EUROFIX Regional Area Augmentation System Reducing spatial decorrelation with Extended DGPS

R.F van Essen Delft University of Technology

Electrical Engineering Department Telecommunications- & Trqfficontrolsystemsgroup

Professor: dr.ir. D. van Willigen Mentors: ir. G.W.A. Offennans, if. A.W.S. Helwig Period: July 1996 - March 1997 Assigrul1ent number: 757 Date: 16 maart, 1997

EUROFIX Regional Area Augmentation System: Reducing spatial decorrelation with Extended DGPS

R.F. van Essen Delft University of Technology

Electrical Engineering Department Telecommunications & Traffic-control systemsgroup

ABSTRACT Eurofix is an integrated navigation system, which com­bines Differential GNSS and Loran-C. The Loran-C system is used to transmit messages which contain dif­ferential corrections for GNSS by additional modulation of the transmitted signals. It has been shown that reli­able data transmission with Loran-C stations up to J, 000 /em distance is feasible. The differential corrections are generated by a DGPS reference station located at the Loran-C transmitter site, providing single DGPS to all users within the datalink range. Unfortunately, single DGPS corrections suffer from spatial- and temporal decorrelation, degrading the differential peiformance with increasing distance from the reference station.

It can be shown that for most of the Eurofix service area, data transmissions from more than one Loran-C station can be received. By applying the information from the differential corrections received from all stations instead of one, overall navigation peiformance can be im­proved; networked DGPS.

This paper focuses on a specific implementation of re­gional area networked DGPS (NDGPS) called Eurofix RAAS. Spatial decorrelation and augmentation systems as a means to counter this, will be outlined. As a test case the peiformance of Eurofix with RAAS is simulated with a post-processing test set-up using real-life GPS data. Single DGPS and NDGPS peiformance results are presented. It will be shown that using Eurofix RAAS, navigation peiformance and integrity can be increased.

Index terms Eurofix, DGPS, Loran-C, spatial decorrelation, Aug­mentation System, RAAS, W AAS, extended/networked differential GPS, RINEX

I. INTRODUCTION The EurofIx integrated navigation system consists of differentially corrected GNSS and Loran-CiChayka. As Chayka is very similar to Loran-C and GNSS to GPS, this paper will focus on Loran-C and GPS. In EurofIx, Loran-C signals are additionally modulated with differential corrections for GPS without any signifIcant degradation in Loran-C navigation performance

The coverage of the Loran-C system currently includes

Professor: drjr. D. van Willigen Mentors: ir. G.W.A. Offerrnans, ir. A.W.S. Helwig Period: July 1996 - march 1997 Assignment number: A 757 Date: 19 March, 1997

the full CONUS, North-West Europe, the Mediterranean and large parts of Russia, Japan and China. This means that the area that can be supplied with DGPS data is quite large. In EurofIx, each Loran-C transmitter acts as a single, local DGPS reference station, transmitting differential corrections to users within datalink range. The range of the EurofIx datalink has been shown to be at least 1,000 km[l]. By providing single DGPS cor­rections over such large areas EurofIx serves as a Wide-Area Augmentation System for GPS.

While the single differential technique can greatly re­duce biases in GPS observations, it is based on the ba­sic premise that the primary error sources of the system are spatially correlated with those measured at the ref­erence station. While this is true for short distances from the reference station, the error sources decorrelate as distance increases. A remote user will not be able to suffIciently reduce the primary error sources in his GPS measurements by using the differential correc­tions computed at the reference station, reducing DGPS navigation accuracy.

Fig.! Approximate Eurofix datalink coverage (range ,.. 1000 km) Numbers indicate number of stations within range.

The error due to spatial decorrelation has been esti­mated at about 0.4 meters per 100 km separation from the reference station[8]. With a typical user always being within distances of 600 to 800 km from a DGPS

1

\

station this would lead to a spatial error of about 3 meters. This is under the assumption that there is no intentional ephemeris error due to SA. If intentional ephemeris errors are introduced, single DGPS has no means of compensating for this.

With a datalink range of about 1000 km, Fig.l shows that, over most of North-West Europe, it is possible to receive more then one Loran-C/Chayka station. In fact over most of the European land area's and the North Sea, it is possible to receive three or more stations. Enabling more reliable DGNSS reception.

To improve integrity and accuracy even further, the Eurofix stations could be incorporated in a network. A network of a few reference stations can already provide a broad area with accurate differential corrections that should almost be comparable to local differential GPS [4, 10]. Networked DGPS also has the potential to be more robust, since it is able to detect and recover from equipment failure in one of the reference stations.

A concept of networked extended differential GPS, known as RAAS (Regional Area Augmentation Sys­tem) is best suited for Eurofix. In the usual RAAS con­figuration, a communication network is needed to con­nect all stations for exchange of locally determined pseudorange corrections. With Eurofix, this network is not necessary. All stations broadcast directly to the Eurofix user. This provides the user with the option of autonomously deciding how he wants to use the re­ceived differential GPS corrections (PRC's).

Theoretical research by Jin [2] has shown that regular RAAS-networks spanning a typical Eurofix region leave only very small remaining errors. The perform­ance of the RAAS-network depends on the number of reference stations used in the network solution. With at least three stations, decorrelation in both latitude and longitude direction can be compensated. With two sta­tions the spatial error remains only minimal on the baseline, with normal LAAS degradation in the direc­tion perpendicular to this baseline.

This paper details the mathematical processing that is required to implement RAAS networking in Eurofix and it describes the research work that was done to simulate the behavior of a Eurofix RAAS using real­life data from the International Geodetic System of GPS reference stations.

II. DGPS ACCURACY LIMITS

When assuming that accurate differential corrections at a reference station can be calculated, there are two general factors that limit the achievable DGPS position accu­racy; temporal and spatial decorrelation of the DGPS correction data.

A. Temporal Decorrelatioll Temporal decorrelation is mainly caused by the data latency of the communication link. This latency should

be less then the time span over which pseudoranges change either due to unpredictable selective availability (SA) or because of variation in the ionospheric and tro­pospheric delays. Offermans and Helwig [1] have shown the temporal decorrelation error in Eurofix to be 1.57 m.

B. Spatial decorrelation The main spatial decorrelation errors are ephemeris er­rors and variations in the ionospheric and tropospheric delays. Jin [2] investigated the non-linearity of these spatial decorrelation errors over distances up to about 1,000 km. For three reference stations, well-spread over the area, and applying linear interpolation and smoothing techniques, Jin found for areas of 500 by 500 and 1,000 by 1,000 square kilometers the remaining errors as listed in Table 1:

Network Remaining errors m) Size Eph. Ion. Tro.

500x500 km2 0.07 0.17 0.23/0.1' 1 OOOx 1 OOOkm 2 0.14 0.23 1.82/0.1' · results usmg a troposphcnc mod.l

Table 1 Remaining effect of ephemeris errors, ionospheric delays and tropospheric delays after application of differential correrctions generated at three reference stations.

The following assumptions have been made • satellite ephemeris error = 10m • ionospheric delay = 4.5 m (vertical, at reference) • elevation = 15° (at reference)" • ~-elevation = 2°1100 km (at reference) • tropospheric delay = 4.5 m (vertica~ at reference) • ~-height = 80 m (between reference and user)

• note: in the later to be explained RAAS simulations, this ele­vation mask has often been used to recreate the conditions as used in this theoretical work.

EPHEMERIS ERROR

The satellites' orbits (ephemeris) are measured by the US Department of Defense and then broaPRCast by the GPS satellites. Under Selective Availability, the orbit parameters are purposefully misreported to cause a con­trolled navigation error for the user. With incorrect orbit parameters, both the reference, and the user will com­pute an incorrect satellite position. Although user and reference will have identical errors in computed satellite position, they will have slightly different errors in their respective computed ranges because of differences in viewing angles (see Fig.2)

As the separation between the reference and user be­comes larger, so does the difference in viewing angle and the difference between the computed range error~. The navigation error caused by satellite position. error ~ highly correlated between viewers and very linear .m nature, i.e. the error is roughly proportional to the dis­tance from the reference station.

2

Differential Orbit Error

(EI' - €u)

Reference

Broadcast lk-o!i--~- Position

Fig.2 Ephemeris errors depend on the viewing angle

IONOSPHERIC ERROR

User

As the GPS signal travels through the ionosphere, it ex­periences a delay. This delay can either be measured with a receiver that is capable of dual frequency code measurement, or it can be modeled. Unlike range error due to orbit parameter error, which behaves very linearly over large distances, ionosphere error is subject to occa­sionally quite non-linear behavior. Long-distance spatial decorrelation studies by Kobluchar indicate correlation distances in thousands of kilometers. Typical decorrela­tion ranges are 200 Ian (disturbed conditions) to 1000 Ian (normal conditions) [4).

TROPOSPHERIC ERROR

The tropospheric delay of the GPS measurement is an unwanted delay in the code and carrier data introduced by the troposphere, which extends from sea level to ap­proximately 50 Ian altitude.

The total delay can be divided into a dry and wet com­ponent. The dry component, which accounts for about 90% of the total delay, can be reasonably well modeled without any meteorological data. The wet component

I ~ .~ '''''<='0;' " ,,~ "'''' 1 ~;~l;S1Code) . ''';

I, 1l~' '} , I;Er.rOI; source . - _Wlca Range\Error , . . . ~jlng~~;, ~10(l khl Rei-I~'" .. ,

1 1! , ,~Err.p~~{ I station .

"- ,- ., '< ~ . '~

SV Clock 1 m -

SV Ephemeris 1 m -

Selective A vailabil- 10 m -

itv Troposphere 1 m -Ionosphere 10 m -

Pseudo-range noise 1 m 1 m

Receiver noise 1 m 1 m

Multipath 0.5 m 0.5 m

RMSError 15 m 1.6 m

Error * (PDOP = 4) 60 m 6 m

Table 2 TYPIcal values for some GPS errors[3]

on the other hand, requires measurements of the local

weather conditions along the line-of-sight for maxi­mum accuracy. All tropospheric models are good above 15 degree mask angles

For navigation networks, with hundreds of kilometers between reference stations, tropospheric error is more or less uncorrelated, and hence considered to be reference station unique. No exact function describing the varia­tion over the coverage area can be constructed.

Typical values for the GPS errors that involve DGPS are listed in Table 2.

III. AUGMENTATION SYSTEMS

Augmentation systems consisting of networks of refer­ence stations are based on the fact that an absolute pseu­dorange correction (PRC) can be defmed for each satel­lite as a function of user location. A map of this function can be constructed, with the "iso-PRC" contours much like isobars on a weather map

As outlined by Loomis[4], the object of the network is to measure the PRCs at a few points, the reference stations, and construct an "iso-PRC" map (fig.3) for each satellite. Because the ionosphere and the line-of-sight to the GPS satellites continuously change over time, this map would have to updated frequently; a heap of maps. In order to be able to take into account as many variations as possi­ble in the PRC function, the reference nodes should cover as large an area as possible, with their spacing being dictated by the range over which the PRC function varies by large amounts and unpredictably.

LAASDGPS

The reference stations, which may be co-located with the Loran-C transmitters in the Eurofix system, provide correction data from a single reference point to users within the Eurofix datalink range. The navigation per­formance a user gets from applying this data depends on the temporal and spatial decorrelation between monitor and user. At best, without any spatial decore­lation, the maximum accuracy is dictated by the Lo­ran-C datatransmission speed[8]). Generally a usuable range of about 100-200 Ian is assumed for LAAS sys­tems. Assuming it would at all be possible to imple­ment such a system, even at sea, one would, by gross estimate, still need more then 60 reference stations to cover the total Eurofix service area.

Several reference stations would have to be linked to each of the Loran-C transmitters. and corrections from all of the linked stations would then have to be trans­mitted via the (on average) 30 bps datalink capability of the Loran-C signal, giving rise to serious delays and temporal decorrelation.

3

Clearly, these problems are not easily solved and a system like this with its infrastructural requirements would be very costly to implement as well. At the same time, users would be dependent on the corrections pro­vided by only one reference station at a time.

It is logical to assume that both efficiency and integrity will be improved if one could use corrections from not one, but multiple DGPS sources; by creating a network of reference stations. When using networked DGPS, there are two basic strategies to improve the differential corrections at a user site : 1. Estimate the components that make up the total GPS

error and model their variation over the service area (WAAS).

2. Model the variation of the total GPS error over the service area using several (Extended (range) DGPS) reference stations.

WAAS

Wide-Area Augmentation System (W AAS) uses 20-30 reference stations at large distances apart[5]. These ref­erence stations transmit their corrections to one or more master station(s) which are then able to estimate correc­tions for the various GPS error components and their variation over the total service area.

Due to its long baselines W AAS is able to extract ephemeris errors using triangulation. Ionospheric de­lays are measured by dual frequency receivers and tro­pospheric delay is modeled using temperature meas­urements and measurements of the humidity and barometric pressure[6]. Both ionospheric and tro­pospheric corrections are estimated using complex models[7].

Because individual error components are modeled over the total service area, navigation performance no longer depends on user position. Rather an average navigation performance over the total service area is realized. By combining the information from all the reference sta­tions, continental-wide DGPS integrity is offered.

Because of the need for information processing at a master station, a large, reliable and costly infrastructure is required. Also high-speed datalinks are required to transmit corrections for all satellites in view in the total service area, such as e.g. satellite links, making this ap­proach especially unattractive for Eurofix with its exist­ing Loran-C infrastructure.

Fig.3 "ISO-PRC"s for each satellite

RAAS

The other, and simpler network strategy, that does take advantage of the existing transmitter network, is the combination of measurements from several reference stations surrounding the user (Regional) and the user applying a w«ighted (least-squares) average of the dif­ferential corrections from each of the reference stations (Common View Network[4]. No attempt is made to es­timate the individual GPS error components. PRC's are merely weighted together, providing a first-order ap­proximation of the v¥iation of the PRC's in the region surrounding the user[8, figA].

By letting the user compute his own weighted correction the need for a, costly, ground network can be eliminated, as is the case with the current single DGPS Eurofix sys­tem. Because a user can use more then one reference station and the fact that faulty corrections from one ref­erence station are smoothed by the others in the averag­ing operation, integrity is improved. When reception of one of the Loran-C signals is lost, regional area aug­mentation will serve as a backup against total DGPS loss.

A Regional Area Augmentation System like this offers

C.~O~~ct~R~.:,. ", ................ ~. ~~r~~tPRcu,.

R~~~:e: -::~j :~:~~;~~~b~~~PR:u,~l~~p~,~~~~:~,'~ ;:::~:;::;::~ DGPS Ref x DGPS User OGPS Ref y

Fig.4 The derivation of the pseudorange corrections at the user's site by linear interpolation of the corrections obtained from two Eurofix reference stations

4

.... ........

• U(A,~)········ ....•..

• ... .. ... ... .. .....

L-----------------------~A

Fig.5 Calculating the correction weights using relative geometry of the stations.

average navigation performance away from the refer­ence stations and when moving close to one of the refer­ences even local area performance. Fig.4 illustrates the calculation of a user correction from interpolation of the surrounding corrections.

Due to the short baselines it is not practical to estimate ephemeris errors in a regional area network. Further im­provements could be found in modeling the variation of the iono- and troposphere over the service area (differential ionosphere[9])

Theoretically, a hybrid version of both the regional sys­tem and local DGPS could also be implemented. Close to a transmitter (according to a set range threshold) cor­rections from a single transmitter could be used while switching to a networked regional mode farther away. A disadvantage of this Mixed Area system would be the loss of integrity protection when using the single station DGPS as in the LAAS case.

IV. EUROFIXRAAS The RAAS system for Eurofix is similar to the common view network described by Loomis. It is assumed that the differential user will navigate only with satellites visible to all the reference nodes. Obviously, the larger the region that is spanned by the network, the more diffi­cult it becomes to fmd 4 or more satellites that qualify.

Since the common view network area is relatively small, one can assume that the PRCs are basically a linear function over the area. Over a regional area , this as­sumption would certainly be accurate for orbit error and reasonable for a single-frequency ionospheric model and may perhaps extend to tropospheric models as well. This assumption may be stretched a little in the case of very low elevation satellites[4].

WEIGHTED AVERAGE

The PRC that the common-view Networked DGPS (NDGPS) user applies is a weighted average, or blend, of he PRCs from the reference nodes. The weights for the average are determined solely by the relative ge­ometry of the user and reference nodes (fig.S). If the user is close to one of the nodes, of course the data from that node is more highly weighted [4,10].

The weighting coefficients can either be determined analytically or statistically[ 4]. The three weighting coef­ficients al> ~, and a3 for a three node network can be determined analytically by solving the three equations

(1)

(2)

(3)

with ~ = user latitude and A = user longitude.

The error introduced by each monitor receiver is thus diluted by its weight, so that if, for example, the weights were all equal, then each monitor receiver er­ror would be diluted by a factor of 1/ n . But since the

errors are uncorrelated, the standard deviation of their

sum is 1/..r;;; thus, the standard deviation of the total

error due to the monitors is decreased by a factor of

..r;; from that of one monitor [10].

It is healthy practice to include more than three nodes in the network. Using least squares analysis techniques, the extra data can be used for checking the linearity assumptions and to check for reference station failure. Also, the extra stations can provide protection against equipment failure.

When implementing the above weighting method in Eurofix, it should be realized that the number of stations that can be received may vary, as will the processing required.

Assume that at nr reference stations n' satellites have been simultaneously observed and the

PRCV~(i=l, ... ,n';j=l, ... ,nr) and its rate of

change have been computed at each of these reference stations. By means of the Loran-C transmissions, all the PRCs are transmitted to the user. Jin[2] has shown that in an area occupied by the nr reference stations, although

the PRC will not be the same for all of the nr reference

stations, it can be regarded as a linear function of x and y. The above result of equations 1-3 can therefore be expressed as

where now x and y are the latitude and longitude coordi­

nates in the WGS84 system. The parameters a; and a~ are coefficients of a plane. It follows from (4) that for a DGPS network with three reference stations, we have

5

(5)

or

(6)

where Ax . = X . -XI and~" =y -y J J 'Jj j 1

This method is extremely simple to retrofit to existing DGPS installations, as all the network-specific algo­rithms are contained in the user receiver.

WEIGHTED LEAST-SQUARES

For the case of four or more reference stations, the same procedure can be followed by using least-squares tech­niques to solve the over-determined set of equations [see also Appendix 1],:

X 2 Y2

X3 Y3

with G = x4 Y4

Xr Yr

the coefficients become

(8)

Instead of using least-squares techniques, it would also be possible to use an extra parameter a3 and the extra equation, to model the effect of e.g. height variations. While this approach makes sense for small networks with a large height variations, it is a poor solution for Eurofrx:. The long baselines and the relatively small variations in height over the service area (bad VDOP) will make the Eurofrx: network correction very suscepti­ble to reference station deviations. Instead of a smooth­ing effect, it has been noticed in simulation that this can lead to large jumps in the navigation solution and sig­nificant loss of performance.

PROJECTION

In case only two reference stations can be received, net­work corrections can only be modeled over the baseline between the two reference stations. Perpendicular to this line, the spatial decorrelation error grows with the same

amount as in the conventional LAAS mode. The user differential correction can be written as:

(10)

with a; being the gradient of the differential correction

over the line connecting the two reference stations' ,

(11)

and Pj being the being the factor of the projection of the users position onto the line connecting the two reference stations[ll];

(12)

with Ax j = X j - Xl' ~Y j = Y j - Yl .

The difference in PRCs between reference stations j and 1 for a particular satellite does not include the satellite clock bias. It is, therefore, only a function of the differ­ence of ephemeris errors, tropospheric delays, iono­spheric delays and receiver clock biases between these

two stations, and so are the parameters a; and a;. Sec­

ond, the difference of receiver clock bias included in

(V~-V:) has the same effect on a;and a~,

i = 1, ... , nS , for all satellites, thus it will only result in a

bias in the estimate of the receiver clock bias of a u~er. It will not affect the estimate of user positions.

SYSTEM ASPECTS

In general not much design effort has been put into RAAS-like concepts of extending the effective range of DGPS. This is because such a system is inefficient from the standpoint of frequency allocation because multiple DGPS data streams are used, requiring several times the single DGPS communication bandwidth. Since Eurofrx: is uniquely based on the existing Loran-C infrastructure, cost aspects of implementing a data-transmission struc­ture is not an issue, making RAAS very well suited for Eurofrx:.

There are two points to be made about RAAS-type common view-systems that distinguish them from wide­area systems. First the common-view system needs no synchronization between the reference node clocks. Whatever the individual reference clock errors are, they are averaged into the pseudorange corrections to form a blended "network clock" using the same weights that are used to blend the PRCs. The NDGPS user clock error is relative to the blended clock, just as the DGPS user

6

Reference Position (EUREF/ITRF) PRC

Pseudoranges (RINEX) Generator

: Mask angle, sats to use, ODOP

~=-=-=..:....::~=f·············· ···· · ······ · ·· ············· ··· ..

Pseudoranges (RINEX)

Reference Position (EUREF/ITRF)

PRC Generator

Generator

clock is relative to the DGPS reference station clock. Second, because the area of coverage is relatively small, there is no need to try to separate the satellite clock error from the satellite radial error (or more exactly, line-of­sight error). Consequently, the satellite position is not fully determined by the common view network[4].

v. RAAS TEST SET -UP

SIMULATOR

In order to test the proposed Eurofrx RAAS system a Windows-test bed DGPS Engine has been created.

This test bed consists of three integrated parts. 1. Differential Corrections generator. Generating dif­

ferential corrections from code-based pseudorange measurements and a specified reference station po­sition.

2. RAAS network vector generator. Applies the weighted (least-squares) network algorithm as de­scribed in the previous section to calculate a PRC for a given user location.

3. GPS Navigator. Calculates user position from user pseudorange data using:

a. no corrections at all (stand-alone GPS)

Vi 2

RAAS

Network PRC Vi.

i

generator

GPS P user Navigator p

-calc

Solves position

with 4 .. 11 sats

~p

b. single DGPS corrections from one refer­ence station (standard Eurofix)

c. networked DGPS from two or more refer­ence stations

The Navigator includes options for • specifying the maximum number of satellites to use

(preferably all), • the masking angle for elevation (in order to e.g. use

only satellites higher then 15 degrees above the ho­rizon) and

• the maximum acceptable GDOP.

No code-smoothing techniques have been employed when generating the differential corrections.

Fig.6 shows the functional diagram of the test set-up.

GPSDATA

For simulating spatial decorrelation, it is essential to have access to GPS measurements taken at different locations over the Eurofix service area, all at the same time instance. To solve for this problem in the simulation raw GPS data are used from the international geodetic system (IGS). This system is made up of reference sta­tions worldwide which continuously log raw GPS data at 30 second intervals. All navigation data from the GPS

7

r

Fig.7 Selected IGS Stations with atomic clocks and fidu­cial

satellites is logged as well as one or more observables (Code-, carrier, Doppler). Data from the reference sta­tions is distributed in the Receiver Independent Ex­change (RINEX) format (see appendix II) and is avail­able via special servers on the Internet in datafiles com­prising one whole day oflogdata.

REFERENCE SITES

Since only errors due to spatial decorrelation are to be investigated, it was decided to try and minimize un­wanted errors by careful selection of the reference sites that would provide GPS data. A selection of 14 IGS fi­ducial sites (fig.7) was made using the following criteria: • known, exact and trusted position (EUREF) • stable clock (atomic standard) • datafiles adhere strictly to RINEX specification

Using the exact location of a reference station is very important for DGPS to work, for any survey errors will translate directly into user position offsets. Stable clocks are not strictly required for synchronous DGPS process­ing. Since receiver clockerrors apply to all PRC's from a reference station they will be solved in the GPS Navi­gator. Only when an asynchronous scheme is used, such as is the case when using the slow Loran-C datalink, the clock error should remain extremely stable during the time the correction data for all satellites are broadcast.

In EuroflX a system is used whereby the receiver clock­bias is estimated by averaging all satellite PRC's[8]. To

be as close to true EuroflX as possible, the same tech­nique is also implemented in the RAAS test bed as an option. In the simulator this technique serves as an analysis tool; scaling the PRC's of the different reference stations to the same order of magnitude, making com­parisons easier.

OUTPUT

To verify the calculated networked PRC's, one of the IGS stations is selected as user position with one or more other station serving as reference stations. Logs are cre­ated with the users stand-alone GPS solution, single­DGPS solutions for each reference station at the user site and if applicable the users position when applying the network vector PRe.

VI. TEST RESULTS

NOISE

~efore investigating spatial decorrelation, it is useful to get an impression of the positioning performance of the simulator, using a short baseline (little spatial decorrela­tion). Fig.8 (see also appendix V) shows the noisy nature of the GPS solution when using only the minimum re­quired set of 4 satellites to solve for position.

I g ., ~ 0 N ·c 0 .r=

40.00

20.00

.- - - - - -. - - - - - -. - - - - - - - - - - 30.00

, , '. , . , ..

, : :. :: I:'

, , . , . ' .. , .. ,- ---: ~t j -~ --J -\ --~ ! -\ -

-\- - '-\-: - :.-\ ~ - - - -I \ I .~

20.00

0.. o o (!)

10.00

0.00

2:00:00 3:00:00 4:00:00 5:00:00 6:00:00 7:00:00 Time (hours)

Fig.8 Noisy Single DGPS solution when using first 4 com­mon satellites (183 km reference station baseline) Missing data (gaps) are epochs with less then 4 common satellites. Plus-signs indicate value ofGDOP (same axis).

Because of the 30 second interval it is difficult to use code smoothing techniques to lower noise levels. Fortu­nately, as can be seen in Fig.9, using all available satel­lites in the GPS solution significantly improves perform­ance, reducing standard deviation fivefold (from 3.26 m to 0.70 m) and the average by 50% (from 2.12 m to 1.12 m.)

8

"..... 8 .00 -------------------------.s ... e Q;

~ o N .;:: o :J:

, ,

4 .00

0.00

2:00:00 4:00:00 6:00:00 Time (hours)

8.0ll

c.. o 4 .00 0 C>

0.00

Fig.9 Single DGPS solution when using all available com­mon satellites (same GPS dataset as fig.8). Line indicates GDOP values.

At the expense of availability, further improvements can be made by fIltering; setting upper limits to the usable Dilution of Precision and lowest elevation angle (Fig.IO). Recall that as mentioned before setting eleva­tion masks has also been adopted by Jin in his theoretical work on networked DGPS. So this fIltering technique should improve similarity between actual simulator re­sults and the theoretical ones.

§: 8.00 ------------,------------r---- 8.00

~ - 4.00

!L

4.008 (!) 1

~ 0.00 __ IIMi_IIIIIU ••• II.~II.IIL. 0.00

2:00:00 4:00:00 6:00:00 Time (hours)

Fig.IO Single DGPS solution when selecting only satellites that meet criteria. Filtering on elevation of more then 15 degr. and epoch GDOP < 4 (Same GPS dataset as fig.8) Line indicates GDOP values.

.SPATIAL DECORRELATION

To investigate the effect of spatial decorrelation, single DGPS solutions over varying baselines were calculated. Fig.I2 shows a typical case using long (1000 km) base­lines.

If there were to be perfect spatial correlation between the single DGPS reference station and the remote user loca­tion, all position dots would be right in the center (0,0) of the grid, namely exactly on the users true position. Due to receiver unique errors as e.g. multipath and re­ceiver noise a certain spread is inevitable, but as these errors are uncorrelated they should not cause an average offset.

There are two effects that are assumed to be a possible cause the observed offset: 1. Spatial Decorrelation 2. Survey errors in the location of the reference site.

(i.e. an erroneous reference position is used in cal­culating differential corrections)

Since differential GPS positioning relates the users posi­tion to the reference station (which is assumed to have a precise knowledge of its position), survey errors will directly translate into navigation errors (offsets) at a user. To prevent this from happening very precise geodetic coordinates (EUREF ) have been used in the RAAS

10.00

5.00

0.00

-5.00

-10.00

-5.00- 0.00 5.00 10 .00 longitude error (m)

Fig.12 Single DGPS errors with Graz as user station and Kosg, Madr, Mate as references (Filtering applied)

simulator. The surveying error in the positions for all stations used in this paper should thus be less then a few centimeters.

This leads to the conclusion that the observed offsets in Fig.I2 can only be caused by spatial decorrelation.

To evaluate the proposed RAAS network DGPS it is not absolutely necessary to know the exact size of the error caused by spatial decorrelation. It is just possible to compare the performance of the various networked po­sition solutions to the single DGPS solutions.

10.00 ~------~- - -----------~-----. I

..-E 5.00 -- I I I I

~------~------~------~-----. I I I

L.

~ L. Cl) 0.00 Cl)

'"0 :::s -~ -5.00 ~

I I I

I I. I I I.. I I

i-----~-- - i- - ----i-----I I I I I I'!. I I

: \'" ,:~ Nefworked D~PS I I.. I using 3 reference stations ~- - ----~ - -----~------~----- . I I I I

I

-10.00

-5.00 0 .00 5 .00 10.00 longitude error (m)

Fig. I I Networked DGPS error using same stations as in the case study of fig. I I

RAAS NETWORK DGPS

Using the three single DGPS reference stations from the previous case, a networked DGPS is generated, the results of which are plotted in Fig. I 1 , as well as listed in Table 3.

9

Positioning NDGPS Kosg Madr Mate Average 0.930m 2.332m 4.763m 1.33 m Std.dev. 0.668m 1.007 m 2.513 m 0.632 m

95% 2.320m 4.329m 9.574m 2.381 m . . Table 3 PosltIonmg results Smgle DGPS and 3 reference Network DGPS

It can be seen that the network performance is better then any of the individual singe DGPS reference sta­tions. Although, there is not much difference between the single DGPS performance of Mate, a user would not have known which station to use best. It is only in these simulations that a 'best' reference station shows up. The network has the added bonus that it always gives good performance without any need for reference station se­lection.

A similar result is obtained using another set of reference stations. This time four reference stations are used to obtain a RAAS networked DGPS result with baselines up to 1000 km. (Table 4)

Position NDGPS Hers Brus Onsa Wett

Average 1.269m 2.327m 1.187 m 2.534m 2.362 m

Std.Dev. 1.174m 2.131 m 0.920m 2.442m 2.677m 95% 3.l06m 5.542m 2.834m 7.557m 5.675 m

.. Table 4 Poslttonmg results Smgle DGPS and 4 reference Network DGPS at user-node Kosg

In this case, the nearby station Bros has just a bit better performance compared to the network solution. The reason being the rather bad performance of the Hers station which is also relatively close by. This is the result to be expected with applying an averaging op­eration to obtain the network corrections. Still the smoothing effect of the network on the 'bad' data is such, that if a user had selected any of the other refer­ence stations, performance would have been worse than the current network DGPS solution.

Results for different user stations but using the same

10.00 - - - - - - - - - 1 - - - - - - - - - -,

g ". ...

e lii

0.00 Q) --------;

'0 .a Legend 'Cl • c Brus .Q

+ Graz '. ,

, • Onsa

-10.00

-10.00 0.00 10.00 latitude error (m)

Fig.13 Position error for NDGPS users at different locations . .

nsa

0.558 m 0.668 m 1.422 m 95% 1.898 m 1.797 m 4.758 m Table 5 NDGPS Positioning error for users at different locations using the same 3 network reference nodes

network of reference stations as in the fIrst network example (Fig.l3, Table 5), show that for stations within the edge formed by the reference stations, the average offset in user position is within meter-level and 95% values are within 2 meters .

The station with the large(st) errors is ansa, 700 km away from the nearest network reference node and outside the edge of the area circled by the reference nodes. The maximum distance between ansa and a reference station is 2215 km., a distance unobtainable using the Loran-C datalink, resulting in often very poor numbers of observable satellites. Still its 95% error is within 5 meters.

........ E -­L.

5.00

g 0.00 CD CD 'C .a ~

..!! -5.00

-----,--------------T-------------, • < , I ~ ~ I

t1

, -----.-------------~ , ,

". +: ~ I •

, , I ._. I I

............ -:- _t.; .... - .......... - -1- -- ........... -- ....... -; : • +c • • I I

5.00

0.00 10.00 longitude error (m)

Fig.14 The effect of a 2 reference network solution being only capable of compensating in one gradient direction

Finally, Fig.14 shows three network soultions for a user at Graz, Austria using a network of two reference stations to calculate a correction. Each of the pairs forming a network has been marked on the fIgure. On the IGS-station map it can be seen that the baselines of Madr-Mate and Kosg-Madr are almost perpendicular to each other. Since a network with two stations can only compensate using a gradient along its baseline, this results in the fIrst network to compensate using a northing gradient and the latter to compensate using an eastbound gradient. Since neither of the two has its baseline close to the userposition, this should in both cases result in a residual error (offset). As can be seen this is the case. The third netowrk consisting of reference stations Kosg and Mate has a baseline that both comes relatively close to the userposition and which has a baseline which is diagonal to both others giving it a gradient that compensates for both the variation in latitude and longitude. One should therefore expect on the basis of the RAAS network theory, that the Kosg-Mate network should best be able to compensate in this case with a network solution which is between the offsets of the two others. This is exactly what happens in practive as the fIg.shows.

10

VII. CONCLUSIONS AND FUTURE WORK

CONCLUSIONS

This paper has shown that it is feasible to implement a wide-area augmentation system for Eurofix and that a regional area common-view system is best suited for Eurofix. Algorithms for using regional augmentation of Eurofix using two, three or more reference stations have been proposed. A method and implementation of simulating the RAAS system using real-life GPS data was shown and the first simulator test results were pre­sented. Based on the noisy nature of the supplied data, input limits had to be imposed to lower the noise level of the simulation results, trading availability for qual­ity.

The following observations can be made about the proposed RAAS system for Eurofix.

Eurofix RAAS: • indicates in simulations that, within typical

Eurofix navigation ranges ofless than 1000 km, meter-level accuracy is obtainable

• does not degrade the performance of Eurofix compared to the 'standard' LAAS system

• adds integrity monitoring capability • smoothes irregular PRC's • makes use of the existing Loran-C infrastructure • needs no additional hardware or communication

networks to be installed • is easy to upgrade (user software only)

Extensive checks and the simulation results indicate proper operation of all software, which means a system is now in place to validate the RAAS system with ex­tensive simulation over long periods of time.

FURTHER WORK

Apart from further validating the existing RAAS pro­posal, it should be possible to improve upon the current 'simple' linearity assumption for the variation of the gradients.

Currently no attempt has been made to extract the two error components that most likely vary non-linearly over the coverage area; namely ionospheric- and tro­pospheric delay. Using models for these errors, theory suggests[2] that even better differential corrections could be obtained at a user position.

To make enhance visibility of the improvements that are to be implemented, it is very desirable to obtain better GPS data to serve as input for the Eurofix RAAS simulator with : 1. a much smaller sampling interval (a few seconds

or less), smoothing techniques could then be used to lower the current noise level in the current code-based positioning algorithm.

2. a much higher density in reference stations loca­tions. Having more reference stations will enable a

more detailed picture of the behavior of the PRC­error over the coverage area and the creation of "virtual Eurofix ", a network with identical ge­ometry to the Loran-C chains, in post-processing.

Also the current assumption is one of a fixed reception area for the Eurofix stations. Since it is unlikely that in practice one could receive a station all the time in this coverage area, further studies could investigate the avail­ability of the signals and techniques to temporally cor­relate the spatial PRC gradients to counter the effects of sudden loss of reception of data from a reference station.

ACKNOWLEDGEMENTS The author would like to thank dr. J. van der Marel and dr. x.x. Jin of the Geodetic Engineering Dept. at Delft University for their help with the precise reference sta­tion positions and RINEX processing. Also prof. F. van Graas of the Avionics Engineering Center at Ohio Uni­versity for his advice on W AAS DGPS networking.

REFERENCES

-[1] Offermans, G.W.A., Helwig, A.W.S., Van Willigen,D., "The EuroflX Datalink Concept: Reliable Data Transmission Using Loran-C", Proceedings of the 25th

Annual Technical Symposium of the International Loran Association, San Diego, CA, 3-7 November, 1996.

[2] Jin, XX, Theory of Carrier Adjusted DGPS Positioning Approach and Some Experimental Results. Ph.D. thesis, Delft University Press, ISBN 90-407-1379-0, 14 October, 1996.

[3] Dana, Peter H, "The Geographer's Craft Project", Department of Geography, University of Texas at Austin, U.S.A., http://www.utexas.edu/depts/grg/gcrafilnotes/gps/gps.h trnl

[4] Loomis, P., Sheynblatt, L., Mueller, T., "Differential GPS Network Design ", Proceedings of ION-GPS '95, The Institute of Navigation., Alexandria, VA, U.S.A., p.511-520

[5] R. Loh, et ai., "The u.s. Wide-Area Augmentation System (WAAS)",Navigation, The Journal of the Institute of Navigation, pp.435-465, VoI.42, No.3, Fall 1995

[6] Van de Linde, E., "Free Flight ",Technews 33-4, Ministerie van Economische Zakan, The Hague, Netherlands

[7] Kee, C. et aI., "Wide Area Differential GPS", Navigation, The Journal of the Institute of Navigation, Vo1.38, No.2, pp.l23-143, Summer 1991

[8] Van Willigen, D., Offermans, G.W.A, Helwig, A.W.S., Breeuwer, E.1., "New Views on the System Aspects of EuroflX", Proceedings of the 25th Annual Technical Symposium of the International Loran Association, San Diego, CA, 3-7 November 1996.

[9] Georgiadou, Y. "Ionospheric Delay Modellingfor GPS Relative Positioning", GPS'90 Proceedings, Ottawa, Canada, 1990

[10] Lapucha, D., M. Huff, "Multi-Site Real-Time DGPS System using StarfIX Link: Operational Results", ION GPS '92, Alburquerque, NM, pp.581-588, Sept.16-18, 1992.

[11] Simonis, 1., Lineaire Algebra ET deel 1, dictaat Faculteit der Technische Wiskunde en Informatica, Technische Universiteit Delft, pp.58-59, 1990

11

APPENDIX I - SUMMARY OF ORDINARY LEAST SQUARES

Consider fitting a line

J..t(0), P) = O)tPI + 0)2P2 + .. ·+rokPk

so that at the points {(X nt .Xn2 , ••• , Xllk ); n = 1,2, ... , N} the line is close to the corresponding values

{Y n ; n = 1,2, ... , N} in sense that we minimize the sum of squared deviations

(1)

over the values of PI"" Pk .

In matrix notation, we let y be'the vector whose elements are the YII (n = 1, ... , N) and X be a matrix whose columns

contain K explanatory variable vectors with elements x nk (n = 1, ... , N) in the eh column. The method of OLS com-A A

putes a coefficient vector P so that the fitted vector XJ3 minimizes the sum of the squared elements from the deviation A

vector Y - XJ3 . If the rank of X equals K, then the solution can be written

From: "The Geometry of the Gauss-Markov Theorem", Paul A. Ruud Econometrics Laboratory, University of California, Berkeley (http://elsa.berkeley.eduiGMTheoreml)

(2)

12

APPENDIX II - RINEX DATA

RINEX data from the following site was used . A complete specification of the RINEX format can be found on this server, under the name RINEX2.TXT.

Short Name Institution Function within IGS E-Mail FTP Access Access Restrictions Computer/Operating System Amount of data on line Access to off-line data Other Important Information:

IGS DATA CENTER

JPL Jet Propulsion Laboratory Special Data Center gpsops@pyros . jpl.nasa.gov ( internet bodhi.jpl.nasa.gov (128 . 149 . 70.66) Anonymous FTP only DEC Alpha OSF1, VMS 6 months Special arrangements, on time available

DIRECTORY STRUCTURE

Directory Filenames Description

directory specifications are for our guest computer BODHI.

pub

YYYY = year DDD = day of year

/pro/yYYYY/dDDD /raw/yYYYY/dDDD

top level rinex data indexed by day of year raw data indexed by day of year

13

APPENDIX III - IGS STATION-TO-STATION DISTANCE

European IGS Station-to-station distance (in km)

Station id bor1 brus gnu: hers kiru kosg lama madr masl mate mdvo medi mets noto nya1 ober onsa penc sfer trom viII wett wtzr I.borl 0,00 896,15 590,54 1168,27 1748,45 768,95 300,59 2090,53 3839,29 1292,87 1375,36 983,79 992,46 1719,21 2978,25 622,93 658,40 523,53 2534,74 1939,57 2071,92 457,26 457,26 2.brus 896,15 000 913,96 283,48 2106,55 183,68 1160,63 1331,70 3062,95 1477,86 2237,95 896,08 1632,42 1763,25 3149,97 585,18 884,45 1133,55 1802,79 2237,60 1318,86 637,85 637,85 3.!ITaz 590,54 913,96 0,00 1184,88 2336,25 900,23 842,92 1746,44 3451,49 719,69 1795,17 445,62 1574,25 1132,71 3553,83 336,59 1174,38 296,83 2143,87 2523,68 1724,09 302,05 302,05i 4.hers 1168,27 28348 1184,88 0,00 2202,54 406,80 1419,56 1213,35 2897,11 1699,38 2485,12 1105,50 1824,73 1942,72 3161,26 850,25 1047,10 1414,69 1683,90 2310,98 1205,25 918,14 918,14 5.kiru 1748,48 2106,58 2336,36 2202,57 0,00 1928,22 1556,13 3413,63 5077,23 3039,60 1559,66 2684,85 867,65 3467,83 1265,67 2269,02 1251,94 2237,03 3885,53 217,44 3404,17 2132,78 2132,78 6.kosg 768,95 183,68 900,23 406,80 1928,20 0,00 1012,96 1515,37 3244,83 1527,34 2079,89 970,18 1451,67 1846,91 2991,64 599,79 700,87 1080,24 1986,46 2063,56 1502,54 602,72 602,72 7.1ama 300,59 1160,63 842,92 1419,56 1556,11 1012,96 0,00 2388,80 4138,39 1501,99 1083,86 1263,83 739,46 1941,25 2811,70 921,54 673,90 685,88 2834,82 1759,60 2370,48 755,1 8 755,18 8.madr 2090,53 1331,69 1746,44 1213,34 3413,43 1515,36 2388,81 0,00 1750,85 1771,16 3462,72 1354,37 2954,94 1716,81 4346,58 1499,50 2215,64 2043,25 472,63 3524,12 25,31 1659,69 1659,69 9.masl 3839,30 3062,86 3451,53 2897,00 5076,48 3244,72 4138,42 1750,85 0,00 3280,13 5207,37 3023,61 4694,75 3039,70 5847,66 3237,42 3936,54 3743,99 1310,37 5157,82 1768,48 3401 ,00 3401,00 10.mate 1292,86 1477,86 719,69 1699,38 3039,26 1527,33 1501,98 1771,16 3280,10 0,00 2271,01 595,11 224060 444,54 4268,81 932,11 1893,66 819,58 2044,46 3232,17 1745,91 990,89 990,89 Il.mdvo 1375,36 2237,95 1795,17 2485,12 1559,65 207989 1083,86 3462,67 5207,Q9 2271,02 0,00 2240,75 886,20 2704,17 2718,99 1970,69 1547,69 1530,20 3898,54 1766,51 3443,43 1806,48 1806,48 12.medi 983,79 896,07 445,62 1105,50 2684,68 970,17 1263,83 1354,37 3023,59 595,11 2240,76 0,00 1975,35 876,90 3860,37 423,15 1459,48 724,94 1722,64 2858,42 1330,59 552,71 552,71 13 .mets 992,47 1632,42 1574,26 1824,73 867,65 1451,67 739,46 2954,95 4694,82 2240,69 886,20 1975,38 0,00 2680,70 2132,16 1592,77 784,73 1422,28 3420,73 1083,15 2940,14 1434,55 1434,55 14.noto 1719,18 1763,24 1132,70 1942,71 3467,27 1846,88 1941,20 1716,81 3039,69 444,54 2704,14 876,90 2680,52 0,00 4684,18 1281,65 2292,35 1262,28 1891,87 3656,02 1691,96 1373,57 1373,57 15.nya! 2978,49 3150,27 3554,37 3161,55 1265,67 2991,88 2811,87 4347,68 5850,87 4269,98 2719,07 3861,14 2132,20 4685,95 000 3437,93 2401,74 3484,16 4801,62 1054,27 4343,96 3320,41 3320,41 16.ober 622,93 585,18 336,59 850,25 2268,94 599,79 921,54 1499,49 3237,42 932,11 1970,69 423,15 1592,77 1281,66 3437,47 0,00 1036,82 598,48 1928,02 2439,09 1479,09 166,55 166,55 17.onsa 658,40 884,45 1174,38 1047,10 1251,94 700,87 673,90 2215,66 3936,75 1893,70 1547,69 1459,50 784,73 2292,47 2401,64 1036,83 0,00 1177,82 2687,15 1409,01 2203,13 920,45 920,45 18.penc 523,53 1133,55 296,83 1414,69 2236,94 1080,24 685,88 2043,25 3743,93 819,59 1530,20 724,94 142227 1262,29 3483,69 598,48 1177,82 0,00 2437,89 2436,32 2020,87 496,67 496,67 19.sfer 2534,74 1802,77 2143,88 1683,88 3885,18 1986,44 2834,83 472,63 1310,37 2044,46 3898,63 1722,64 3420,70 1891,87 479998 1928,02 2687,08 2437,90 0,00 3993,73 484,09 2092,28 2092,28 20.trom 1939,62 2237,66 2523,83 2311,03 217,44 2063,60 1759,63 3524,41 5158,88 3232,59 1766,52 2858,66 1083,15 3656,72 1054,27 2439,20 1409,02 2436,45 3994,23 0,00 3516,30 2308,83 2308,83 21.vill 2071,93 1318,86 1724,10 1205,24 3403,97 1502,54 2370,49 25,31 1768,48 1745,91 3443,48 1330,59 2940,13 1691,96 4342,86 1479,09 2203,10 2020,88 484,09 3516,00 0,00 1639,73 1639,73 22.wett 457,26 63785 302,05 918,14 2132,71 602,72 755,18 1659,69 3400,99 990,90 1806,48 552,71 1434,54 1373,58 3320,02 166,55 920,45 496,67 2092,27 2308,73 1639,72 0,00 0,00 23 .wtzr 457,26 637,85 302,05 918,14 2132,71 602,72 755,18 1659,69 3400,99 990,90 1806,48 552,71 1434,54 1373,58 3320,02 166,55 920,45 496,67 2092,27 2308,73 1639,72 0,00 0,00

14

APPENDIX IV - BASELINE LENGTHS IN NELS

Emission Chain Station Delay [~s] Distance [km] [essay [essay, France 0 GRI6731 Soustons, France 13000

Loophead, Ireland 27300 Sylt, Germany 42100

BII BII, Norway 0 GRI7001 Jan Mayen, Norway 14100

Berlevag, Norway 29100

Sylt Sylt, Germany 0 GRI7499 Lessay, France 14100

Vaerlandet, Norway 29500

Ejde Ejde, Faroe Islands 0 GRI9007 Jan Mayen, Norway 14200

BII, Norway 28000 Vaerlandet, Norway 41100 Loophead, Ireland 55700

Source: Northwest European Loran-C System Norwegian defence communications and Data services administration Oslo millakershus N-0015 oslo

0 601,331 698,347 920,304

0 924,233 618,956

0 920,304 752,983

0 963,344

1212,504 629,863

1094,290

Baseline Coding Delay Length [~s] [~s]

0 0 2007,47 10992,53 2331,39 24968,61 3072,46 39027,54

0 0 3085,58 11014,42 2066,32 27033,68

0 0 3072,46 11027,54 2513,81 26986,19

0 0 3216,17 10983,83 4048,08 23951,92 2102,73 38997,27 3653,38 52046,62

15

.-. E -­I-o l­I-Q)

CO +-' C o N ·c o

..c

40.00

20.00

0.00

APPENDIX V - SIMULATION RESULTS

- - - - - - .+. - - - - - - -

.,. +

.,. .f.

+ .~ .

.;. .f.

------,.-'fo---- --+ ~

~ . +

I - - - -to. - - - - - - - - - - - I - ~ - - - - - - - - - - - - - - I - - - -.;.- - - - - - - - - -

;.

+ .f.

I I .~

I +'"

, , ,. , . : .. , ,. ,+

~ - - - j·t __ T _+_ - - _,. _+ ___ ~ _ .;. ~. _____________ ~ ___ .... ___________ _

.. -1 - t +

+ , ,. , +

·t -I-

+ '+ '. f .t

30.

20.

c.. o o (9

10.

0.00

0:00:00 3:00:00 9:00:00 12:00:00

Fig.IS Noisy data using just first 4 available cornmon satellites (baseline 183 Ian) Bars show horizontal error, plus-signs show GDOP. Missing GDOP and error indicates a lack of 4 cornmon satellites. No filtering was applied in elevation and all GDOP values accepted.

Stations: Kosg-Bruss (baseline 183 kIn) This graph is the full run of Fig.8 in the paper.

Statistics' 1080 Number of measurements 2.123913 m Average 3.263303 m Standard Deviation 0.0346747 m Minimum 63.77184 m Maximum

16

...- 8.00 -------------------------------------------------- 8.00 E --­s-O s­s-ID

CO +"' c: o N ·c o I

, , ,

4.00

0.00

0:00:00

Fig.16 Single DGPS solution using all available common satellites over 183 km baseline No filtering has been applied in elevations, nor in GDOP's. Date and times are equal to Fig.15. This fig. shows the full run of Fig.9 in the paper (bars show horizontal error, line shows GDOP).

Statistics:

1177 1.124724 m 0.7020159 m 8.509901E-3 m 6.968943 m

E 8.00 -­l-e I-Q)

~ C o N ·c o I

4.00

0.00

0:00:00

Number of measurements Avera e Standard Deviation Minimum Maximum

------------------,

Fig.l? Single DGPS solutions over 183 km baseline using selected satellites by filtering.

CL o 4.00 0 C>

0.00

12:00:00

4.00

a.. o 2.00 0 (9

----10.00

12:00:00

All common satellites above 15 degr. elevation and all epochs giving a GDOP of max. 4 have been processed. Gaps indicate epochs failing to meet the above mentioned criteria or simply a lack of 4 usable satellites to solve position.

Date and times equal those of figures Fig.15, Fig.16. This fig.is the full run of Fig. 10 in the paper.

Statistics'

1068 Number of measurements 0.9702286 m Average O.570224m Standard Deviation 8.50990lE-3 m Minimum 4.941751 m Maximum

17