A Technique for Precise Positioning of High

A Technique for Precise Positioning of High Altitude Platforms System (HAPS) Using a GPS Ground Reference Network Toshiaki Tsujii, Jinling Wang, Liwen Dai, Chris Rizos, School of Surveying & Spatial Information Systems, The University of New South Wales, Australia (UNSW) Masatoshi Harigae, Toshiharu Inagaki, Takeshi Fujiwara, Flight Systems Research Center, National Aerospace Laboratory, Japan (NAL) Teruyuki Kato, Meteorological Research Institute, Japan (MRI)

relating to GPS and positioning technologies. He is Secretary of Section 1 'Positioning', of the International Association of Geodesy.

BIOGRAPHIES Toshiaki Tsujii is a senior researcher at the Flight Systems Research Center, NAL, Japan, where he has been investigating aspects of satellite navigation and positioning for ten years. In February 2000 he commenced a two year visit with the Satellite Navigation and Positioning (SNAP) Group, at the School of Surveying & Spatial Information Systems, UNSW, as a JST postdoctoral research fellow. He holds a Ph.D. in applied mathematics and physics from Kyoto University.

Masatoshi Harigae is the leader of the Navigation Systems Group, Flight Systems Research Center, NAL, and has over 15 years experience in the development of GPS/INS navigation systems for automatic landing applications. He is now engaged in the High Speed Demonstration project that is carried out in cooperation with NASDA. He has a B.S., a M.S. and a Ph.D. from the University of Tokyo in aerospace engineering.

Jinling Wang holds a Ph.D. from the Curtin University of Technology, Perth, Australia. He is currently an Australian Research Council Postdoctoral Fellow in the School of Surveying & Spatial Information Systems, UNSW. He is a member of the Editorial Advisory Board of the journal GPS Solutions, and Chairman of the Working Group "Pseudolite applications in Engineering Geodesy", the International Association of Geodesy's Special Commission 4. His research interests are GPS modeling, GPS and INS integration, and pseudolites.

Toshiharu Inagaki is a senior researcher of the Flight Systems Research Center, NAL, where he has been engaged in the research and development of advanced flight instruments for thirty years. He has also worked as a mission operations planner for the automatic landing project using NAL’s in-flight simulator. Takeshi Fujiwara received a Ph.D. in aerospace engineering from the University of Tokyo in 1999. He is currently a researcher in the Flight Systems Research Center, NAL, where he has been working on the analysis of flight data obtained through flight tests. He has been also engaged in research and development of advanced navigation for the lunar and planetary orbiters.

Liwen Dai received a B.Sc. and M.Sc. in Geodesy in 1995 and 1998 respectively, from the Wuhan Technical University of Surveying and Mapping, P.R. China, and subsequently joined the SNAP group, UNSW, as a Visiting Fellow in November 1998. At the start of 2000 he commenced full-time Ph.D. research into algorithm development for rapid static and kinematic positioning (and attitude determination) using integrated GPS, Glonass and pseudolite systems. He is currently a software engineer with Magellan Corporation.

Teruyuki Kato is a senior researcher of the Meteorological Research Institute of the Japan Meterorological Agency (JMA), engaging in developing a nonhydrostatic mesoscale model and investigating the processes of mesoscale meteorology. He holds a Ph.D. in physics from Tokyo University, and got a "Yamamoto-Shono" prize from the Japan Meterological Society two year ago.

Chris Rizos is a Professor at the School of Surveying & Spatial Information Systems, UNSW, and leader of the SNAP Group. Chris holds a B.Surv. and Ph.D., both obtained from UNSW, and has published over 100 papers, as well as having authored and co-authored several books ION GPS 2001, 11-14 September 2001, Salt Lake City, UT

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However, the accuracy of the pseudolite positions would be a limiting factor for such a service since the PL 'ephemeris error' is more serious than GPS due to the lower height of the airship (Dai et al, 2000; Wang et al, 2001). Therefore, the precise positioning of the airship is one of the most important technical tasks for such an augmentation service, as well as for other applications such as remote sensing.

ABSTRACT GPS can play an important role in the positioning of High Altitude Platforms Systems (HAPS). In such GPS applications the residual tropospheric delay in GPS measurements is a major error source. Contrary to the case of static GPS applications, it is difficult to estimate the tropospheric delay simultaneously with the ambiguities and coordinates in kinematic mode. In this paper four techniques to mitigate the tropospheric delay error are compared. Preliminary tests using an aircraft has shown that the global tropospheric model may not be adequate for precise positioning. Both the method using a numerical weather model and the method using surface meteorological measurements significantly improved the performance of ambiguity resolution on-the-fly. However, the method using meteorological data obtained by the aircraft and the zenith tropospheric delay, estimated from a ground GPS network, has shown the best performance.

For the precise positioning of the HAPS, the residual tropospheric delay in GPS carrier phase observations is one of the most significant sources of error. The typical error mitigation methodology is to estimate the effect of residual delay on the user receiver by interpolating the delay determined at reference network receivers (e.g. Han & Rizos, 1996; Gao et al, 1997; Wanninger, 1997; Zhang, 1999). However, because the tropospheric delay depends on receiver altitude this technique is effective only when all receivers (including the user receiver) are located at a similar altitude, and therefore this is not feasible for the HAPS. Tsujii et al (2000) has proposed a new functional model for the residual tropospheric delay which is explicitly height-dependent, and demonstrated the effectiveness of the model for the precise positioning of the HAPS in cases where the ambiguities were resolved beforehand. However, it is difficult to estimate the tropospheric delay simultaneously with the ambiguities and coordinates in kinematic mode, contrary to static GPS applications. This is mainly due to the lack of observed satellites since only low elevation satellites have the observability for the estimation of the tropospheric delay.

INTRODUCTION Recently some countries have begun conducting feasibility studies and R&D projects into High Altitude Platforms Systems (HAPS). Japan has been investigating the use of an airship system that will function as a stratospheric platform (altitude of about 20km) for applications such as environmental monitoring, communications and broadcasting (Yokomaku, 2000). In addition, the airship can be considered as a signal source for a navigation/positioning service because of the airship’s station-keeping characteristics (Figure 1). If pseudolites (PL) were mounted on the airships, their GPS-like signals would be stable augmentations that could improve the accuracy, availability, and integrity of GPS-based positioning systems (Tsujii et al, 2001; Dai et al, 2001).

In this paper the tropospheric delay was estimated by using four kinds of datasets/models: 1) a global tropospheric model, 2)

grid point values from a numerical weather model,

3)

surface meteorological measurements and the lapse rates of temperature and water vapor pressure estimated using regional/temporal meteorological data, and

4) meteorological data measured by the high altitude vehicle, and the zenith total delay estimated from a ground GPS network.

Figure 1. Navigation/positioning pseudolites on stratospheric platforms.

service

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Prior to the flight experiment of the stratospheric vehicle, a preliminary experiment using an aircraft was conducted by the National Aerospace Laboratory (NAL), Japan. In order to evaluate the performance of the four techniques mentioned above, tests of ambiguity resolution on-the-fly (OTF) were carried out, and the estimated ambiguities were compared with pre-determined values of the ambiguities. All of the analyses in this paper were

using

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The Saastamoinen’s hydrostatic zenith delay model is highly accurate and is frequently used by many authors (Saastamoinen, 1973):

performed using a modified version of the kinematic GPS software (KINGS) developed at NAL (Tsujii et al, 1998). TROPOSPHERC DELAY

d hZ =

The tropospheric propagation delay of GPS signals can be written in general form as follows (in meters):

gm d trop = d hZ mh + d wZ mw

d wZ : wet zenith delay

d wZ =

mh : hydrostatic mapping function mw : water vapor mapping function

β λ′ Tm

Niell’s mapping function is used in this work (Niell, 1996). The hydrostatic and wet zenith delays can be written in the integration forms as follows (Thayer, 1974; Davis et al, 1985):

d = 10 Z h

−6

∫

∞

∞

h0

(5)

: temperature lapse rate : = λ + 1 ( λ is water vapor lapse rate) : mean temperature of water vapor

= T (1 − βRd g m λ ′)

N hyd ( h )dh

water vapor pressure [mbar] measured at the observation site where the ellipsoidal height is h0 [m]. It is noted that

(2)

equation (5) is very sensitive to the variations in

h0

h0

e e   = 10 ∫ k 2′ ⋅ + k 3 ⋅ 2  ⋅ Z w−1dh h0 T   T ∞

constants used in Saastamoinen’s formula. Smith (1966) gives a global value of λ ( λ = 2.61 ). In the U.S. Standard Atmosphere, a constant value of β ( β = 6.5 ) is used for the troposphere.

(3)

where

TECHNIQUES FOR TROPOSPHERC ERROR MITIGATION

N hyd , N wet : hydrostatic and wet term of the refractivity k1 , k 2′ , k 3 : refractivity constants (Thayer, 1974)

DELAY

Global Tropospheric Delay Model

: inverse compressibility for water vapor

When airborne meteorological data are available, the tropospheric delay for the aircraft can be calculated according to equations (4) and (5). Otherwise, the meteorological data obtained by the aircraft are computed from the surface meteorological data using model

: gas constant for dry air : total mass density


β and

λ . Equation (5) agrees numerically with Saastamoinen’s formula, by using β = 6.2, λ = 3 and the refractivity

∞

d wZ = 10 −6 ∫ N wet ( h )dh −6

10−6 (Tm k2′ + k3 ) Rd e0 ⋅ g m λ ′ − βRd T0

P0 , T0 , e0 are pressure [mbar], temperature [K], and

= 10 −6 ∫ k1 Rd ρ ( h )dh

Rd ρ

: gravity acceleration at the mass center of a

Although a number of zenith wet delay models have been developed in the last two decades (see Mendes & Langley, 1995), the two parameter formula of Askne & Nordius (1987) is used in this work:

d hZ : hydrostatic zenith delay

Z

(4)

vertical column of the atmosphere

(1)

where

−1 w

10 −6 k1 Rd ⋅ P0 gm

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tropospheric delay, and other meteorological parameters (Numerical Prediction Division/JMA, 1997).

formulae. The following formulae are frequently used (Askne & Nordius 1987; Collins et al, 1996b): g

 β ( h − h0 )  Rd β  P = P0 1 − T 0   e e0 = T T0

 β ( h − h0 )  1 −  T0  

λ ′g −1 Rd β

pn , Tn , en

zn

(6)

β n−1 , qn−1

(7)

zn−1

pn−1 , Tn−1 , en −1

zk +1

pk +1 , Tk +1 , ek +1

zk P, T , e are pressure, temperature, water vapor pressure at height h , and g is the gravity acceleration at

β k , qk

* user

pk , Tk , ek

where

z3 β2 , q2 z2 β1 , q1 z1 ( surface)

the surface. However, since the surface meteorological data are not always available for airborne users, a number of global tropospheric delay models for airborne navigation have been developed (see Collins & Langley 1996a). As an example of a global tropospheric model, the UNB4 model (Collins et al, 1996b), which gives five parameters ( P0 , T0 , e0 , β , λ ) to compute the total

950, T3 , e3 1000, T2 , e2 p1 , T1 , e1

Figure 2. Structure of GPV data and the parameters to be computed.

tropospheric delay, was used in this paper. The zenith tropospheric delay at the user (either the ground receiver or the aircraft) is estimated using GPV data as follows, where the user is assumed to be between the k-th and (k+1)-th layer (Figure 2).

Grid Point Values from Numerical Weather Model Recently numerical weather models (NWM) have been used to estimate the tropospheric delay for GPS applications (Ichikawa, 1995; Schueler et al, 2000) as well as for InSAR applications (Shimada et al, 2000). Ichikawa (1995) and Shimada et al (2000) used the ray-tracing method to compute the tropospheric delay for each satellite, whilst Schueler et al (2000) computed the zenith delay and used a mapping function. In this work, the latter method is used, and the ray-tracing method will be examined in a future study.

a)

 e e  N wet ,k = k 2′ ⋅ k + k 3 ⋅ k2  ⋅ Z w−1,k Tk Tk  

(8)

b) Computation of the zenith wet delay at each layer:

The grid point values (GPV) from the NWM used in this work were generated by the Meteorological Research Institute (MRI), Japan. There are three levels of NWMs, namely, a global spectral model (GSM), a regional spectral model (RSM), and a Meso-Scale model (MSM). The GSM, RSM, and MSM consist of 30, 36, and 40 vertical layers in addition to the surface, whilst the horizontal resolutions are 0.5625 degrees, 20km, and 10km, respectively. The number of vertical layers was increased to 40 for GSM and RSM from March 2001.The GPV files of these models have been distributed by the Japan Meteorological Business Support Center (JMBSC) since September 2000. The surface and each vertical layer in GPV files contain the geopotential height for the corresponding pressure level, temperature, and relative humidity, which are necessary to compute the ION GPS 2001, 11-14 September 2001, Salt Lake City, UT

Computation of the wet refractivity at each layer based on equation (3):

∞

d wZ,k = 10−6 ∫ N wet ,k ( z )dz zk n N wet ,i + N wet ,i −1 −6 = 10 ∑ ⋅ ( zi − zi −1 ) 2 i = k +1 c)

Computation of the temperature lapse rate, the scale height of the zenith wet delay,

β k = (Tk +1 − Tk ) /( z k +1 − z k )

d wZ,k +1 = d wZ,k ⋅ exp{− ( z k +1 − z k ) qk } 1020

(9)

β k , and

qk :

(10)

measurements may be useful. However, the measurement of relative humidity at the surface would not reflect the inhomogeneous nature of the water vapor in the lower troposphere. Although the wet delay can be measured by a water vapor radiometer, it is extremely costly. On the other hand, a number of ground-based continuous GPS arrays have been established around the world, which can be used to estimate the tropospheric delay. For example, the GPS network established and operated by the Geographical Survey Institute (GSI), referred to as the GEONET, covers all of Japan, and this data can be obtained via the Internet. The ground GPS data are affected by the tropospheric delay error. In other words, the tropospheric delay is implicitly observed by the network. The tropospheric error mitigation technique using the ADS data and the ZTD estimated from a GPS network may be suited to the precise positioning of the HAPS.

d) Computation of the zenith hydrostatic and wet delay at the user height. If the user is close to the lower layer (k), the following equations are used:

10 −6 k1 Rd d = ⋅ Pk gm Z h

gk

 β ( z − z k )  Rd β k  ⋅ 1 − k Tk  

d wZ = d wZ,k ⋅ exp{− ( z − z k ) qk }

(11)

(12)

If the user is close to the upper layer (k+1),

Tk , Pk , z k , d wZ, k are replaced by the values at the (k+1)-th layer.

FLIGHT EXPERIMENT

The procedure from a) to d) is carried out for all model grid points neighboring the user. e)

Flight tests using NAL research aircraft (Dornier-228) were conducted on 7 August 2000 at Chofu, in Tokyo, Japan. An Ashtech Z-XII dual-frequency GPS receiver was installed in the aircraft. A reference receiver, a Trimble 4000SSI, was set up near the Chofu airfield. While the maximum distance from the aircraft to the airfield was less than 15km, the aircraft flew as high as it could. The aircraft flew up and down along a virtual cylinder in the air. Flight data were recorded from 1h30m to 2h40m, UTC.

The total zenith delay is computed by taking the weighted average of zenith delays at all neighboring grid points. The weight is defined by the reciprocal of the squared horizontal distance between the user and the grid point.

Surface Meteorological Measurement Similar to the global tropospheric model described above, equations (4) and (5) are used to compute the tropospheric delay at the surface, and equations (6) and (7) are used to obtain the delay at the user. However, the real measurements at the surface are used instead of the global parameters. The lapse rate of temperature and water vapor pressure are estimated by taking into account the regional and temporal weather conditions. ADS Data and ZTD from a Ground GPS Network An Air Data Sensor (ADS) would normally be installed on the HAPS because the platform will be used for remote sensing applications. The tropospheric delay at the platform computed by the direct measurements of ADS would be very accurate because the wet delay in the stratosphere is negligible, and the hydrostatic delay is well modeled. With regards to the tropospheric delay at the ground GPS receiver, the surface meteorological


Figure 3. Horizontal trajectory of the aircraft, and the locations of the reference receiver (CHOFU), surface meteorological measurement site (TOKYO), and the grid points of WNM (described in the next section).

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2) The GPV data of NWM (GPV) The 24-hour numerical integration data of RSM, which is lapsed from 0 UTC, 7th August 2000, and stored every 3-hours, were used. The meteorological data during the flight experiment were linearly interpolated using the data at 0 and 3 UTC. The horizontal separation between the grids was 40km, shown as ‘o’ in Figure 3. The GPV analysis data of RSM with 20km resolution were also available every 12 hours (the grid points are shown marked ‘x’ in Figure 3). However, the results obtained by using these data were worse than those using the 3-hour data with 40km resolution. This is probably due to insufficient temporal resolution. Therefore, the GPV integration data with 40km resolution were used in the analyses described below.

Figure 4. The height profile of the aircraft and the distance from the reference receiver at Chofu.

3) Surface meteorological data (SURFACE) The surface meteorological data measured by JMA (Japan Meteorological Agency) at the Tokyo site, which is shown in Fig.3, were used to compute the tropospheric delay. Although the Tokyo measurement site is about 20km away from the Chofu airfield, the meteorological conditions may not be very different because both sites are located in the Kanto Plain. The height difference between Tokyo and Chofu was considered and the data were adjusted. The lapse rate of temperature and water vapor pressure were estimated using the averaged radiosonde data of August obtained at Hamamatsu, which is the nearest radiosonde site to Chofu although it is about 196km away. The estimated values are β , λ = 5.50, 2.19 . The case using the standard values β , λ = 6.5, 3.0 is also shown in Figure 6. It seems that the standard values do not represent well the regional meteorological conditions.

Figure 5. Elevations of the observed GPS satellites. METHOD/DATA DESCRIPTIONS 1) Global tropospheric delay model (denoted as GLOBAL) The UNB4 tropospheric delay model (Collins et al, 1996b) was used as the global model. The parameters for the UNB4 model at the reference receiver are:

P0 , T0 , e0 = 1013.54, 301.94, 26.09

β , λ = 6.50, 3.30 . Since the meteorological parameters are the mean sea level values, those were adjusted by considering the height of the reference receiver.


Figure 6. Temperature and water vapor pressure profiles using β and λ estimated from the averaged radiosonde data (o) in August obtained at Hamamatsu. The case of standard values β , λ = 6.5, 3.0 are also shown (red lines).

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and cross-checked with ambiguities determined by backward processing. The ionospheric delay error could be ignored because the baseline length was limited to 15 kilometers. The multipath error may be negligible because the results of aircraft positioning on the ground, in static mode, did not show significant variation.

4) ADS data and ZTD from a ground GPS network (ADS&NET) The temperature and pressure data measured by the ADS installed in the Do-228 were used to compute the tropospheric delay at the height of aircraft. Since the relative humidity was not observed by the ADS, the water vapor pressure estimated by using the surface meteorological data and the 2-parameter model were used to compute the wet delay at the aircraft. The ZTD at the reference receiver were estimated every half hour by the Bernese software using the data from a GPS ground network, as shown in Figure 7.

Figure 8. SSR/df in the L1-carrier positioning using the GLOBAL, GPV, SURFACE, and ADS&NET method (mask angle = 15 degrees). Figure 8 shows the sum of squared residuals (SSR) of L1 carrier phase divided by the degrees of freedom (df) for the four tropospheric error mitigation techniques. The correct ambiguities were used and the elevation mask angle was set at 15 degrees. There seems to be no significant difference between these techniques. Also, tests of OTF ambiguity resolution were conducted to analyse the effects of the techniques in detail. The single-epoch OTF tests using the LAMBDA method (Teunissen, 1993) were carried out during the flight (the cases where the aircraft was on the ground were excluded), and the results are shown in Table 1. The first column shows the success rate (Number of correct solutions / Number of total solutions), where the solution was obtained if the ratio value was larger than 2, or all but one candidate were rejected. The second column shows the rate of failure (Number of wrong solutions / Number of total solutions), whislt the last column shows the percentage of the cases where no solution was obtained. The OTF performance could be improved by using multiple epochs or other techniques. However, it is beyond the scope of this paper, because the purpose here is to compare the performance of the various tropospheric error mitigation techniques.

Figure 7. Ground GPS network used for the estimation of ZTD at the ground reference receiver (CHOFU), where the ZTD at TSKB site was fixed in the processing. The data of observation sites other than Chofu were provided by GSI. Since the size of the network was not large enough to estimate the absolute tropospheric delay, the initial value of the ZTD is set to be equivalent with that computed using the surface meteorological data. RESULTS There are two methods to evaluate the performance of the tropospheric error mitigation technique. One is a test in the positioning domain, and the other is in the measurement domain. However, the former may not be possible because it is indeed difficult to obtain the true position of the aircraft during the flight, even if accurate meteorological measurements are obtained by the aircraft. Performance evaluation in the measurement domain would be possible if the measurement errors other than the tropospheric delay error were negligible. The carrier ambiguities must be resolved correctly. In this experiment the integer ambiguities were determined prior to the flight, ION GPS 2001, 11-14 September 2001, Salt Lake City, UT

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Table 2. OTF results during the flight (mask angle = 10 degrees).

Table 1. OTF results during the flight (mask angle = 15 degrees).

GLOBAL GPV SURFACE ADS&NET

Success (%) 89.6 98.9 99.5 99.1

Failure (%) 10.4 1.1 0.5 0.9

NO-solution (%) 40.0 40.5 36.6 36.1


Success (%) 77.2 85.2 90.2 92.9

Failure (%) 22.8 14.8 9.8 7.1

NO-solution (%) 50.3 38.9 40.1 38.8

In order to simulate the situation of the HAPS, the OTF tests were carried out when the altitude of the aircraft was higher than three kilometers, where the wet zenith delay is not significant. Although the OTF performance was generally degraded, the ADS&NET method was the best, while the second best was the SURFACE method, as shown in Table 3. It should be noted that the percentage of ‘No solution’ becomes larger when the altitude of the aircraft is increased. This fact indicates that the tropospheric delays would not cancel by taking double-differences if the height difference between the reference and the rover is large. Therefore the modeling and the estimation of tropospheric delay would become more important for the precise positioning of the HAPS.

Although the GPV, SURFACE, and ADS&NET methods seem slightly better than the GLOBAL model, the differences between the former three methods are not clear. Therefore, the elevation mask angle was reduced to 10 degrees to amplify the differences (the larger the tropospheric delay error, the lower the satellite elevation).

Table 3. OTF results when the aircraft was higher than three kilometers (mask angle = 10 degrees).


Figure 9. SSR/df in the L1-carrier positioning using the GLOBAL, GPV, SURFACE, and ADS&NET method (mask angle = 10 degrees). As seen in Figure 9, the residual errors differ considerably depending on the tropospheric error mitigation technique applied. The largest residual error seen at around GPS time 93500 is due to the setting satellite (PRN 7), whilst the error at around 94700 is caused by the rising satellite (PRN 6). Although there may be residual ionospheric delay error and multipath error, the magnitude of these errors should be the same for the four methods. Therefore, it can be considered that the differences seen in the Figure are attributed to the differences of the techniques.

Failure (%) 50.8 30.8 20.7 14.6

NO-solution (%) 62.9 50.2 52.2 49.9

SUMMARY AND FUTURE WORK The performance of four techniques to mitigate the tropospheric delay error for the precise positioning of the HAPS was evaluated using aircraft flight data. The following conclusions can be drawn: 1) The use of the global tropospheric delay model may not be adequate for the precise positioning of the HAPS.

The results of the OTF tests are summarized in Table 2. Although the ADS&NET method seems to be superior to the others, the difference from the SURFACE method is still not clear. It is evident that the three methods using regional measurements are better than the method using the global model. ION GPS 2001, 11-14 September 2001, Salt Lake City, UT

Success (%) 49.2 69.2 79.3 85.4

2) The GPV of NWM reduces the residual tropospheric delay error significantly, compared with the global model. The GPV data can easily be obtained from JMBSC, therefore the user does not need to measure

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modelling for GPS airborne navigation. 52nd ION Annual Meeting, Cambridge, Mass, 19-21 June. Dai L., J. Zhang, C. Rizos, S. Han, & J. Wang (2000). GPS and pseudolite integration for deformation monitoring applications. 13th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Salt Lake City, Utah, 19-22 September, 1-8. Dai L., J. Wang, T. Tsujii & C. Rizos (2001). Pseudolite-based inverted positioning and its applications. 5th Int. Symp. on Satellite Navigation Technology & Applications, Canberra, Australia, 24-27 July, CD-ROM. Davis J.L., T.A. Herring, I.I. Shapiro, A.E.E. Rogers & G. Elgered (1985). Geodesy by radio interferometry: Effects of atmospheric modeling errors on estimates of baseline length. Radio Science, 20(6), 1593-1607. Gao Y., Z. Li & J. McLellan (1997). Carrier phase based regional area differential GPS for decimeter-level positioning and navigation. 10th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Kansas City, Missouri, 16-19 Sept., 1305-1313. Han S. & C. Rizos (1996). GPS network design and error mitigation for real-time continuous array monitoring systems. 9th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Kansas City, Missouri, 17-20 Sept., 1827-1836. Ichikawa R., M. Kasahara, N. Mannoji & I. Naito (1995). Estimation of atmospheric excess path delay based on three dimensional numerical prediction model data. Journal of the Geodetic Society of Japan, 41(4), 379-408. Mendes V.B. & R.B. Langley (1995). Zenith wet tropospheric delay determination using prediction models: Accuracy analysis. Cartografia e Cadastro, Instituto Portugues de Cartografia e Cadastro, 2, 41-47. Niell A.E. (1996). Global mapping functions for the atmosphere delay at radio wavelengths. Journal of Geophysical Research, 101(B2), 3227-3246. NOAA, NASA, U.S. Air Force (1976), U. S. Standard Atmosphere, 1976, Washington D.C. Numerical Prediction Division/Japan Meteorological Agency (1997). Outline of the operational numerical weather prediction of the Japan Meteorological Agency, 126pp. [Available from JMA, 1-3-4 Otemachi, Chiyoda-ku, Tokyo 100-8122, Japan.] Saastamoinen J. (1973). Contributions to the theory of atmospheric refraction. In three parts. Bulletin Geodesique, 105, 279-298; 106, 383-397; 107, 13-34. Schueler T., G.W. Hein, & B. Eissfeller (2000). Improved Tropospheric delay modeling using an integrated approach of numerical weather models and GPS, 13th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Salt Lake City, Utah, 19-22 September, 600-615. Shimada M. (1999). Correction of the satellite’s state vector and the atmospheric excess path delay in SAR interferometry – Application to surface deformation

and process meteorological data. Also, the forecast data would be useful for real-time positioning. In future work, the denser and more frequent GPV data (a 10km mesh data, available every hour) will be used. The ray-tracing method to compute the tropospheric delay for the individual satellite would be promising because a mapping function is not necessary and, therefore, the method may not be erroneous in a situation where the tropospheric delay differs directionally. 3) The use of surface meteorological measurements can mitigate the tropospheric delay error. However, it is recommended that the lapse rates of the temperature and the water vapor pressure are estimated from the regional radiosonde data, because the two-parameter formula (Askne & Nordius, 1987) used to compute the tropospheric delay at the aircraft is very sensitive to these values. 4) The technique of using the ADS data at the aircraft, and the ZTD values estimated from the processing of a ground GPS network, seems to be the best among the four methods evaluated in this paper. However, the effect of the humidity measurements by the aircraft (not measured in the current study) should be investigated in future work. Furthermore, an experiment using the absolute ZTD estimated from a larger GPS network will be conducted. ACKNOWLEDGMENTS We would like to thank Dr. Yuki Hatanaka of GSI and Mr. Hamaki Inokuchi of NAL for useful discussions; Dr. Horng-Yue Chen of the Institute of Earth Sciences, Taiwan, for discussions and data analysis; and all members of the Satellite Navigation and Positioning group (SNAP) of the School of Surveying & Spatial Information Systems, UNSW, for their assistance. The first author would like to acknowledge support from the Japan Science and Technology Corporation (JST) postdoctoral fellowship scheme. REFERENCES Askne J. & H. Nordius (1987). Estimation of tropospheric delay for microwaves from surface weather data. Radio Science, 22(3), 379-386. Collins J.P. & R.B. Langley (1996a). Mitigating tropospheric propagation delay errors in precise airborne GPS navigation. PLANS ’96, IEEE, Atlanta, Georgia, 22-26 April, 582-589. Collins J.P., R.B. Langley & J. LaMance (1996b). Limiting factors in tropospheric propagation delay error ION GPS 2001, 11-14 September 2001, Salt Lake City, UT

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detection. Journal of the Geodetic Society of Japan 45(4), 327-346. Smith W.L. (1966). Note on the relationship between total precipitable water and surface dew point. Journal of Applied Meteorology, 5, 726-727. Thayer G.D. (1974). An improved equation for the radio refractive index of air. Radio Science, 9(10), 803-807. Teunissen P.J.G. (1993). Least-squares estimation of the integer GPS ambiguities. Delft Geodetic Computing Centre LGR-series No. 6. Tsujii T., M. Murata, M. Harigae, T. Ono & T. Inagaki (1998). Development of Kinematic GPS Software, KINGS, and flight test evaluation. Technical Report of National Aerospace Laboratory, Japan, TR-1357T. Tsujii T., J. Wang, C. Rizos, M. Harigae, & T. Inagaki (2000). Estimation of residual tropospheric delay for high-altitude vehicles: Towards precise positioning of a stratosphere airship. 13th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Salt Lake City, Utah, 19-22 September, 696-704. Tsujii T., C. Rizos, J. Wang, L. Dai, C. Roberts & M. Harigae (2001). A navigation/positioning service based on pseudolites installed on stratospheric airships. 5th Int. Symp. on Satellite Navigation Technology & Applications, Canberra, Australia, 24-27 July, CD-ROM. Wang J., T. Tsujii, C. Rizos, L. Dai & M. Moore (2001). GPS and pseudo-satellites integration for precise positioning. Geomatics Research Australasia, 74, 103-117. Wanninger L. (1997). Real-time differential GPS error modeling in regional reference station networks. Proc. IAG Symp. 118, Rio de Janeiro, Brazil, 86-92. Yokomaku Y. (2000), Overview of stratospheric platform airship R&D program in Japan. Stratospheric Platform Systems Workshop SPSW2000, Tokyo, Japan, 21-22 September, 15-23. Zhang J. (1999). Precise estimation of residual tropospheric delays in a spatial GPS network. 12th Int. Tech. Meeting of the Satellite Division of the U.S. Inst. of Navigation, Nashville, Tennessee, 14-17 Sept., 1391-1400.


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