time and geomagnetic latitude, as described by eight coefficients. This model has been designed to mitigate range errors arising from large-scale ionosphere features, and model estimates are within 50% of the true ionospheric delay values.

[16] In recent years, more refined ionosphere models have been derived for real-time wide area DGPS operations [e.g Mannucci et al., 1998]. The wide area technique incorporates observations from multiple reference stations to model individual error components. Separate models are derived for ionospheric corrections, satellite clocks, and satellite orbits. Correction messages are generally provided via geostationary satellite downlink. Such satellite-based augmentation systems are being developed worldwide (e.g. the Wide Area Augmentation System, EGNOS, MSAS, GPS·C).

[17] In order to assess user accuracies achieved with such an approach, further processing was conducted for station UEPP. Ionospheric corrections were derived using the regional TEC model described in section 3. Station UEPP was excluded from the ionosphere estimation process. Rapid clocks and predicted orbits [Skone et al., 1997] were used to simulate wide area clock and orbit corrections with accuracies at the sub-meter level. Processing was conducted for the period March 2000, in order to obtain statistics for direct comparison with tests in section 4.1. The results are summarized in Table 1 (local times 1800–0200) and clearly indicate a significant improvement (by a factor of five) over standard single baseline DGPS processing. The improved results were achieved primarily through better resolution of the ionosphere.

Table 1. 95-th Percentile Positioning Accuracies at Reference Station UEPP, Local Times 1800–0200 in March 2000
Processing TechniqueHorizontal (m)Vertical (m)
Single baseline DGPS17.7821.60
Wide Area DGPS3.274.63

[18] It must be noted, however, that the ionosphere model in this section has been computed from a dense network of reference stations in the local vicinity of UEPP. Accuracies of wide area ionosphere corrections depend very strongly on the reference network geometry. For a sparse network of reference stations (e.g. station spacings of several thousand kilometers in South America), localised ionospheric gradients may not be resolved and the positioning results would be significantly degraded, relative to those presented here. This is an important consideration in assessing the potential performance of a given wide area DGPS system. There is significant potential, however, for employing a wide area approach to improve DGPS positioning results at low latitudes.

5. Conclusion

[19] Variations in the magnitude of absolute TEC and large-scale TEC gradients were observed in the equatorial region. Dayside vertical TEC values were 100–120 TECU during the equinoctial months, in contrast to values of less than 60 TECU during the summer months. Enhancements of the secondary diurnal peak occurred during the equinox, with associated ionospheric gradients as large as 30 TECU per 100 km in the evening sector. The impact of these ionospheric effects on DGPS positioning accuracies was investigated, using the L1 code pseudoranges.

[20] For single baseline DGPS processing, positioning errors of 1–5 m (95%) are observed during the summer months at all local times. At the equinoxes, however, position errors of 25 (30) m are observed in the horizontal (vertical) components in the evening sector (95% confidence level). Such horizontal accuracies exceed the DGPS error bounds required for many hydrographic surveying applications.

[21] In order for single frequency users to achieve improved positioning accuracies consistently at low latitudes, a further option to use wide area DGPS exists. The wide area ionosphere model may allow resolution of localised features if reference station spacing is adequate. Application of wide area corrections can result in positioning accuracies of better than 4 (5) meters in the horizontal (vertical) component (95% confidence level). These accuracies represent a significant improvement over standard DGPS processing during the equinoctial period at solar maximum.


[22] The authors acknowledge the IBGE, Department of Geodesy, for providing GPS data.