Improvement of GPS Ambiguity Resolution Using Height Constraint for Bathymetric Surveys

Transcription

1 Improvement of GPS Ambiguity Resolution Using Height Constraint for Bathymetric Surveys Mami Ueno (Centre for Research in Geomatics, Laval University, Ste-Foy, QC G1K 7P4, Canada; (418) #7149; Rock Santerre (Centre for Research in Geomatics, Laval University, Ste-Foy, QC G1K 7P4, Canada; (418) ; Daniel Langelier (Canadian Hydrographique Service, Institut Maurice Lamontagne, 850, route de la Mer, Mont-Joli, QC, G5H 3Z4 Canada; (418) Guy Marceau (Canadian Coast Guard, 104, rue Dalhousie, Quebec, QC, G1K 4B8, Canada; (418) ; Introduction The traditional sounding method requires the strategic placement of tide staffs as close as possible to the working area. An observer takes regularly an on-the-spot reading from the staff and transmits it verbally by radio to the sounding ship. Each year, tide staffs are deployed for every sounding season. This technology is costly, limited and outdated (Marceau et al. 1996; Marceau & Langelier 1997). In order to facilitate the survey and increase the safety of navigation, the Canadian Hydrographic Service (CHS) has gradually implemented digital tide gauges (type TMS- 1000) and developed a network of 15 tide gauges along the St. Lawrence River (COWLIS: Coastal and Oceanic Water Level Information System). The tide gauges provide regular tidal reading and possibility of use and transmission of the tidal information in real time. 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 introduction of the OTF system will improve the quality of the data collection and operational efficiency by eliminating costly deployment (support and maintenance) of the tide staffs. 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 OTF phase ambiguity resolution) over long distances, for the support of bathymetric surveys in real time. This project covers different research initiatives: 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 (which includes the problem of time latency). Objectives The OTF network of the Canadian Coast Guard (CCG) for the bathymetric survey operations on the St. Lawrence River is composed of 3 GPS reference stations which use high-quality GPS equipment and allows real-time broadcasting toward a sounding ship. The distance between the GPS reference stations is more than 100 km and the distance between a reference station and a sounding ship can be 75 km. Kinematic GPS positioning over long distances requires to use the ionospheric-effect-free band (L3) to reduce the ionospheric effects. This implies the ambiguity resolution on the two frequencies of L1 and L2. The Bathykin OTF software, which has been developed for

2 the CCG by the Viasat Géo-Technologie Inc. in collaboration with the Centre for Research in Geomatics at Laval University, takes 4 steps using linear combinations of dual frequency observations to obtain L3 solutions: i) float L3 solutions, ii) wide-lane solutions (the wavelength 86 cm), iii) narrow-lane or L1 solutions (an effective wavelength 20 cm), and iv) L3 solutions. The solution gets more precise with steps. The ambiguity resolution on L1 or narrow-lane band is more difficult to achieve than that for the wide-lane band, especially when the distance between the survey ship and the GPS reference station gets longer. The objective of this study is to improve the method of phase ambiguity resolution and the algorithms for kinematic GPS positioning on long baseline vectors using height constraint obtained from the network of the COWLIS tide gauges on the St. Lawrence. Most of these tide gauges are located in the vicinity of the wharf of base ports used by the CHS survey ships. The reading of the COWLIS tide gauges is as accurate as ±3 cm under ideal conditions (CHS 1997). This information could be used to assist the resolution of GPS phase ambiguities when the ship is still at the wharf. However, making use of COWLIS measurements as constraints for GPS positioning requires a conversion of altitude. The study was conducted to validate the quality of the height information obtained from the COWLIS and to find the efficient way of using it. GPS GPS Squat + Heave Ref. station Z A Tide gauge T COWLIS Dt Geoid N CD Depth h OTF Chart Datum Ellipsoid Reduction of GPS-OTF altitude to the Chart Datum 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 water level measured by the tide gauge is given with respect to the local CD, while GPS height positioning refers to the WGS-84 ellipsoid. The datum separation between the ellipsoid and the CD is represented by the symbol (N CD ). Note that the ellipsoid is always above the CD in the sounding sectors of the Montreal-Quebec region. 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 & Langelier 1997). To reduce the ellipsoidal altitudes (determined by GPS- OTF) to the CD, the Bathykin OTF software, 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 (Z A ), which is the distance from any point

3 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 (h OTF ) 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 (h OTF ) and tide gauge measurement (T COWLIS ). 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. The difference of the tide between GPS and COWLIS reading, represented by the symbol () in Equation (1), has to be small. The height information obtained from the COWLIS can provide approximate GPS height (h OTF ) used as height constraint reciprocally using Equation (1). T COWLIS = h OTF N CD Z A + Dt (Sq + Hv + RHv) + ε (1) Integrating a priori height information 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 COWLIS tide gauges. 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. Results: Comparison of COWLIS Reading with reduced GPS height The quality of the a priori height information was first assessed by comparing the tide gauge reading with the reduced GPS height, 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 COWLIS readings from a tide gauge at an interval of 15 min were temporally interpolated to compare the tide obtained from the GPS. 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 is used SINEM, which is a spatial interpolation of COWLIS tide measurements, the errors in interpolation would be included as well. The magnitude of the over all errors would be about ±10 cm (Michaud et al. 1997).

4 The investigations were made on i) the magnitude of tidal difference (height above the CD) between GPS and a COWLIS gauge, and ii) the relationship between the difference of tide and the distance to the COWLIS gauge from the ship. The difference of tide was analysed for two cases of ship's dynamics, i.e., being moored in a marina and in a sounding operation. For the former case, the use of two different GPS reference stations (distance to the ship: 7 and 103 km) was compared. The closest COWLIS tide gauge was located about 5 km away. For the latter case, the corrections for squat, heave and draught of the ship were applied for more rigorous comparison of the results obtained from the OTF. The RMS values were about ±3 cm when the GPS reference station at 7 km was used and ±4 cm with the other reference station at 103 km. The mean difference between COWLIS and GPS on L3 varied between -2~10 cm. When the ship moved away from the COWLIS gauge, the difference of tide increased linearly as the distance to the COWLIS got longer. In the case where a ship was in sounding operation, the mean of the difference of tide with COWLIS was larger in the sector where the distance to the tide gauge was longer. The mean varied between ±10 cm. The RMS values were ±2~3 cm. Results: Comparison of success rate for ambiguity search In order to find out the usefulness of the height information for the ambiguity resolution, the ambiguity search on L1 was performed with or without the a priori information. 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 (h OTF ) is reciprocally calculated using Equation (1). The success rate of instantaneously finding the correct ambiguity set was compared for the cases with and without the a priori height information by launching a new search attempt at each 5 s. The term "instantaneous" means finding a combination of the L1 ambiguities within 5 s after each initialisation. The initial L1 ambiguities were calculated from the position obtained from the wide-lane solution every 5 s. The pseudoobservation method with the COWLIS height (reduced to the ellipsoid) was also introduced to obtain the initial ambiguities. The height obtained from the wide-lane was good enough to make a search with a small search window of ±2 cycles and ±1 cycle on L1 for most of the cases. The ratio of finding the correct combination of ambiguities was calculated with respect to the number of solutions for each case. The epochs with more than two candidates, were removed for the calculation of statistics. The correct ambiguities were identified from the common solutions of the Bathykin and the software developed in this research by checking the residuals on wide-lane, L1 and L3 GPS solutions. The a priori 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). 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%. When the GPS reference station at 103 km was used, the success rate was not improved although the frequency of finding a single combination was increased. The ionospheric effect might be present and the model proposed by St-Pierre et al. (1999) would improve the solution. Conclusions This study was conducted to improve the method of phase ambiguity resolution on L1 or narrow-lane band (with an effective wavelength of about 20 cm) which is more difficult to achieve than that for the wide-lane band (the wavelength of the wide-lane is 86 cm) for kinematic GPS positioning on long baseline vectors using the a priori height information.

5 The height of water level on the St. Lawrence is easily accessible from the network of automated tide gauges deployed by the CHS. When the ship was a few km away from the COWLIS tide gauge and about 10 km from the GPS reference station, the difference of tide between GPS on the ionospheric-effect-free band and the COWLIS reading was about 10 cm. The difference of tide grew with distance between the ship and COWLIS gauge. 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 the predefined threshold. This information helped eliminate incorrect combinations of ambiguities and fix the ambiguities by leaving a single combination. The results show an improvement of ambiguity resolution using the height information from the COWLIS (when its accuracy 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%. 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. Marceau, G., Langelier, D. (1997). Déploiement sur le Saint-Laurent d'un réseau GPS on-the-fly - temps réel, Proceedings of Géomatique VI Symposium, Montreal, Quebec, Canada, November, pp Marceau, G., Morse, B., Bouchard, G., Santerre, R., Parrot, D., Roy, É. (1996). A GPS application and real-time On-the-Fly approach for bathymetric surveys, Proceedings of Canadian Hydrographic Conference, Halifax, Nova Scotia, Canada, June, pp Michaud, S., Santerre, R., Condal, A. (1997). Comparaison de l'altitude GPS d'un navire avec des données marémétriques, Paper accepted for Lighthouse, July, 19 p. St-Pierre, C., Parrot, D., Santerre, R. (1999). Improvement of OTF-kinematic GPS positioning over long distances using ionospheric regional modelling, GEOMATICA, Vol. 53, No. 4, pp