Assessment of a New Rover-Enhanced NetworkBased Real Time Kinematic GNSS Data Processing Strategy Nicholas Zinas University College London
success rates of the estimated between the references stations relative zenith ionospheric delay from the proposed algorithm is discussed and compared against a standard ionospheric model. The effectiveness of the method is demonstrated through data from the South California Integrated GNSS Network (SCING), processed with software developed for this research.
BIOGRAPHY Nicholas Zinas is a PhD candidate in the Department of Civil, Environmental and Geomatic Engineering at University College London. He holds an MSc degree in Geodetic Surveying from University of Nottingham and a Bachelor in Surveying and Mapping Sciences from the University of East London. His research interest is Network RTK processing techniques.
INTRODUCTION A wireless sensor network (WSN) is a wireless network consisting of spatially distributed autonomous devices using sensors to cooperatively monitor physical or environmental conditions, such as temperature, sound, vibration, pressure, motion or pollutants, at different locations [Kay et al, 2004].
ABSTRACT Real Time GNSS networks established across countries over the last fifteen years, provide centimetre level accuracy for a wide range of applications differing from precise ship docking to land surveying. The number of users of these networks has steadily increased over the years, and a potential new market has been created. Public sector organizations deploy GNSS Networks to support infrastructure projects. Private companies establish their own networks for commercial or private use. This paper focuses on the exploitation of the advantages of using multiple users operating within a GNSS network as part of the system, as a virtual network of stations that can operate autonomously and combined with the reference station network. A proposed network-RTK methodology that encompasses the multiple users of network RTK services for instantaneous GPS-RTK positioning, is presented. Users are equipped with two way communication means, to transmit their data to a central processing facility (CPF) on an epoch by epoch basis. A centralised approach reduces the need for complex algorithms at the user side. This methodology increases significantly the ambiguity success rate for users that operate near the border limits of the network, or even tens of kilometers outside them. In this case regional GNSS networks could expand their sphere of influence, without the need for additional reference stations. Also the impact on the ambiguity
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
A real time GNSS network consists of spatially distributed sensors of GNSS signals. Users of the network services can be considered as additional sensors, operating on an ad-hoc basis. They can cooperate with the network by transmitting their data to the CPF via established communication means. In this case the user becomes part of the network and could act as a new node, densifying the existing station infrastructure. The rover multiplicity concept has initially been proposed by Lachapelle et al [1993] and later by Luo et al [2003]. Alves [2004] proposes an in-receiver method of multiple reference station positioning, introducing the rover data into the network ambiguity estimation filter to estimate the position of the rover in a tightly coupled approach. The same method can be extended to include any number of rovers, where the shortest independent set of baselines in the network is selected for processing. In this approach the ambiguities between the reference
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stations are not being resolved in a separate process rather estimated in a common filter with the additional rover information taking measurement correlation into account by using an adaptive covariance function.
refraction for the rest of the reference stations can be written as follows:
The user acts for the benefit of the network. Since ambiguity resolution performance is a function of interreceiver distances because of the distance dependence of the correlated errors, optimally connecting baselines between the users and the reference stations will shorten the between receivers separation in the network. The ambiguity resolution process is then more likely to be successful, since the baselines to be resolved are the shortest ones in the network.
zenith I Bzenith = I Azenith + dI AB , L1 , L1 , L1
(1)
zenith I Czenith = I Azenith + dI AC , L1 , L1 , L1
(2)
The double difference ionospheric parameter in the observation equations for baseline A → B is defined as: ij I AB = OFAij × I Azenith − OFBij I Bzenith , L1 , L1 , L1
(3)
, with OF being the obliquity factor that maps the zenith
This paper exploits the impact of using the multiple users operating in a network for their own benefit and presents a methodology for a complete network-RTK process. This is described through a three step process. Firstly, a weighted least squares model is introduced with two sets of parameters the carrier phase ambiguities and the relative zenith ionospheric delays between the reference stations. The Helmert-Wolf method is employed for their estimation in a multiple epoch approach, assuming it is the initial period of the network’s operation. Ambiguities are then kept fixed and the necessary algorithms account for events that can disrupt the network’s continuous operation. Secondly an exponential moving average filter is applied on the time series of the ionospheric estimates to smooth the data and attenuate any induced noise. The estimates are then linearly interpolated for the user position. Thirdly, a single epoch model for instantaneous user positioning is presented. Instantaneous positioning has the advantage of being immune to cycle slips, there is no need for an initialization period and centimetre level accuracies are achievable immediately. To achieve this, the multiple users in an area have to combine all their information into a coherent model, benefiting thus by the shortest inter-receiver distances. Instead of broadcasting corrections from the reference stations, the users transmit their observations at the CPF, where their positions are estimated on an epoch by epoch basis and transmitted back to users. The method has been validated by processing a data set from the SCIGN network. Three stations were used as reference stations while four others as users operating in the area.
ionospheric delay to the signal travelled path. I B , L1 can be written as a function of the zenith ionospheric delay at station A .Substituting to equation 3 it follows:
ESTIMATION OF THE IONOSPHERIC DELAY
Given a sequence { xk }k =1 a
RELATIVE
zenith
ij
ij
zenith
zenith
ij
(4)
zenith
Similarly,
ij I BC = OFBij × I Bzenith − OFCij × I Czenith , L1 , L1 , L1 zenith zenith = OFBCij × I Azenith + OFBij × dI AB − OFCij × dI AC , L1 , L1 , L1
(5)
zenith
An estimate for I A, L1 is derived from a standard model, i.e. an IONEX map or the Klobuchar Broadcast model and the terms
OFABij × I Azenith , L1
and
OFBCij × I Azenith of , L1
equations respectively, are moved to the left hand side of the double difference carrier phase observation equations. Once the ionospheric parameters have been estimated for the required time span that is needed for the resolution of the double differenced ambiguities, are then filtered to attenuate the noise and account for the temporal correlation of the estimates. To achieve this, an exponential moving average (EMA) filter is applied to the time series.
ZENITH
N
at any instant of sets of
xk ( MA) =
n moving average ( xk ( MA) )
k is defined from xk by taking the average
n subsequent terms as follows: 1 n
k −1
∑
j =k −n
1
x j + ( xk − xk −1 ) n
(6)
This is illustrated in figure 1, using a moving window of n data points.
defining the L1 zenith ionospheric refraction parameter for in metres, the zenith ionospheric
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
zenith
ij
For a network of three reference stations A , B and C zenith
ij
= OFAB × I A , L1 − OFB × dI AB , L1
Solving for the between reference stations zenith ionospheric corrections instead of the double difference corrections, has the advantage of not failing to compute corrections when a reference station’s observations to a specific satellite are missing.
station A as I A ,L 1
zenith
I AB , L1 = OFA × I A , L1 − OFB ( I A , L1 + dI AB , L1 )
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The lower limit is between 10-20 km range, and the upper limit is between 100-300km [Teunissen, 1998]. The resolution of the double difference ambiguities between the reference stations is the kernel for the Network-RTK GPS positioning. It enables the generation of the corrections transmitted to the users, to be then interpolated for their position. Various techniques have been developed for the determination of the correct integers for reference stations at medium distances at the beginning of the network’s operation, using data over several hours. Sun et al [1999] and Chen et al [2000] discuss extensively this issue.
Figure 1: Moving window of n- data points The EMA for an instant k of the sequence
{x } k
N k =1
is
computed from the following formula:
xk ( EMA) = xk −1( EMA) + γ × ( xk − xk −1( EMA) )
In this paper for the resolution of the ambiguities during the initial period of the network’s operation, the HelmertWolf method [Cross, 1994] has been implemented. Since there are two sets of parameters to be estimated, the relative zenith ionospheric delays and the float double difference ambiguities, the Helmert-Wolf method is convenient because it enables the computation of different groups of parameters at different times. The design and the parameter matrix are partitioned to hold the so called
(7)
The smoothing factor γ dictates the degree of filtering. It is expressed in terms of the variable n defined above as: γ =
n
(8)
n +1
local
to epoch i while the latter remain constant. Equation 10 illustrates the basic model.
and since n ≥ 0 , then 0 ≤ γ ≤ 1 . The derived filtered values are then double differenced
⎡ xi ⎤ [ Ai | Bi ] ⎢⎢ − ⎥⎥ = [bi ] + [ vi ] ⎢⎣ y ⎥⎦
( ∇ΔI ) and interpolated at the user position. A distance r
based linear interpolation algorithm suggested by Gao et al [1997] has been adopted. The double difference ionospheric delay at the user u , is described by the following equation:
ωr ∇ΔI r r =1 ω
while the weight
(9)
( ∑(B W b − B W A ( A W A )
)
−1
−1 ⎧q ⎫ y$ = ⎨∑ Bi T Wi Bi − Bi T Wi Ai ( AiTWi Ai ) AiTWi Bi ⎬ ⎩ i =1 ⎭ (11)
ωr for the r th reference station is the
inverse of the distance between this reference station and the user, ω is the sum of the n − 1 weights for n reference stations. In order to derive precise estimates for the relative ionospheric delays, the ambiguities between the reference stations have first to be resolved, enabling thus the use of the phase-range observable.
q
T
i
T
T
i
i
i
i
i
i
i
−1
i
i =1
AiTWi bi
)
The Least-Squares AMBiguity Decorrelation Adjustment (LAMBDA) is used in order to fix the ambiguities to their integer values [Teunissen, 1994]. The validation procedure is accomplished using the ratio test [Verhagen, 2004]. If the tests pass the predefined critical value, then the values of the local parameters are computed with back-substitution for every epoch from the following equation.
AMBIGUITY RESOLUTION AND VALIDATION FOR REFERENCE STATION NETWORKS A continuously operating regional GNSS network consists of a number of reference stations at medium baseline distances. A lower limit for the length of a medium baseline can be defined as the shortest distance at which residual ionospheric refraction, tropospheric refraction and orbital errors between sites are greater than receiver and site specific errors. An upper limit can be defined as the minimum distance at which double frequency ambiguity resolution is no longer feasible or frame and orbital errors are the dominant error source.
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
(10)
The float estimates y$ of the double difference ambiguities are computed as follows for q epochs of data:
n −1
∇ΔI u = ∑
xi and global y parameters. The former are unique
$) x$i = ( Ai Wi Ai ) ( Ai Wi b i − Ai Wi Bi y T
−1
T
T
(12)
While the ambiguities after the initial period are kept fixed, the integer values have to be re-determined when tracking a satellite results in cycle slips or a long data gap occurs. It is also crucial to resolve the ambiguities for newly risen satellites and handle efficiently a reference
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the ambiguities between them can be beneficial, since this could enable a regional atmospheric monitoring process and the computation of their precise positions. To achieve this, information from the reference station network has to be introduced. Solving one set of ambiguities between one reference station and one rover, will tie the two systems, reference stations and rovers, together. This allows the determination of a ‘walk’ connecting the users, ideally using the shortest independent baselines between them. This approach is illustrated in figures 3-6.
satellite change when necessary. For that reason instantaneous ambiguity resolution is crucial for the smooth operation of the network. Figure 2 illustrates the algorithmic approach implemented for that purpose. Relative zenith ionospheric corrections can be predicted from the existing time series and applied on the new observations. Collect Epoch Phase Data for all PRNs
Collect Epoch Phase Data for acquired PRN and reference satellite
Compute Float Solution
Next Epoch
The model that has been developed for the multiple rover approach presented in this paper is a Weighted Least Squares estimator incorporating all the available information, carrier phase and pseudorange observations, of the user – reference station system. It is assumed that the users have dual frequency geodetic quality GPS receivers. However this is not a limitation, since the same model can be extended to include single frequency information, if available. The only pre-requisite is that both carrier phase and pseudorange data are available on any frequency. Observations from all reference stations and all users are processed in a single epoch for the estimation of the unknown parameter vector, that consist of the user position vectors and the necessary independent sets of double difference ambiguities. The advantages of a single epoch solutions are that there is no data accumulation, hence solution is resistant to cycle slips and can provide centimetre level accuracy immediately, without any delay needed for initialization of several seconds or minutes as required by the most of the OTF techniques. Single epoch processing however, is strongly dependent on the distance between the reference stations and the rovers.
Compute Ionospheric Parameters & DD Baseline Residuals FOR THIS EPOCH
PRNs acquired Transform Ambiguities
LAMBDA for Ambiguity Resolution
YES
NO
YES
Ambiguities Fixed?
Reference Satellite the Same?
YES NO
YES
NO
PRNs lost ?
Is this the Initial Period?
NO
YES
NO
Is this the Initial Period
Populate the resolved Ambiguity YES for the new satellite
PRNs the same ?
NO
Set of DD Existing Resolved Ambiguities
Compute Ionospheric Parameters & DD Baseline Residuals FOR INITIAL PERIOD
Figure 2: Reference Station Ambiguity Resolution Algorithm
The low level of redundancy varies from epoch to epoch since it is based on the number of available satellites. The multiple rover approach aims to reduce these limitations of the instantaneous positioning, by introducing a step by step approach from a selected reference station to the rest of the rovers based on the shortest between stations baseline lengths. The redundancy of the system on the other hand is increased by using ambiguity constraints.
MULTIPLE ROVER ALGORITHM Network RTK consists of three steps. The first step is the resolution of the ambiguities between the reference stations and the estimation of corrections. The second step is the interpolation of the corrections at the user location and the third step is the transmission of the corrections to the rover. In the multiple rover approach described herein, all information from both the reference stations and the users are transmitted to a Central Processing Facility (CPF). All necessary processing takes place at the CPF on an epoch by epoch basis using all available information. The CPF transmits back to the user its estimated position, instead of any corrections, along with a flag to indicate the quality of the estimate. For this purpose an NMEA0183 GGA string can be used.
Figure 3 illustrates a network of three reference stations r , A , B and C at medium baseline lengths ,and three users
1 , 2 and 3 , operating within the
network.
The reference stations and the users operating within the network area constitute the user-reference station system. The integer ambiguities between the reference stations are already known and this is a pre-requisite for the implementation of the multiple rover approach, as for every other network RTK positioning approach. In an area where multiple users operate simultaneously, solving
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
( u ) namely,
Figure 3: GPS Network consisting of three reference stations and three users
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further increase in the number of platforms, and the performance is dependent on the magnitude of the observational errors. The use of ambiguity constraints also enhanced the ability to detect wrong fixes. However only the accurate relative position vector between the rovers can be estimated from this technique and a multiple epoch estimation approach is a pre-requisite.
For the reference station system the between reference ij ij ij stations ambiguity sets N AB , N BC and N CA are known integers. They have been resolved in the beginning of the network’s operation using several hours of data and then appropriate algorithms make sure that they are kept fixed in real time every epoch. For the user system, preserving the condition of linear independence, the shortest baselines are illustrated in figure 4.
Encompassing the information from a GPS reference station network, the accurate position of the rovers can be estimated relative to the fixed position of a reference station. To achieve this, the rover and the reference station system have to be connected in a way, by introducing as unknowns in the WLS estimator the necessary sets of double difference ambiguities between them (figure 5). In this case, constraint equations can be applied to increase the degrees of freedom of the model and solve only for the shortest reference station to rover baseline.
Figure 4: Shortest baselines for the rover system Users u and reference stations r are assumed to observe a common set of satellites s , an assumption that is reasonable for regional GPS networks and reduces computational complexity. The independent set of double differenced ambiguities for the rovers 1 , 2 and 3 following from figure 4, are N 12ij and N 23ij . The rover ij
ij
positions and the N 12 and N 23 ambiguity sets are unknown. The observation vector consists of 4 × (u − 1) × ( s − 1) observations while the unknown parameters are 2 × (u − 1) × ( s − 1) + 3 × u , using all available carrier phase and pseudorange observations on both frequencies. Assuming that there are no reference stations, when the baseline between the rovers are short enough for the atmospheric biases to cancel in double differencing, a WLS adjustment will lead to the estimation of the parameter vector defined above, assuming availability of all observations to common satellites and that u ≥ 2 and s ≥ 4 so that the degrees of freedom DOF ≥ 0 . In that case, only the relative position vector between the rovers will be accurately determined. When more than two rover receivers, u ≥ 3 , operate simultaneously the integer ambiguity closure constraint can be applied. Following from figure 4:
N12ij + N 23ij + N 31ij = 0
Figure 5: Tie between the rover & reference system
The shortest rover-reference station baseline in the network of figure 5 is 1 → A . This set of double difference ambiguities constitutes the ideal independent set that needs to be resolved along with the between rovers independent set of figure 4. This will enable the derivation of every other ambiguity in the user-reference station system. The selected rover, in this example rover 1 ,is called the primary rover, and reference station A , primary reference station.
The redundancy of the system can be increased by introducing information from the rest of the reference stations B and C without the need to include their respective ambiguities. These ambiguities can be written as a function of the known ones between them and the ones to be estimated. For example, using the ambiguity constraint equations, the ambiguities for the baselines 1 → B and 1 → C can be written as a function of the known ambiguity between reference stations A and
(13)
Luo and Lachapelle [1999] have shown that for three moving platforms the time to ambiguity fixing can be reduced up to 50%, by applying ambiguity constraints and depending on the magnitude of the system errors. Luo [2000] and Luo and Lachapelle [2003] investigated the improvement of ambiguity resolution with the increase in the number of platforms. The results show that the time to fix when using up to 10 platforms and applying constraint equations can improve by almost 70% compared to the case where no constraints applied. The improvement rate of ambiguity resolution however diminishes with the
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
ij B ( N AB ) , and the one to be estimated N1ijA (figure 6).
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ij ⎡ b uu, ⎤ L1 ⎢ ij ⎥ b ur, L1 ⎢ ⎥ ij ⎢b uu, ⎥ C/A ⎢ ij ⎥ ⎢ b ur,C / A ⎥ ⎢ b ij ⎥ ⎢ uu, L 2 ⎥ ij ⎢ b ur, ⎥ L2 ⎢ ij ⎥ b ⎢ uu, P 2 ⎥ ij ⎢⎣ b ur, ⎥ P2 ⎦t
Figure 6: Ambiguity constraints
The constraint equations applied are:
N +N ij 1A
ij AB
+N
ij B1
= 0∴ N
ij B1
= −N − N ij 1A
ij AB
N 1 A + N AC + N C 1 = 0 ∴ N C 1 = − N 1 A − N AC ij
ij
ij
ij
ij
ij
(14) (15)
This concludes that the only ambiguity set to be estimated in order to tie the two systems is the one from the primary rover to the primary reference station, 1 → A . This
ij ⎡ dφUU , L1 ⎢ r d x U ⎢ ij ⎢ dφUU , L1 ⎢ r ⎢ d xU ij ⎢ dφUU ,C / A ⎢ r d x U ⎢ ⎢ dφ ij ⎢ UUr ,C / A ⎢ d xU = ⎢ dφ ij ⎢ UU r ,L2 ⎢ d xU ⎢ ij ⎢ dφUU r ,L2 ⎢ d xU ⎢ ij ⎢ dφUU r ,P2 ⎢ d xU ⎢ ij ⎢ dφUU r ,P2 ⎢⎣ d x U
λ1
0
0
λ1
0
M
0
M
M
0
0
λ2
M
0
M 0
⎤
0⎥
⎥ ⎥ ⎥ ⎥ ⎥ M⎥ r ⎥ ⎡ xU ⎤ ⎥ ⎢ ij ⎥ ⎥ ⎢ N uu, L1 ⎥ ⎥ ⎢ ij ⎥ ⎥ ⎢ N u'r', L1 ⎥ 0 ⎥ ⎢ N ij ⎥ ⎥ ⎢ uu, L 2 ⎥ ij ⎥ ⎥ ⎢⎣ N u'r', L2 ⎦t ⎥ λ2 ⎥ ⎥ 0⎥ ⎥ ⎥ ⎥ M ⎥⎦ t
(16) The design matrix can be extended to accept any number of rovers. The use of dual frequency receivers is not necessary. The model can include both dual frequency and single frequency observations from different rovers.
ij
set, N 1 A ,has to be included in parameter vector of the geometry based WLS model along with the between ij ij rovers ambiguity sets N 23 and N 12 . The single epoch WLS deterministic model that has been described above, and follows from figure 6 is formed in ij
dφUU
r
are the partial derivatives between d xU any two users and a pair of satellites ij ,with respect to the equation 16.
r
unknown position vector x U , λ1 and λ2 are the known wavelengths of L1 and L2 frequencies respectively, while C / A represents the pseudorange observable on
L1 and P2 the pseudorange observable on L2 . Figure 7 summarises the multiple rover methodology.
u1
u2
M
M
Figure 7: Multiple Rover Methodology
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
⎡ ν xr U ⎤ ⎢ ⎥ ij ⎢ ν Nuu, ⎥ L1 ⎢ ⎥ ij ⎥ − ⎢ ν Nu'r', L1 ⎢ ⎥ ij ⎢ ν Nuu, ⎥ L2 ⎢ ⎥ ij ⎢⎣ ν Nu'r', ⎥ L 2 ⎦t
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All stations are equipped with ASH701945B_M GPS antennas except reference station CLAR equipped with an ASH700936A_M antenna. However, the different types of radomes used at the station, make the application of an antenna model necessary to increase the algorithm’s performance. Phase centre offsets and elevation dependent variations correction values are derived for these antenna models and their respective radomes with codes SCIT, SCPL and SCIS from the Antex file [Schmid et al, 2006]. The tropospheric delay is mitigated using the ESA tropospheric model [ESA, 2004], while the ionospheric effect is estimated and applied as already described. The value of the ionospheric delay for one of the reference stations, as required by the relative zenith ionospheric delay estimation algorithm, is derived from the IONEX map, produced at CODE IGS analysis centre. All of the processing simulates real time performance. Once the network’s ambiguities are resolved during the initial period of its operation, the model of equation 16 is called on an epoch by epoch basis.
EXPERIMENTAL RESULTS AND ANALYSIS
In order to test the performance of the multiple rover proposed algorithm, a dataset from the SCIGN network was analysed. The station set consists of three reference stations and four rovers at medium baseline lengths. Dual frequency receivers were occupied, with a sampling rate of 30s on 18th of December 2007 starting at midnight for a period of 2hrs and 8mins (172,860 to 180,540 GPS time). An 1s sampling interval can be processed with the same efficiency, in the case where this is necessary. Figure 8 shows the configuration of the station set, consisting of the user and reference station system.
Table 1 summarises the distances in kilometers for the reference station-user system. Lengths vary from 13 km for the users BGIS and RHCL to 106km for the reference stations LINJ and VTIS. Table 1: Summary of all baseline lengths between the rovers and the reference stations in the test network WRHS
Figure 8 The SCIGN test sub-network
Stations VTIS, LINJ and CLAR constitute the network’s reference stations, while stations BGIS, OXYC, RHCL and WHRS simulate the users simultaneously operating in the area. Station WRHS is located outside the working network at a distance of about 30 km from the closest reference station VTIS. It is an extrapolation from the reference station network and perhaps is the most challenging site to determine its ambiguity fixed solution. OXYC provides a site at reasonably far distances from the reference stations (>45km) and also at a challenging position to interpolate to, since it is less than 2km away from the network’s area limit. Finally, RHCL and BGIS stations are reasonably close to each other ( ≈ 13km) at a distance of ≈ 31km from the closest reference stations, CLAR and VTIS respectively.
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
OXYC
27.79
RHCL
37.71
20.62
BGIS
24.78
18.62
13.38
LINJ
82.47
59.03
71.41
76.26
VTIS
29.91
47.02
41.84
30.43
105.95
CLAR
68.48
46.13
31.08
44.9
72.61
WRHS
OXYC
RHCL BGIS
LINJ
69.46 VTIS
The ambiguities for the shortest reference station baselines VTIS to CLAR and CLAR to LINJ were resolved after 41mins since the beginning of the network’s operation. To check the validity of the ambiguity sets a different set of baselines was selected consisting of the baselines VTIS to LINJ and VTIS to CLAR. The time needed for the success of the ratio test for the second set was 1hr and 2mins. Since the longest baseline in the network (VTIS-LINJ) was involved in this set, it was expected that the residual atmospheric errors would have an impact on the required time period for ambiguity resolution. The ambiguity constraints condition was then tested and satisfied for the reference station network after all ambiguity sets were resolved, while the misclosures averages of the post-fit residuals around the
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closed loop were at the sub-millimeter level for the whole period of the dataset.
ionospheric delay for the same two baselines. The higher ionospheric decorrelation over the longest baseline VTISLINJ can be seen when comparing the two graphs.
Figure 9 shows the double difference L1 and L2 residuals after fixing the network ambiguities, for baselines VTISCLAR and VTIS-LINJ, for the first and second highest elevation satellites, PRN 18 and PRN 21 respectively. The standard deviations of the residuals for both frequencies are summarized in table 2. It can be seen that for the 106 km long baseline VTIS-LINJ, the standard deviations of the L1 and L2 residuals are higher compared to the 72km baseline VTIS-CLAR.
(a)
Table 2: Standard deviations (m) of the double difference L1and L2 residuals Baseline
σ L1
σ L2
VTIS-LINJ VTIS-CLAR
0.017 0.012
0.027 0.022
(b)
(a)
Figure 10: Filtered Zenith Relative Ionospheric Delay for: (a) VTIS-CLAR (72 km) and (b) VTIS-LINJ (106 km).
(b)
To check the efficiency of the estimated ionospheric estimates, the double differenced post fit ionospheric residuals were computed from equation 17, referred as geometry free linear combination ( L4 ) in the literature.
L4 = ∇ΔΦ L1 − ∇ΔΦ L 2 − ∇ΔN L1 + ∇ΔN L 2 − ∇ΔI L1 + ∇ΔI L 2 (17) While figure 11a clearly indicates that the pattern of the time series is similar to the one of the residuals of figure 9a, figure b follows a closely similar pattern as the L1 and L2 residuals of figure 9b. This suggests that for both baselines, the double difference L1 and L2 ionospheric residuals dominate the other error sources present in the post fit observation double difference residuals.
Figure 9: Double Difference L1 and L2 residuals for satellite PRN pair 18-21 for: (a) VTIS-CLAR (72km) and (b) VTIS-LINJ (106km)
Following from equation 12, the relative zenith ionospheric estimates for baselines VTIS-CLAR and VTIS-LINJ are computed for the initial period. After the network ambiguity resolution, the ionospheric estimates are computed on an epoch by epoch basis. Figure 10 presents the time series of the filtered relative zenith
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
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Table 3: Ambiguity success rates for each rover applying the estimated relative zenith ionospheric estimates
(a)
Station
Network
MultipleRover
BGIS RHCL OXYC WRHS
99.3% 99.3% 96% 79.5%
99.3% 99.3% 99.3% 97.4%
From table 3 it can be seen that the multiple rover solution increases the chance to fix the ambiguity for rover OXYC that is situated close to the border limit of the reference station network. A significant improvement however is seen for rover WRHS that is situated 17 km outside the network’s border. This improvement stems for the shortest between rover baseline selection, and it is feasible only when all rovers in the area are taken into account.
(b)
(a)
Figure 11: Post-fit ionospheric residuals for satellite PRN pair 18-21 using the geometry free linear combination for: (a) VTIS-CLAR (72km) and (b) VTIS-LINJ (106km)
(b)
The multiple rover positioning algorithm summarized in figure 7, was compared against the single rover network solution. For the latter each rover was processed epoch by epoch in a WLS model with all reference stations. The instantaneous ambiguity resolution for both approaches was carried out using the LAMBDA method. Both dual frequency carrier phase and pseudorange measurements, were used. A new ambiguity was obtained for every epoch, using only the data from that epoch. If successful, a geometry based fixed solution for the computation of the relative coordinate correction vector was applied. The ‘true’ position of the rover stations were computed from a daily file of observations processed with GIPSY in PPP mode. The validity of the fixed ambiguities was then verified by comparing the rover position estimates from the algorithm and the PPP results. A summary of the ambiguity resolution success rates is presented in table 3. Figure 12 shows the topocentric position residuals for the multiple rover approach computed epoch by epoch, for stations RHCL, OXYC and WRHS. For both table 3 and figure 12 presented results, the regionally estimated relative zenith ionospheric delay has been applied.
22nd International Meeting of the Satellite Division of The Institute of Navigation, Savannah, GA, September 22-25, 2009
( c)
Figure 12: True (PPP) minus Multiple Rover Approach Computed Topocentric Position (a) RHCL, (b) OXYC, and (c) WRHS
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From figure 12 the effect of the network geometry on the computed rover position can be seen. While the residuals for station RHCL (fig. 12a) present an almost identical magnitude extent in the east-west direction, for station OXYC that is located near the western border of the network, there is a slight offset towards the eastern direction (fig. 12b). This effect is clearer for station WRHS, that is located 17 km outside the western border of the network (fig. 12c). The topocentric position residuals show an eastward offset that is due to the eastern orientation of the network with respect to the station.
of many users being concentrated in a region is surely greater than a few years ago. Taking into account the single frequency users, new prospects are available. The approach presented herein, does not limit itself to any number of users or frequencies. In the same model single and dual frequency data can be included for mutual user benefit. Considering that all processing takes place at a central processing facility, the user is free of any computational burden. Its precise position is transmitted from the CPF epoch by epoch. Since more processing power is available at the central facility, more sophisticated algorithms can be implemented. The availability of both reference station and user data, introduces the opportunity for better error modeling. Multiple rovers in the area can give a better indication of the local atmospheric conditions, since as demonstrated in this paper, using the multiple rover approach all ambiguities in the network can be determined. The impact of the number of users in the quality of the derived atmospheric corrections is a topic of further research. Single frequency users could benefit from regionally derived corrections, by a well densified network of stations. It will be a significant market change, the introduction of single frequency cheap receiver users to the RTK networks that are currently dominated by geodetic quality GNSS receiver users.
Table 4 shows the success rates when applying a standard ionospheric model, rather than the regionally estimated relative ionospheric delay. Table 4: Ambiguity success rates for each rover applying an ionospheric correction from IONEX map Station
Network
MultipleRover
BGIS RHCL OXYC WRHS
94.1% 96.1% 94.7% 73.5%
94.1% 94.1 % 92.8% 90.2%
From tables 3 and 4, it can be seen that while overall there is an improvement in the ambiguities success rates for every rover, the most significant improvement when applying the estimated ionospheric delays rather than the model derived ones, is for station WRHS. The improvement is for the 7.2% of the time.
Finally, the multiple rover approach fits with the current sensor network trend. Communication protocols are becoming standardized, and this supports a bilinear communication implementation. Centralised processing creates new opportunities for novel services to be introduced while total control of the overall service operation is feasible. In a few years, GNSS users may not be subscribers to an RTK service, but they may be detected by the potential service provider for a pay on demand application.
SUMMARY AND CONCLUSIONS
A three step centralised network-RTK approach has been presented and tested. It is shown that the regional estimation of relative ionospheric corrections has a positive effect on the overall ambiguity resolution success rates when compared to the use of a standard ionospheric model. However, the post fit ionospheric residuals and their impact on the double difference observation residuals need to be investigated further.
ACKNOWLEDGMENTS
The author would like to thank his project supervisors Prof. Paul Cross and Prof. Marek Ziebart for their encouragement and recommendations on this research.
It has also been demonstrated that the multiple rover positioning algorithm increases the ambiguity success rates for rovers near or outside the boundaries of a GNSS reference station network. This could be beneficial for the network operators and service providers that want to expand their area of influence, without the need and subsequently the additional costs of establishing new reference stations. The area outside the network that this approach will prove to be feasible is a function of the number of users of the network services and an individual study by each network operator will be required.
REFERENCES
Alves P., Lachapelle G., Cannon M.E. (2004) In-Receiver Multiple Reference Station RTK Solution. ION GNSS 17thInternational Technical Meeting of the Satellite Division, 21-24 Sept., Long Beach, California. Scmid R., Rothacher M. (2006) Antex: The antenna Exchange Format Version 1.3. International GNSS Service. Chen HY, Rizos C, Han S (2004) An instantaneous ambiguity resolution procedure suitable for medium-scale GPS reference station networks. Surv Rev 37(291):396– 410
The proposed methodology was tested with double frequency GPS receiver data, and it has assumed that four users were operating simultaneously. In an era where GPS receivers are becoming even more popular, the possibility
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Cross P. A. (1994) Advanced Least Squares applied to position-fixing. Working Paper No 6,School of Surveying, University of East London. European Space Agency (2004) Galileo: Galileo Reference Troposphere Model for the User Receiver. ESA-APPNG-REF/00621-AM. Gao Y., Li Z., McLellan J. F. (1997) Carrier Phase based regional area differential GPS for decimetre-level positioning and navigation. 10th Int. Tech. Meeting of the Satellite Div. Of the US Institute of Navigation, Kansas City, Missouri, 16-19 September, 1305-1313. Kay R., Mattern F. (2004) The design of Wireless Sensor Networks. IEEE Wireless Communications 11 (6) 54-61. Lachapelle, G., Liu C., Lu G. (1993) Quadruple Single Frequency Receiver System for Ambiguity Resolution on the Fly. Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS/03, 1167-1172. Luo N., Lachapelle G. (2003) Relative Positioning of Multiple Moving Platforms using GPS. IEEE Transactions on Aerospace and Electronic Systems, 39(3), 936-948. Sun,H., Cannon, M.E., Melgard, T.E. (1999) Real Time GPS Reference Network Carrier Phase Ambiguity Resolution. Proc. Institute of Navigation National Technical Meeting San Diego, California, 25-27 January: 193-199 Teunissen P. J. G. (1994) A new method for fast carrier phase ambiguity estimation. Proceedings of IEEE PLANS ’94, Las Vegas, NV, April 11-15, pp 562-573. Teunissen P. J. G., Kleusberg A. (1998) GPS for Geodesy . 2nd Edition, Springer, Germany, pp 483-484. Verhagen A. A. (2004) The GNSS integer ambiguities: estimation and validation. Phd Thesis, University of Delft.
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