research initiatives are considered, namely: i) GPS relative positioning with multiple ...... specifically, an efficient ambiguity search engine named as the OMEGA ...
IMPROVEMENT OF KINEMATIC OTF-GPS POSITIONING OVER LONG DISTANCES : APPLICATIONS TO BATHYMETRIC SURVEYS R. Santerre1, R.B. Langley2, M. Ueno1, A. Biron1, D. Kim2 D. Parrot3, C. St-Pierre3, P. Tétreault4, G. Marceau5, D. Langelier6 1
2
Centre for Research in Geomatics, Laval University Department of Geodesy and Geomatics Engineering, UNB 3 VIASAT Geo-Technologie 4 Geodetic Survey Division, Geomatics Canada 5 Canadian Coast Guard, DFO 6 Canadian Hydrographic Service, DFO
ABSTRACT This research project, which is part of the Canadian GEOIDE (GEOmatics for Informed DEcisions) Network of Centres of Excellence, is dedicated to the improvement of the methodology and the algorithms to achieve more precise and more reliable kinematic GPS positioning which implies more reliable and efficient On-The-Fly (OTF) phase ambiguity resolution over distances up to 75 km, for the support of bathymetric surveys in real-time. To reach these goals, different research initiatives are considered, namely: i) GPS relative positioning with multiple reference stations, ii) the improvement of ionospheric modelling, iii) the use of precise real-time orbits, iv) the integration of Glonass observations and v) radio-communication management. The GEOIDE Network of Centres of Excellence started its research activities in March 1999. In this presentation, we will summarise research performed during the first year of our 3-year project. The results are mainly related to the use of a priori water level information (from tide gauges) to constrain the OTF-GPS solutions and the interpolation of relative ionospheric delays. Other activities conducted within our GEOIDE project will also be briefly discussed, namely, the development of improved algorithms for OTF ambiguity resolution and the processing of carrier phase observations from Glonass satellites. RÉSUMÉ Ce projet de recherche, qui fait partie du Réseau canadien de Centres d’Excellence en Géomatique GEOIDE (La GÉOmatique pour des Informations et des Décisions Éclairées), est dédié à l’amélioration de la méthodologie et des algorithmes pour obtenir un positionnement cinématique GPS plus précis et plus fiable ce qui implique la résolution fiable et efficace des ambiguïtés de phase en mouvement ou OTF (On-The-Fly) sur des vecteurs jusqu’à 75 km de longueur, pour le support des levés bathymétriques en temps réel. Pour atteindre ces objectifs, différentes initiatives sont considérées, à savoir : i) le positionnement relatif à partir de plusieurs stations de référence, ii) l’amélioration de la modélisation ionosphérique, iii) l’utilisation d’éphémérides précises en temps réel, iv) l’intégration des observations Glonass et v) la gérance de la communication des données. Le Réseau de Centres d’Excellence GEOIDE a débuté ses activités de recherche en mars 1999. Dans cette présentation, nous résumerons les résultats obtenus au cours de cette première année de notre projet de recherche qui est échelonné sur 3 ans. Ces résultats sont principalement reliés à l’utilisation de l’information a priori sur le niveau de l’eau (obtenue de marémètres) pour contraindre les solutions GPS et à l’interpolation des délais ionosphériques relatifs. D’autres activités de recherche conduites dans notre projet de recherche GEOIDE seront également exposées brièvement, à savoir, le développement d’algorithmes améliorés pour la résolution des ambiguïtés de phase OTF et le traitement des observations de phase des satellites Glonass. THE GEOIDE NETWORK OF CENTRES OF EXCELLENCE In October 1998, The Canadian Government announced the launch of the GEOIDE (GEOmatics for Informed DEcisions) Network. The organisation of the GEOIDE Network is an initiative of the Centre for Research in Geomatics (CRG) at Laval University. The Networks of Centres of Excellence (NCE) program will spend close to $12 million over
the next four years for the creation of this network. The project will generate an estimated $30 million worth of investment throughout its life span – extending at least until 2005. The management of the whole network is under the responsibility of a new administrative centre located at Laval University, in Quebec City. This centre co-ordinates the efforts of 100 researchers from 24 universities, 26 enterprises and 16 government agencies. The GEOIDE Network will focus on projects with commercial and marketable applications. More specifically, it seeks to: better exploit the Canadian geomatics infrastructure; develop tools and technologies for decision making and information dissemination; co-ordinate fundamental research in multidisciplinary pan-Canadian teams; broaden the range of applications based on geomatics technologies. The GEOIDE Network (http://www.geoide.ulaval.ca) is actually a network of networks. It is currently composed of 23 projects, all multi-sectorial (i.e., private sector, government and academia) and multidisciplinary. The selected projects fall into three categories. First, the Natural Resource category covers more traditional applications of expertise developed in Geomatics (e.g., the development of an integrated decision support system for watershed and coastal zone management). The Environmental Monitoring category addresses issues such as detecting environmental disasters and using remote sensing for search and rescue operations. Lastly, and less traditionally the third category covers health, commerce and social policy, e.g., projects tracking key health indicators on the internet; and the use of Geomatics for strategic planning in the business/commercial sector. More information about the GEOIDE Network can de found in [Edwards and DeGroeve, 1999]. THE GEOIDE’S PROJECT ENV#14 The research results reported in this paper have been conducted within the project ENV#14 sponsored by the GEOIDE Network. This project is dedicated to the improvement of the methodology and the algorithms to achieve more precise and more reliable kinematic GPS positioning which implies more reliable and efficient On-The-Fly (OTF) phase ambiguity resolution over distances up to 75 km, for the support of bathymetric surveys in real-time. To reach these goals, different research initiatives are considered, namely: i) GPS relative positioning with multiple reference stations, ii) the improvement of ionospheric modelling, iii) the use of precise real-time orbits, iv) the integration of Glonass observations and v) radio-communication management. Multiple reference stations: As in geodetic networks, redundant observations provide more precise and reliable results. A solution from multiple baselines is more reliable than that obtained from a single baseline (the 3D positioning of a vessel only from 1 reference station, as presently used). Weighted least squares adjustments, taking into account mathematical and physical correlations in phase observations between GPS receivers at the reference stations and onboard the survey vessel have then to be considered. Ignoring those correlations can lead to an unrealistic estimation of the positioning precision. If antennas of different makers are used, antenna phase centre variation must be calibrated. Relative phase centre determination with a small calibration beam (developed at the CRG) will be used. Such analyses will be compared with an antenna calibration in an anechoic chamber (like the one located in the Department of Electrical and Computer Engineering at UNB). Ionospheric modelling: To complement the interpolation of the (systematic) ionospheric refraction, the modelling of the stochastic part of the relative ionospheric correction should be considered, for example, with Kalman filtering algorithms and external input sources such as an indication of the prevalent solar and geomagnetic activity. Such activity generates a phenomenon called ionospheric scintillation. Ionospheric scintillation provokes rapid variations in the phase measurements which could be erroneously interpreted as cycle slips (discontinuity in the phase observations). Reduction of the effects of multipath (interference between the direct signal and those reflected off the surfaces close to the antenna) will help to have a more realistic interpolation of ionospheric refraction. At the reference (fixed) stations, this could be done with the spectral analysis of a number of days of data, because for fixed stations, multipath repeats itself as a function of satellite configuration which repeats itself every day (in fact, it comes 4 minutes earlier each day). To reduce multipath effects at the mobile receiver, an approach which uses indices like signal to noise ratio associated with GPS observations seems promising. Precise real-time orbits: For GPS positioning, the positions of the satellites are assumed to be known. Errors in the satellite position will propagate into relative positioning solutions and can create errors of about 1 ppm (10 cm for a 100 km baseline) if broadcast ephemerides are used. Satellite position errors will also reduce the chance of successful phase ambiguity resolution. Precise orbits, as determined from data from the Active Control System (ACS, developed by the
Geodetic Survey Division) are 10-20 times more precise than broadcast orbits. Within the coming months, precise orbits will also be available in real time. Then, precise orbits will meet two goals. First they will facilitate the resolution of GPS phase ambiguities on long baselines and secondly, they will provide more precise relative positioning. Glonass observations: Some receivers currently available on the market allow the reception of both GPS and Glonass signals simultaneously. Glonass is the Russian GPS-like satellite positioning system. More visible satellites usually give a better PDOP (a factor to quantify the goodness of satellite geometry) and better positioning precision. This also increases the reliability of phase ambiguity resolution. However, the following points have to be dealt with to efficiently integrate Glonass observations into a GPS solution: Glonass and GPS time scales and coordinate systems are different and the phase ambiguity resolution associated with Glonass satellites is more tedious because Glonass satellites do not operate on the same carrier frequencies. Radio-communication management: For real-time operation, all the information (GPS and Glonass phase observations, ionospheric corrections, precise orbits, …) will have to be communicated from the reference stations to the mobile receiver(s). Attention must be paid to the radio communication link. Right now, a VHF radio link with a 9600 bps data rate supporting RTCM-SC104 protocol is used to transmit the data (the mobile unit receives observations only from 1 reference station) at a maximal distance of 75 km. When more information will have to be transmitted, the transmission time would be slowed down. Time latency would have to be dealt with involving prediction algorithms for the correction to the phase observations. For expanded coverage, relay stations could be used, but this could add even more time latency into the data transmission. To perform all these researches, our mini-network gathers six groups: two universities (Laval and UNB), one private company (VIASAT) and three governmental agencies (Geodetic Survey Division, Canadian Coast Guard and Canadian Hydrographic Service). Our research team regroups specialists in geodesy, satellite positioning (GPS and Glonass), hydrography, physics, mathematics, engineering and radio-communication. The research activities within the GEOIDE ENV#14 Project are quite closely related to the scope of Special Study Groups sponsored by the International Association of Geodesy. Drs. Santerre and Kim are members of the Special Study Group SSG1.179 – Wide Area Modelling for Precise Satellite Positioning and Dr. Langley is member of the Ad Hoc Working Group – Refractive Indices of Light, Infrared, and Radio Waves in the Atmosphere. There also exist links between our team with the GEOIDE Network of Centres of Excellence in Geomatics: Richard Langley is participating in two other GEOIDE projects (ENV#17, RES#47); Denis Parrot is member of the GEOIDE Board of Directors; and seven other researchers of the CRG at Laval University and three other professors from UNB are participating at 16 of the 23 GEOIDE projects. The next section is related to the use of a priori water level information (from tide gauges) to constrain the OTF-GPS solutions. Another section is dedicated to the interpolation of relative ionospheric delays. Other activities conducted within our GEOIDE project are also briefly discussed in the last section of this paper. HEIGHT CONSTRAINT FOR GPS AMBIGUITY RESOLUTION Precise centimetre-level positioning is potentially achievable from GPS carrier phase observations. In order to achieve such accuracy, carrier phase ambiguities, a number of cycles which is not measured by a GPS receiver, must correctly be resolved. The determination of the ambiguity parameters while a remote receiver is moving, is called "on-the-fly" (OTF) ambiguity resolution. The ambiguity resolution on L1 or narrow-lane band (with an effective wavelength of about 20 cm) is more difficult to achieve than that for the wide-lane band (the wavelength of the wide-lane is 86 cm), especially when the distance between the survey ship and the GPS reference station gets longer. For the bathymetric survey operations on the St. Lawrence River, the closest GPS reference station can be as far as 75 km. The objective is to improve the method of phase ambiguity resolution and the algorithms for kinematic GPS positioning on long baseline vectors using height constraint. A height constraint is the most intuitive type of constraint available in a marine environment. The height of water level on the St. Lawrence is easily accessible from the network of the automated COWLIS tide gauges deployed by the Canadian Hydrographic Service (CHS). Most of these tide gauges are located in the vicinity of the wharf of base ports used by the CHS survey ships. This information could be used to assist the resolution of GPS
phase ambiguities when the ship is still at the wharf. However, the water level measured by the tide gauge is given with respect to the local Chart Datum (CD), while GPS height positioning refers to the WGS-84 ellipsoid. Therefore, making use of COWLIS measurements as constraints for GPS positioning, requires a conversion of altitude. The Chart Datum (CD) is a reference surface from which the CHS establishes bathymetric depth. Figure 1 shows the vertical profile of the measurements. The datum separation between the ellipsoid and the CD is represented by the symbol (NCD).
GPS
GPS Ref. station
Squat + Heave Tide gauge
ZA Dt
TCOWLIS
Geoid Chart Datum NCD
Depth
hOTF Ellipsoid
Figure 1: Relationship between the GPS height and the COWLIS reading. The relationship between the CD and the geodetic reference ellipsoid on the St. Lawrence is known thanks to the previous works performed by the CCG and the CHS [Marceau and Langelier, 1997]. To reduce the ellipsoidal altitudes (determined by GPS-OTF) to the CD, one interpolates the datum separation between the CD and the ellipsoid using a grid established by the CCG and the CHS. The height of the GPS antenna (mounted on the mast of the ship) from the water surface must be measured. Antenna height (ZA), which is the distance from any point attached to the ship (reference point) to the antenna phase centre, can be measured. A reference point such as the transducer of echo sounder or bottom of keel can be measured beforehand. The vertical distance from GPS antenna to the reference point is fixed and independent of the ship's draught. Once the reduction of GPS height (hOTF) to the ship's draught line is done, the tide obtained by OTF technique is the difference between the draught (floating) line and the CD. As tide, swell, draught, and squat are measured all together on board a sounding ship, the current sounding method requires a heave sensor to make correction of the effect caused by the ship's movement. If the GPS antenna is not located above the heave sensor, remote heave measurements also have to be taken into account. This proposed approach, however, does not require a heave sensor, if the ambiguity initialisation was successfully performed before leaving the wharf and the GPS solutions were kept even with occasional loss of GPS signal during a sounding operation. Equation (1) shows the relationship between the ellipsoidal height of a sounding ship obtained by the OTF (hOTF) and tide gauge measurement (TCOWLIS). The symbol, Dt is the draught of the sounding ship. The symbols, Hv, Sq and RHv, represent the heave, the squat and the remote heave, respectively.
TCOWLIS = hOTF – NCD – ZA + Dt – (Sq + Hv + RHv) + ε
(1)
The difference of the tide between GPS and COWLIS reading, represented by the symbol (ε) in Equation (1), has to be small. The height information obtained from the COWLIS can provide approximate GPS height (hOTF) used as height constraint reciprocally using Equation (1).
The COWLIS readings from a tide gauge at an interval of 15 minutes were temporally interpolated to compare the tide obtained from the GPS and to introduce the height constraint test for ambiguity search. The accuracy of the COWLIS tide gauges is about 3 cm under ideal conditions [CHS, 1997]. The corrections for squat, heave and draught of the ship have to be applied for more rigorous comparison of the results obtained from the OTF measurements and better estimation of the a priori height information. However, the comparison cannot be perfect because the errors are inevitable in the COWLIS readings and in each of the components used to calculate the height from the CD: datum separation, GPS antenna height, draught, heave, estimation of squat from the speed log reading. When SINEM (which is a spatial interpolation of COWLIS tide measurements) is used the errors in interpolation would be included as well. The information on the water level (reduced to ellipsoidal height) would be helpful for the ambiguity resolution if it has sufficient accuracy. Once the ambiguities have been resolved, however, the height will become known and in a case where all ambiguities are lost, the average height over the previous epochs could be used to help the ambiguity resolution. Introducing the height into the GPS observation equation is also possible by using the pseudo-observation method. Pseudo-observation deals with the situation where the variables, e.g., position, ambiguities, are known at certain precision. When the precision of the height from the COWLIS tide gauges is known and is high enough, the initial values of ambiguities would be known with sufficient accuracy and therefore the ambiguity search space could be reduced. The height information can be used inside the ambiguity search routine as well. The ambiguity search is performed by varying the integer numbers in a nested loop. A combination of ambiguities, which gives a height solution beyond the predefined threshold, e.g. 15 cm, is rejected. This method could also be used for reducing the ambiguity search space and potentially eliminating incorrect combinations of ambiguities. Different data sets for the season in 1998 were provided by the CHS and the CCG, and the new trials were also conducted during the season in 1999. The data of the 1999 session were used for validating the a priori height information from the COWLIS tide gauges. Some of the worst cases in the 1998 session, where the OTF software showed difficulty in finding the correct ambiguity solutions, were selected to investigate the cause of wrong solutions and to improve the OTF method. Table 1 summarises the condition of the tests used for the analysis. Table 1: Test sites and conditions. Test Sector Date Duration (h:m)
#1
#2
#3
#4
D14
D11
Sillery
Sillery
30 Sept. 1998
22 Oct. 1998
15 Oct. 1999
17 Oct. 1999
1:35
0:53
0:24
1:08
Distance to GPS Ref. Station
33-35 km
43-45 km
7 (103) km
7 km
Distance to COWLIS station
6-8 km
2-5 km
5 km
5 km
Name of the ship
Smith
Smith
Puffin
Puffin
Test in the 1998 season (Tests #1 and #2) The first data set (Test #1) was observed on 30 September, 1998. The sounding sector was in the Lake St-Pierre, about 35 km from the GPS reference station at Trois-Rivières and about 6-8 km from the COWLIS gauge in the lake (Section D14). A 35-m sounding ship, the F.C.G. Smith, was used for the test. The length of the sounding sector was about 1.5 km. The ship repeated the movement of back and forth in the sounding area. The elevation mask 10° was used. Up to 10 satellites in total were available. The PDOP values varied from 1.4 to 2.6 during the test. The second data set (Test #2) was observed on 22 October, 1998. The sounding sector was also in the Lake St-Pierre but the distance was about 45 km from the GPS reference station at Trois-Rivières and about 2-5 km from the COWLIS gauge in the lake (Section D11). The same ship, the F.C.G. Smith, was used for the test. The length of the sounding sector was about 1.5 km. The elevation mask 10° was used. Up to 10 satellites in total were available. The PDOP values varied from 1.5 to 2.6 during the test.
Test in the 1999 season (Tests #3 and #4) The trials in 1999 season were conducted in October in the region of Quebec City which has a daily tidal difference of about 4 m. Another ship of the CHS, the Puffin, was used for the data collection. Tests #3 and #4 were conducted on 15 and 17 October and the data were recorded while the ship was at wharf of the Sillery marina. The distance to the COWLIS station in the Port of Quebec was about 5 km and that to the GPS reference station at Lauzon was about 7 km. The GPS reference station at Trois-Rivières was 103 km away. More than 6 satellites were available. The PDOP values was about 1.7 during Test #3 and they varied from 1.6 to 3.4 during Test #4. The tide was rising during Test #3 and ebbing during Test #4. In order to make use of the information, the assessment of the quality of the a priori height information was performed. This was done by comparing the tide gauge reading with the GPS height of the antenna (taken into account the reductions described above), when the ship is in the vicinity of a GPS reference station and a tide gauge. Equation (1) was used to convert the ellipsoidal height to the GPS tide. The OTF software computes the ionospheric-effect-free solution (L3) after resolving the wide-lane ambiguities and then L1 ambiguities. The ionospheric-free combination is used to reduce the ionospheric effects, in particular, on long baselines. Table 2 summarises the difference of tide (height above the CD) between GPS and the COWLIS tide gauge in the Port of Quebec when the ship was at wharf. When the ship was about 5 km away from the COWLIS gauge and the GPS reference station at Lauzon was used, the mean difference between COWLIS and GPS on L3 was -10 cm for Test #3 and -2 cm for Test #4. The RMS values were about ±3 cm. When the GPS station at Trois-Rivières was used, the mean difference was about -2 cm and the RMS values were ±4 cm. Table 2: Difference of tide between GPS and COWLIS tide gauge. (cm)
Test #3 (Lauzon)
Test #3 (Trois-Rivières)
Test #4 (Lauzon)
Mean
-9.5
-1.8
-1.9
RMS
±3.0
±3.9
±2.5
Figure 2 shows the difference of the tide between SINEM and GPS for the cases with and without correction for the squat and heave for the sector D11 (Test #2).
Figure 2: Difference of tide between GPS and SINEM for the cases with and without corrections (Test #2: D11). Table 3 shows the comparison of the difference of tide between GPS and various tide gauges. D11 and D14 sounding sectors were located in the Lake St-Pierre. SINEM is a spatial interpolation of COWLIS tide gauge measurements. Auto tide represents on-the-spot readings of tide staffs in the vicinity of the sounding area. With correction means the case where the correction of the squat and heave was applied to the L3 solution. Without correction represents the case
without these corrections for the L3 solutions. The draught correction was applied for both cases of with and without correction. The mean of the difference of tide is smaller with SINEM in these sounding sectors. The mean of the difference of tide with COWLIS was larger in the sector D14 where the distance to the tide gauge was longer. By applying the correction for the squat and heave, the RMS values became smaller. The RMS values were ±2-3 cm. Table 3: Comparison of the difference of height between GPS and various tide sensors. Test #2 (D11)
Test #1 (D14)
(cm)
COWLIS
SINEM
Auto tide
COWLIS
SINEM
Auto tide
Without
Mean
-6.8
-4.5
-9.0
5.8
2.4
1.2
correction
RMS
±2.8
±3.0
±3.0
±2.3
±2.5
±2.5
With
Mean
-1.6
0.0
-4.2
10.2
6.7
5.5
correction
RMS
±2.8
±2.8
±2.8
±1.5
±1.7
±1.6
The GPS phase ambiguity resolution on L1 or narrow-lane band (with an effective wavelength of about 20 cm) is more difficult to achieve than that for the wide-lane band (the wavelength of the wide-lane is 86 cm), especially when the distance between the survey ship and the GPS reference station gets longer. In order to find out the usefulness of the height information for the ambiguity resolution, the ambiguity search on L1 was made without a priori height information, and with a priori information used for testing the combinations. The initial L1 ambiguities were calculated from the position obtained from the wide-lane solution. The pseudo-observation method with the COWLIS height (reduced to the ellipsoid) was also introduced to obtain the initial ambiguities. In order to compare the success rate of instantaneously finding the correct ambiguity set for the cases with and without a priori height information, the ambiguity search was reinitialised at each 5 seconds. The term "instantaneous" in this section means finding a combination of the L1 ambiguities within 5 seconds after each initialisation. The initial ambiguities were recalculated every 5 seconds from the wide-lane solution or the pseudo-observation method and ambiguity search was performed. The epochs with more than two candidates, were removed for the calculation of statistics. The correct ambiguities were identified by checking the residuals on L4, L1 and L3 GPS solutions. Table 4 shows the comparison of success rate of finding instantaneously (within 5 seconds) the correct ambiguity set with and without height information from the COWLIS height. The first row of each case shows the number of incidents to find the correct combination of ambiguities and the ratio with respect to the incidents of finding a solution and the second row shows the number of incidents to find a solution and the ratio with respect to the number of ambiguity initialisations. For the case with the a priori height, the COWLIS height was introduced in the search routine as the a priori information to test if a combination of ambiguities is within the predefined threshold, e.g. 15 cm. The a priori GPS height (hOTF) is reciprocally calculated using Equation (1). This information helped to eliminate incorrect combinations of ambiguities and fix the ambiguities by leaving a single combination. It was in particular useful, when the variation and mean difference between the COWLIS and GPS height was small (when its accuracy is about ±15 cm or better and the distance to the COWLIS station is less than 10 km). Table 4: Success rate for finding the set of correct phase ambiguities within 5 seconds of initialisation period.
Without a priori height
With a priori height
Test #1 (D14)
Test #2 (D11)
Test #3 (Lauzon) Test #4 (Lauzon)
563/846
67%
313/462
68%
11/56
20%
429/698
62%
846/1140
74%
462/636
73%
56/288
19%
698/988
71%
850/940
90%
392/463
85%
59/84
70%
718/759
95%
940/1140
82%
463/636
73%
84/288
29%
759/988
77%
The results show an improvement of ambiguity resolution using the height information from the COWLIS when the GPS reference station was up to 45 km. The success rate was, in general, improved by about 20%, typically from 70% to 90%. The principal reasons for the failure of finding the correct solution using the height constraints were: (1) a 5-second
initialisation period was rather short, and (2) a tight threshold of 15 cm. In general, the number of incidents to find a solution was increased. Additional results and analyses can be found in [Ueno et al., 2000]. REGIONAL IONOSPHERIC MODELLING This section is related to the regional modelling of the relative ionospheric error. The dilemma of the ionospheric effect on the phase ambiguity resolution (even with dual frequency receivers) is outlined in the steps of the OTF phase ambiguity resolution scheme. Figure 3 schematically illustrates those steps.
Ionospheric free solution with float ambiguities (F3)
Float ambiguities Fixed ambiguities
1 PROBLEM Wide-lane solution (L4)
2
Narrow-lane solution (L5) 3
3
Retrieval of L1 and L2 ambiguities 4
Ionospheric free solution with fixed ambiguities (L3)
Figure 3: The steps of the OTF phase ambiguity resolution process. Step 1 : Fix the L4 ambiguity with the coordinates of the mobile receiver obtained from the F3 float solution :
∇∆N4 = [(∇∆Φ4 - ∇∆ρ - ∇∆dtrop + ∇∆dion4 + ε4) / λ4]
(2)
Step 2 : Fix the L5 ambiguity with the coordinates of the mobile receiver obtained from the L4 fixed solution :
∇∆N5 = [(∇∆Φ5 - ∇∆ρ - ∇∆dtrop + ∇∆dion5 + ε5) / λ5 ]
(3)
Step 3 : Retrieve the L1 and L2 ambiguities (∇∆N1 , ∇∆N2) with ∇∆N4 and ∇∆N5 obtained with Equations (2 and 3) :
∇∆N1 = (∇∆N5 + ∇∆N4 ) / 2 ∇∆N2 = (∇∆N5 - ∇∆N4 ) / 2
(4)
Step 4 : Form unambiguous L3 ionospheric free phase observation.
∇∆Φ 3 =
f 12 f 22 ( ∇ ∆Φ − λ ∇ ∆Ν ) − (∇∆Φ 2 − λ2 ∇∆Ν 2 ) 1 1 1 f 12 − f 22 f 12 − f 22
(5)
The problem comes from Step 2 (Equation 3). Ignoring the term ∇∆dion5 can make it impossible to find the correct ∇∆N5 ambiguities, if the term ∇∆dion5 gets larger than λ5 / 2 = 5.4 cm. This corresponds to a value of 4.2 cm for the ionospheric delay on L1 (∇∆dion1). Unfortunately, this delay cannot be calculated from the original L1 and L2 phase
observations since they are ambiguous. The problematic is based on the following dilemma: in order to model the ionospheric delay on the phase measurements, the ambiguities must be resolved, but to resolve those ambiguities, the ionospheric delay must be modelled to an order of half of a wavelength. A solution to brake this vicious circle is to get a priori information on ∇∆dion1 from a relative ionospheric error model. The goal of the regional relative ionospheric error modelling is to increase the success rate of the OTF phase ambiguity resolution. The approach has already been documented in Wanninger [1997]. In order to determine the phase ambiguities between a mobile receiver and a reference station, it is proposed to use the relative ionospheric delay information obtained at 2 reference stations, for example, located on each side of this mobile receiver (see Figure 4). A complete procedure that regroups all necessary steps to the modelling and use of the relative ionospheric delay is presented in [St-Pierre, 1999]. The model can be divided in 4 steps: 1.
Phase ambiguity resolution between 2 reference stations (in our case, up to 150 km on the St. Lawrence river).
2.
Estimation of relative ionospheric delay between the 2 reference stations with Equation (6).
∇∆dion AB = 3.
(6)
Interpolation of relative ionospheric delay between the ship’s position and the closest reference station (see Figure 4). This distance can be up to 75 km on the St. Lawrence river. The linear interpolation between the 2 reference stations is calculated from:
∇∆dion AM = 4.
f 22 (∇∆Φ 1 − ∇∆Φ 2 − λ1 ⋅ ∇∆Ν 1 + λ2 ⋅ ∇∆Ν 2 ) f12 − f 22
AM ' ∇∆dion AB AB
(7)
Use of the interpolated relative ionospheric delay to improve the OTF algorithm (L5 ambiguity resolution, Equation (3)).
Infinitesimal ionospheric layer
B M M A
Figure 4: Interpolation of the relative ionospheric delay. To illustrate the approach, some results are presented in the following paragraphs. More results can be found in [StPierre, 1999], [Santerre and St-Pierre, 1999] and [St-Pierre et al., 2000]. The first session, Trois-Rivières - Neuville (75 km), was conducted on November 12, 1997 from 11:00 to 12:30 (Eastern Time). The second session, Trois-Rivières Deschambault (50 km), took place on the same day from 13:30 to 15:30. The modelled values of the ionospheric delays
(30391 values for the first session and 45842 values for the second session) were interpolated from the Lauzon and TroisRivières reference stations which are 110 km apart. For the first session, 45% of the ionospheric delays (on L1) exceed the critical threshold of 4 cm (see Figure 5). This means that for 45% of the time, it would have been difficult or even impossible to correctly fix the L5 phase ambiguities. Fortunately, the values of these delays have been correctly interpolated from the reference stations (better than 4 cm for 99% of the time and only 1% of the values exceed 4 cm). The second session is less dramatic, 7% of the ionospheric delays exceed 4 cm. The interpolated values of the relative ionospheric delays allow to diminish this statistic to less than 1%. One can note that the linear interpolation between the 2 reference stations (Trois-Rivières and Lauzon) is suitable in the cases where there is no large transversal offset between the interpolation point (Neuville or Deschambault) and the line defined by the 2 reference stations.
Deschambault
75 km
50 km
Lauzon
Neuville
110 km
Trois-Rivières
Sessions
Processed delays
| ∇∆dion1 | > 4 cm Without model
With model
T.-Rivières -Neuville
30391
45%
1%
T.-Rivières – Desch.
45842
7%
1%
Figure 5 : Relative ionospheric residuals (unmodelled part) for sessions with a small transversal offset. Table 5 summarises the results obtained from the first session discussed above. The results illustrate the success rate of the L5 phase ambiguity resolution when the good a priori value of the ionospheric delays is available. In this test, the ambiguity resolution on the narrow-lane (L5) was reinitialised at every 5 minutes. For example, for satellite PRN 5, the success rate is 77% (10/13) without ionospheric error modelling, and the success rate increases to 92% (12/13) with ionospheric error modelling. The statistics for all the other satellites are presented in Table 5. Overall, for the 10 satellites, the success rate is 77% (76/99) without ionospheric error modelling, and the success rate increases to 95% (94/99) with ionospheric error modelling. A substantial gain in the performance of the OTF algorithm for long baselines was provided by the interpolation of the ionospheric delays from the reference stations. Table 5: L5 ambiguity resolution success rate for a baseline of 75 km (Trois-Rivières – Neuville) with an elevation mask angle of 10º (November 12, 1997 from 11:00 to 12:30, Eastern Time). PRN
5
9
15
17
21
23
25
26
29
30
Total
without
10 13
13 17
5 7
2 4
14 17
14 17
5 8
2 3
2 2
9 11
76 99
model
77%
77%
71%
50%
82%
82%
63%
67%
100%
82%
77%
with
12 13
17 17
6 7
4 4
17 17
17 17
7 8
2 3
2 2
10 11
94 99
model
92%
100%
86%
100%
100%
100%
88%
67%
100%
91%
95%
CONCLUSIONS AND OTHER RESEARCH ACTIVITIES The COWLIS height (reduced to the ellipsoid) was introduced in the search routine as the a priori information to test if a combination of GPS ambiguities is within a predefined threshold. This information helped to eliminate incorrect combinations of ambiguities and fix the ambiguities by leaving a single combination. The results show an improvement of GPS ambiguity resolution using the height information from the COWLIS (when the accuracy of the a priori height, reduced to the ellipsoid, is about ±15 cm and the distance to the COWLIS gauge is less than 10 km). The success rate of finding the correct ambiguity set was, in general, improved by about 20%, typically from 70% to 90%. Relative ionospheric delay can make OTF phase ambiguity resolution impossible, particularly for long baselines; this is even more critical with the actual solar activity which will peak in 2000-2001. A priori relative ionospheric delay obtained from interpolation between reference stations helps to increase the likelihood of success of OTF phase resolution. Tests on 50-75 km baselines show that the approach is viable with only 2 reference stations (separated by 140 km) as long as the interpolation point is close to the line defined by the 2 reference stations. A third reference station must be used when the interpolation point is not in the alignment of 2 reference stations and when a large transversal ionospheric gradient is present. Preliminary results from such a reference station network can be found in [St-Pierre et al., 2000]. Other research activities have been conducted within our GEOIDE Project. For example, Kim and Langley [1999a, 1999b] worked on an optimised least-squares ambiguity search technique and on the improvement of reliable and robust OTF solutions. Detection of outliers and cycle slips present in phase observations have also been addressed. More specifically, an efficient ambiguity search engine named as the OMEGA (Optimal Method for Estimating GPS Ambiguities) has been developed. The OMEGA provides a substantial reduction factor for the ambiguity search space as well as an improvement in the computational efficiency. Research has also started at the CRG to process carrier phase observations from the Glonass satellites. Coordinate transformation from PZ-90 (the coordinate system used for Glonass) into WGS-84 and the utilisation of two different time scales have been addressed. The GPS algorithms for phase ambiguity resolution have been modified to take into account that the Glonass satellites, unlike GPS satellites, do not broadcast on the same carrier frequency. A combined GPS-Glonass positioning could provide more reliable solutions. Our team’s work will continue for the next two years within the Project ENV#14 of the GEOIDE Network of Centres of Excellence. This research collaborative effort is indeed quite related to the theme of the CHC Conference 2000: People Forging Alliances. ACKNOWLEDGEMENTS This research project is funded by the Canadian Programme of Networks of Centres of Excellence - GEOIDE (GEOmatics for Informed DEcision) Network. Data sets used in this paper were collected by the Canadian Coast Guard and the Canadian Hydrographic Service (Laurentian Region). These supports are very much appreciated.
REFERENCES CHS - Canadian Hydrographic Service (1997). "Proposition de service aux usagers - Système d'information sur les niveaux des eaux côtières et océaniques (SINECO)." August, 28 p. Edwards, G. and T. DeGroeve (1999). "The GEOIDE Network - A lever for growth of the Canadian geomatics community." Geomatica, Journal of the Canadian Institute of Geomatics, 53(4), pp. 430-435. Kim, D. and R.B. Langley (1999a). "A search space optimization technique for improving ambiguity resolution performance and computational efficiency." Proceedings of the International Symposium on GPS-Application to Earth Sciences and Interaction with Other Space Geodetic Techniques, 18-22 October, Tsukuba, Ibaraki, Japan, Presentation Session Number: 10-11. Kim, D. and R.B. Langley (1999b). "An optimized least-squares technique for improving ambiguity resolution and computational efficiency." Proceedings of the U.S. Institute of Navigation ION GPS’99 Conference (CD-ROM), Nashville, U.S.A., 14-17 September, 9 pp. (in press).
Marceau, G. and D. Langelier (1997). "Déploiement sur le Saint-Laurent d'un réseau GPS on-the-fly - temps réel." Proceedings of Geomatics VI Symposium, Montreal, Quebec, Canada, November, pp. 139-151. St-Pierre, C., D. Parrot and R. Santerre (2000). "Reference station network: A solution for precise GPS positioning over long distances." Presented at the Geomatics 2000 Conference, Montreal, Quebec, 8-10 March. St-Pierre, C., R. Santerre and D. Parrot (1999). "Improvement of OTF-kinematic GPS positioning over long distances using ionospheric regional modelling." Geomatica, Journal of the Canadian Institute of Geomatics, 53(4), pp. 395403. St-Pierre, C. (1999). "Modélisation du délai ionosphérique relatif en vue de la détermination des ambiguïtés de phase GPS." Mémoire de maîtrise. Département des sciences géomatiques, Université Laval, Québec, 126 p. Santerre, R. and C. St-Pierre (1999). "Improvement of precise and reliable kinematic GPS positioning in real-time over long distances." Presented at the International Union of Geodesy and Geophysics XXII General Assembly, Birmingham, U.K., 18-30 July. Ueno, M., R. Santerre, D. Langelier and G. Marceau (2000). "Improvement of GPS ambiguity resolution using height constraint for bathymetric surveys." Proceedings of the Geomatics 2000 Conference, GEOIDE Session: Data Acquisition, Montreal, Quebec, 8-10 March. Wanninger, L. (1997). "Real-time differential GPS error modelling in regional reference station networks." International Association of Geodesy Symposia Volume 118 : Advances in Positioning and Reference Frames, Rio de Janeiro, September 3-9, pp. 86-92. Internet Sites Networks of Centres of Excellence: www.nce.gc.ca GEOIDE Network: www.geoide.ulaval.ca GEOIDE-Project ENV#14: www.scg.ulaval.ca/gps-rs/
