Optimising Navigational Precision from Potential GNSS Constellations

Julian Rainbow and Dr Peter Clarke
Department of Geomatics, University of Newcastle, UK.

Abstract

Because of its perceived defects, there has been a move to augment GPS by additional GNSS, either WAAS/LAAS or the proposed European system Galileo. This article looks at some of the potential constellations that could be used and discusses the precision obtained when a dual frequency receiver is employed.

Introduction

GPS has become an accepted method of positioning for many navigators in recent years but there are limitations on it being accepted as the sole means of navigation for safety of life applications. At present, GPS is effectively in a monopoly position as the CIS equivalent, GLONASS, has a doubtful future, and the proposed European “Galileo” system is a considerable time away from deployment. GPS is controlled by the United States Department of Defense and although it is currently freely available, it might not be so if the US thought that their national interests were threatened or if Congress decided that a licence fee should be charged to cover the cost of development. Even if political considerations are discounted, GPS alone cannot guarantee the accuracy, integrity, continuity and availability required for safety-critical areas such as landing and take-off in civil aviation.

This article, examines the effects on navigational precision of the introduction of some realistic candidates for future GNSS constellations. A number of regions were chosen for investigation of the effect of introducing additional constellations on different geographical areas: the British Isles, Europe, the North Pole, Africa and the world as a whole. A program was written in MATLAB to generate positioning precision values within a block of latitudes and longitudes at specified intervals over a given time period. The results were analysed for combinations of GPS with one or more additional GNSS, for both single and dual frequency situations. In this article, the emphasis is on European navigation as this should be the first concern of the Galileo system, and on the dual frequency case as second civil frequencies are well established as a likely component of GPS and other systems in the future.

A standard GPS almanac containing 27 satellites was used as the base case. For potential Mid-Earth Orbit (MEO) and Low-Earth Orbit (LEO) constellations, there is an unlimited choice of orbits; for simplicity, the test cases were based on an actual constellation. Hence, the MEO constellation was based on a 24 satellite GLONASS system and the LEO constellation was based on a 77 satellite constellation developed for Motorola’s Iridium system (which includes 11 spare replacement satellites). Almanac files were found for GLONASS (Deutsches Zentrum für Luft-und Raumfahrt 2001) and Low Earth Orbit (LEO) satellites (McCant 2001). A geostationary (GEO) constellation was constructed from 10 satellites evenly spaced around the Equator. Although a minimum of three geostationary satellites is needed to secure world-wide coverage (Clarke 1945), this would mean that satellites would only be visible at very low elevation angles for many parts of the world with a consequent effect on the precision. The LEO, MEO and GEO constellations were added individually to the GPS almanac file to produce three GPS + augmentation satellite constellations, and finally all the almanacs were amalgamated into one super-constellation.

The time period for computations was set at 12 hours at 15-minute intervals. This was to ensure that all constellations had completed at least one orbital cycle. The calculation of Dilution of Precision (DOP) and actual precision values at 15-minute intervals provides a reasonable interval for a navigator to interpolate. A number of locations were checked at 1-minute intervals to see if any large rapid variations in DOP had been missed, but this was not the case. For a 12-hour time-span (49 15-minute epochs), a certain amount of aliasing (repetition of a particular geometry) occurs. For the 11h 58m GPS orbit, there will only be one almost-repeated GPS set; for the 11h 30m GLONASS orbit there will be three sets, so in these cases the overall mean will be hardly affected. Likewise, for LEOs any aliasing problems will average out over the 7.2 orbits in the 12-hour period.

Three sets of experiments were run with different observation weights. The first set was with a unit weight to provide raw DOP values, and then varying weights were used to simulate the User Equivalent Range Error (UERE) for single and dual frequency receivers. The figures were derived from a number of published sources including (Shaw, Sandhoo et al. 2000) and (Kharisor, Perov et al. 1998). A 10° mask angle was used, but the UERE was not elevation dependent.

Table 1: The User Equivalent Range Error figures adopted (in metres, 1-sigma).

Unless otherwise stated, calculated precisions are quoted as 1-sigma values, corresponding to the 39% confidence interval for 2-D horizontal positioning. It is worth emphasising that the results of our calculations relate to expected positional precision (internal consistency), which may differ from positional accuracy (closeness to the true value, allowing for the possibility of systematic errors).

System requirements

GNSS users primarily fall into three categories: air, sea and land (this article does not consider the use of GNSS for LEO positioning). Each of these classes of user has some quite different requirements in terms of accuracy, reliability and integrity, so they are summarised here.

There are four navigational requirements within aviation: (i) en-route, (ii) non-precision approach, (iii) precision approach, and (iv) terminal area navigation. Typical accuracy requirements for various phases of flight are given in Table 2. Cotton, Jones et al. (1998) states that air traffic is forecast to triple in the period 1998 – 2020 and that the existing infrastructure will not support that. Using a GNSS in aviation would permit direct routing of aircraft rather than the current point-to-point routing. It would be available to all countries without the investment in expensive ground infrastructure, there would be environmental savings in fuel and pollution, and more take-offs and landings would be possible in a shorter time (Frodge 1998).

Table 2: Accuracy requirements (in metres, 95% confidence) for various phases of flight. En-route requirements can vary according to expected proximity to other air routes. The precision approach categories are weather-dependent and will need an augmentation system to achieve them (Diesel and Benoist 1998) and (Breeuwer, Farnworth et al. 1998).

Cotton also states that existing or future aviation uses of GPS would include enhanced early warning systems to prevent Controlled Flight into Terrain (CFIT) and new flying/navigational procedures to permit closer passing of planes Cotton, Jones et al. (1998). Loddo, Flament et al. (1996) states that GPS or GLONASS cannot satisfy the integrity, availability and continuity requirements without augmentations, but that their accuracy could reach the requirements for in-flight, terminal area navigation and non-precision approaches. It is this lack of integrity that is the major objection that the Civil Aviation Authority and Federal Aviation Authority have to sole reliance on GPS for safety critical navigation.

Marine navigation precision requirements are given in Table 3. Loddo, Flament et al. (1996) gives a number of accuracy requirements for maritime work. Berking gives other figures for the Deutscher Satellitennavigationsplan. Other figures are available and at least some of the difference between Sinapi’s and Berking’s figures can be explained by the fact the Sinapi is working to the International Hydrographic Organisation’s minimum standards whereas the German authorities have set their own more rigorous standards. Berking states that the International Maritime Organisation’s sea-going accuracy requirements are 4% of the distance from danger with a maximum accuracy of 4 nautical miles.

Table 3: The navigational requirements for maritime use. 
The figures given are typical 1-sigma accuracies in metres for various types of maritime navigation, unless otherwise stated.

GPS or GLONASS can give the necessary accuracy for either sea or coastal navigation, but at present for seismic acquisition or harbour navigation, differential GNSS techniques are necessary. Seismic exploration companies use differential GPS to achieve the required accuracy and precision. They may use the services provided by an independent contractor such as Racal’s SkyFix, operate their own in-house services such as WesternGeco’s Sargas or install and operate a local reference station for the duration of the project. The client normally requires that a combination of such services be used to provide extra degrees of freedom and as an independent check. A second factor that would interest the seismic industry in an improved GNSS is in the reduction of navigation downtime i.e. time spent not acquiring data whilst on contract due to navigation problems such as bad DOP values. With the advent of 3-D seismic surveying, requirements are considerably tighter than these quoted values. Frodge (1998) points out that marine dredging is one area that could benefit from a GNSS with improved performance, as the ability to accurately determine and check the amount of material removed could lessen the number of expensive law suits.

The requirements on land are different; it is less navigation than vehicle positioning that is required. The two main uses are route optimisation and fleet management (Loddo, Flament et al. 1996) and the accuracy requirements may vary from hundreds of metres down to a few metres and may therefore require differential techniques. Hoff and Kassubek state that Road Transport Informatics systems require a precision of at least 10m (Hoff and Kassubek 1995). DGPS ranges are severely restricted overland and require more rebroadcast stations than when working at sea. Implementation of a GNSS that could remove the necessity to rely on expensive differential services might well be taken up enthusiastically. It would improve the accuracy of positioning, although not the need to use an inertial system to overcome blind spots.

Obtainable precision over Europe

This investigation covered Europe from 35°N – 70°N and 10°W – 60°E, sampling at 2° intervals. Only the DOP and dual-frequency precision values will be discussed because the introduction of the second civil frequency to GPS will soon mean that single-frequency precision is irrelevant to high-precision users. The key statistics are the minimum, mean and maximum precision at each point during the simulated time-span. For each of these statistics the best and worst values found within the geographical region are reported.

Table 4: DOP and precision (m) over Europe for a GPS-only constellation.

Table 4 shows the DOP and precision obtainable from the existing GPS constellation. It is expected that the ratio of HDOP:VDOP ought to be about 1:1.5 and the ratios computed are mostly in this area. Investigation of the worst maximum DOPs (Figure 1) and precisions showed that they were short-lived spikes of a few minutes in duration; however this is sufficient to cause problems in safety-critical applications. The majority of Europe will have a horizontal precision of 10m or less, with only a part of south-west of Ireland, the Western Approaches and the Iberian Peninsula being affected by precision of 20m or worse. This is better than the forecast precision of 20m (Shaw, Sandhoo et al. 2000). Examination of the figures in Table 4 would indicate that a horizontal precision down to approximately the 2m level, at best could be obtained. Most of Europe has a vertical precision of better than 20m and the worst-case again occurs over the Iberian Peninsula.

Table 5: DOP and precision (m) over Europe for a combined GPS + GLONASS constellation.

Fig. 1: Maximum HDOP encountered over Europe using the existing GPS constellation.

The introduction of a second MEO constellation (Table 5) has improved the DOP values obtained, and has, in the main, brought the HDOP down to well below 1 (Figure 2). The maximum HDOP has been reduced to approximately one-third of the GPS value and the VDOP value to approximately one-sixth of the GPS value. There are still spikes in the DOP values, but these have been drastically reduced; yet more satellites in the second MEO constellation would be needed to reduce them. It is interesting to note that the area of worst GLONASS DOP occurs in the same area as one of the worst GPS DOPs and shows that including an additional constellation cannot entirely remove poor DOPs, although it ought to lessen the impact.

Fig. 2: Maximum HDOP encountered over Europe using the existing GPS constellation, augmented by a full GLONASS constellation.

Table 6: DOP and precision (m) over Europe fora combined GPS + geostationary constellation.

Fig. 3: Maximum HDOP encountered over Europe using the existing GPS constellation, 
augmented by a 10-satellite constellation of geostationary navigation satellites.

There are still problems with spikes in the precision when a geostationary constellation is employed (Table 6). The horizontal DOP (Figure 3) is better than when using GLONASS and has a smaller spread than the GLONASS constellation, but the maximum VDOP is worse. Inspection of both the GPS and GPS + geostationary maximum VDOP plots shows that the maxima occur in different areas, and consequent inspection of the minimum availability plots indicate the area of the highest geostationary VDOP occurs in an area and time of changing satellite availability. The geostationary constellation is coming towards the limits of its operational area at 75°N, and as the geostationary constellation is always low to the south it will have a lesser effect on geometry.

Table 7: DOP and precision (m) over Europe for a combined GPS + LEO constellation.

Fig. 4: Maximum HDOP encountered over Europe using the existing GPS constellation, 
augmented by a 77-satellite constellation of Low-Earth Orbit navigation satellites.

Inclusion of a LEO constellation (Table 7) does improve the DOP values (Figure 4), but it gives the smallest average improvement of all the tested constellations and, as when it was tested over the British Isles and Africa, shows that the extremes of bad geometry cannot always be reduced by the introduction of an extra constellation. Subsequent investigation of the failure of a LEO constellation to reduce the worst case values showed that with a 10° mask angle there were short periods of time when no LEO satellite was visible for use. If the worst-case results are ignored then the LEO constellation offers the smallest spread in vertical precision and on average it offers the best vertical precision. The horizontal precision is nowhere near as good as either the results for GLONASS or a geostationary constellation. However, it is noticeable that the LEO constellation does give a horizontal-vertical precision ratio that is closer to unity than all the other constellations.

Table 8: DOP and precision (m) for a combination of all tested constellations.

Combining all the constellations (Table 8) does reduce the DOP values and the combination of constellations at different orbital heights and inclinations overcomes the individual weakness in any one constellation. Although the worst-case VDOP seems bad in comparison with the other VDOP values, it is far better than any of the other constellations’ worst-case values.

Obtainable precision elsewhere

Rather than repeat the above description for each of Africa, the North Pole and world-wide, discussion is limited to some brief summarising comments. For Africa the GPS HDOP values are better than the corresponding values for Europe. This was expected, as GPS HDOP should be at a minimum on the Equator, worsen with latitude as satellites are increasingly confined to the south, then improve again when satellites on the far side of the Pole become visible. On average the GPS VDOP over Africa was better than that for Europe with the exception of the worst-case. For Africa the worst-case GPS vertical precision is about 1m worse than Europe, although the overall positional precision is better. The introduction of additional constellations improves the precision in general, although no augmented constellation improves both components over Africa. Both GPS+GLONASS and the GPS+LEO constellation give better horizontal precision over Africa but their vertical precision is worse, nor does GPS+LEO guarantee to lower the worst-case precision. On the other hand the GPS+geostationary horizontal precision is worse over Africa than it is over Europe and this maybe ascribed to the fact that for much of Africa the geostationary satellites will appear in a narrow band crossing the zenith.

Fig. 5: Maximum HDOP encountered world-wide using the existing GPS constellation, 
augmented by a 10-satellite constellation of geostationary navigation satellites.

Introducing GLONASS around the North Pole made a very small improvement in most of the horizontal and vertical precision results, but did improve the worst-case precision by about 12m horizontally and 76m vertically. The introduction of the geostationary constellation was not expected to improve the precision above 75°N, and this proved to be so (Figure 5), but it did make a small improvement below that latitude. At these latitudes the LEO constellation will improve the worst-case precision at all times of the day. The worst-case of the LEO horizontal precision is about one-quarter of the GPS-only precision and the vertical precision is approximately one-thirteenth of the GPS-only vertical precision. This is because the LEO constellation has a near-polar orbit and consequently a large number of satellites are available. The GPS+LEO constellation offers the best improvement in precision for latitudes above 65°N of any GPS + other constellation. Using all constellations over the Pole did improve the precision, but at the best there was only a 1m improvement in the worst-case horizontal precision compared with the GPS+LEO constellation.

GLONASS offers the best overall improvement for the world because its effects are global, although it does not achieve the local levels of precision that a geostationary constellation offers. Using the geostationary constellation improved the horizontal precision below 75° latitude, with most of the world having a precision of better than 2m, although there were a few small areas where the worst precision was 6m. Similarly with the vertical precision most of the world had a precision of better than 10m although again there were a few exceptions. As discussed previously, the GPS+LEO constellation cannot guarantee to reduce the worst-case precision at all latitudes at all times of the day.

Discussion

Introducing a second constellation will, in general, improve the worst-case precision values; a worst case will remain but the precision of that remaining worst case will be reduced. The only exception to this is that the LEO constellation does not, except above 65° of latitude, improve the worst-case precision. Combining all the tested constellations does overcome individual two-system weaknesses, and the spread of the best- to worst-case precision in both horizontal and vertical is small. Every constellation examined has its advantages and disadvantages in terms of reliability, precision, satellite tracking and orbit determination.

GPS+GLONASS would probably offer the least improvement in terms of precision of all the constellations if it were not for the LEO failure to reduce the worst-case precision values. GPS+GLONASS has a good world-wide availability of satellites, and would be the preferred constellation in equatorial latitudes as the spread of the horizontal precision and its worst-case are better than the equivalent geostationary values. However, the vertical precision is substantially worse than that of the geostationary constellation, at 7m for the dual frequency GPS+GLONASS system.

The GPS+geostationary constellation would be the preferred solution at mid-latitudes. It has a better horizontal and vertical precision than GPS+GLONASS and a smaller spread of precision. As expected it has no effect on the precision above latitudes of 75°. The LEO constellation is only the preferred solution above 65° of latitude where it gives the smallest precision spread of any constellation. It cannot guarantee to improveworst-case precision values in other parts of the world and would have to be used in conjunction with a second MEO or a geostationary system. Some idea of the effect this combination would have can be seen in the all constellation results for the North Pole, where the effect of the geostationary constellation is minimal.

Investigations of the failure of GPS+LEO to improve the worst-case precision compared with GPS-only show that the adopted LEO constellation does suffer from occasional lack of medium-high elevation satellites. Measurements to positioning satellites at low elevation angles are complicated by multipath problems, cycle slips and low signal to noise ratios amongst other problems (Blewitt 1997). It has been customary to avoid these by selecting an elevation mask, commonly 10°. Elevation masks above this angle will quickly decrease the number of usable satellites. Communications users are not interested in the precision of position and therefore they can accept lower elevation angles and consequently will need fewer satellites to achieve global coverage than a navigation constellation will. Inspection of a LEO coverage diagram such as www.geoorbit.org/sizepgs/geodef.html will show that there are a number of locations where the intersection area of satellite coverage is very small, and it may be that a communications constellation cannot provide navigation coverage. Lowering the elevation mask can mitigate this effect, although at the expense of increased noise.

All constellations will need ground-based tracking networks, although satellite-to-satellite ranging could also be used. Such networks need to be well spread geographically, and a LEO network will require a large number of tracking stations. Satellite-to-satellite tracking is probably the answer here. The current GLONASS tracking network is inadequate for the production of precise orbits, although the IGEX tracking stations are available, and the introduction of a second MEO constellation or the restoration of GLONASS to full operational capability will have to plan to overcome this weakness. If an adequate tracking network can be established for any constellation, and satellite-to-satellite tracking is also implemented so that precise ephemerides can be uploaded to satellites more frequently than at present, then the clock and ephemeris errors in the UERE could be reduced, with a consequent improvement in precision. The reduction in UERE will depend upon the constellation design and ground tracking network, but Pieplu et al, postulate that a standalone UERE of approximately 2m or a differentially enhanced UERE of 0.3 – 1.5m could be achieved (Pieplu, Marchal et al. 1996).

Conclusions

So which constellation should be adopted to suit navigational requirements? Ideally, all of them, but the ideal are not always obtainable and which constellation is adopted will depend on geographical location, intended use of the constellation, ease and cost of putting that constellation into orbit.

GPS or GLONASS as standalone systems are acceptable for much marine navigation without augmentation. Combining the two systems and using dual frequency receivers would guarantee acceptable performance in harbour without the need for differential techniques. In fact it has already been shown that a single frequency GPS + GLONASS receiver can achieve non-differential horizontal precisions of 15m (95%), and 0.9m (95%) when differential techniques are applied (Heinrichs and Windl 1998). Seismic exploration work requires better precision and whilst it is probable that any dual frequency system could offer better than 5m performance most of the time, there would still be outliers, so differential techniques would still be required.

For aviation purposes any system including single frequency GPS can satisfy the accuracy requirements for en-route navigation, non-precision approach (NPA) and terminal area movement (Loddo, Flament et al. 1996). It is the requirements for integrity, availability and continuity of service that cannot be met by the existing systems. Table 9 summarises the minimum systems that satisfy the lateral requirements for precision approach formalised by the International Civil Aviation Organisation GNSS-Panel (Loddo, Flament et al. 1996). The validity of use of these systems does, however, depend on constellation geometry being maintained: migration of the satellite orbit caused by the equatorial bulge of the Earth and lesser perturbing forces would, if not corrected, allow gaps to appear in any constellation. Furthermore, integrity and continuity may be compromised by reliance on a non-differential system. None of the systems examined can guarantee the 6m vertical precision (Loddo, Flament et al. 1996) required without augmentation by differential techniques or further improvements to the UERE.

Table 9. The minimum system that satisfies 95% confidence lateral precision requirements for FAA Cat I precision approach. 0 = no system can obtain the necessary precision. 
1 = precision satisfied using a single frequency receiver, 
2 = precision satisfied using a dual frequency receiver

Road and rail users would use additional constellations if available, but could probably be catered for just as well by the implementation of a GIS as the problem here is less navigation than fleet and asset management. Implementing a GIS does assume the existence of reliable base mapping and in the case of railways of recording the infrastructure. Position matching algorithms could be used in the GIS and additional constellations would enable more precise and reliable matching. Additional satellites would help vehicle navigation in urban canyons, but inertial navigation could also be used here.

The proposed European Geostationary Navigation Overlay System (EGNOS) will have a number of geostationary satellites in its constellation; it appears that when Galileo is fully operational that these geostationary satellites will not be used. Results for the GPS+geostationary constellation strongly indicate that serious consideration should be given to retaining a geostationary element in Galileo. Given that the relative costs of launching a 10 satellite geostationary and a 30 satellite MEO constellation are similar, the choice will be made on the availability of satellite slots for the geostationary constellation and whether the navigation payload costs could be offset by using the satellites for communications as well. Probably the solution, certainly for latitudes below 65°, is to use a MEO constellation with a smaller number of augmenting geostationary satellites. The GPS+GLONASS results show increased precision in northern European latitudes (above 54°N) and indicate that the planned orbital inclination for Galileo, 56°, should be increased to an inclination similar to that of GLONASS. At the current planned orbital inclination, Galileo will only improve integrity, and not precision, over large parts of northern Europe.

Foot notes to table 3

¹     Federal Aviation Administration requirements (95%)

²     1 – 2 nautical miles (N.M.)

³     0.25 N.M.

⁴     IHO harbours and approaches requirement

⁵     guns, centre of source, Ocean Bottom Cable(OBC)

⁶       vessels

⁷     first receivers on streamers

⁸     last receivers on streamers

⁹        OBC receiver groups

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Julian Rainbow

served for 20 years as a Royal Artillery surveyor; after leaving the Army he took the Surveying and Mapping Science degree course at the University of Newcastle upon Tyne. On graduating in 1996, he joined Western Geophysical as a navigator on an Ocean Bottom Cable crew working mainly off West Africa. He returned to the Department of Geomatics at Newcastle in 1999 to undertake an MPhil, completed in 2001, and now works for Mason Land Surveys Ltd.

Peter Clarke

obtained his DPhil in Earth Sciences from Oxford University in 1996, and after a two-year period of post-doctoral research there, joined the lecturing staff in Geomatics at Newcastle University. His other research interests include global coordinate reference frames, the use of high-precision GPS and SAR interferometry for geophysical and engineering deformation monitoring, and the integration of geodetic sensors.