oceanic navigation using advanced gps by a haider

8/9/2019 Oceanic Navigation Using Advanced GPS by a Haider

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ABSTRACT

Reliable and accurate positions are required for general

marine navigation and specialized applications such as

buoy tending. The GPS signals are often masked by

obstructions, which results in degraded geometry and

accuracy at best, and unavailable or unreliable positions at

worst. Once Galileo is implemented by the EuropeanUnion, the use of a combined GPS + Galileo receiver will

result in an increase of twice the number of satellites

available above the horizon. The availability and

reliability improvements attained, by augmenting GPS

with Galileo and constraints under isotropic masking

conditions and within a constricted waterway / urban

canyon is illustrated through software simulations. These

results clearly demonstrate the advantage of augmenting

GPS with Galileo for marine navigation, especially under

moderate to extreme masking conditions.

INTRODUCTION

Since the advent of the Global Positioning System (GPS),marine users have migrated from radiobeacon direction

finding, LORAN-C and Transit as their primary electronic

navigational aids to GPS. This trend was accelerated

when differential GPS (DGPS) services became available,

which improved the positioning accuracy several orders

of magnitude from 100 m (2DRMS with Selective

Availability [SA] On) to several meters (2DRMS). With

the deactivation of SA on May 1, 2000 (Office, 2000),

even more mariners will migrate to GPS and DGPS.

However, as the mariner expects and relies more and

more on DGPS, ensuring the reliability of the position

solution becomes paramount. Many previous analysis

(Ryan et al., 1998, Ryan and Lachapelle, 1999, Ryan et

al., 1999a, and Ryan et al., 1999b.) have shown that while

DGPS positions may be available under moderate to

extreme masking conditions, they are often unreliable (the

position may be corrupted by an undetected blunder in the

observations). In order to make the resulting position bothavailable and reliable, DGPS must be augmented with a

combination of constraints and other satellite navigation

systems.

The previous analysis mentioned above used the Russian

Global Navigation Satellite System (GLONASS) as the

primary additional satellite constellation. While

augmenting DGPS with differential GLONASS did

improve the availability and reliability of the navigation

solution, the reduced number of healthy GLONASS

satellites (24 in 1996 to eight in 2000) reduced the

effectiveness of the augmentation.

In this paper instead of dealing with the currently

available augmentations for DGPS, the European Union’s

future satellite based navigation system (Galileo) will be

examined. While Galileo is still in the planning stage and

many technical details must still be ironed out, the system

will:

1) provide world wide coverage

2) employ multiple L-band frequencies

3) provide an open access service (OAS), as well as

controlled access services (CAS)

4) transmit real time integrity data for the CAS

The European Union will decide in December 2000whether to implement Galileo, assuming that the decision

is “yes”, Galileo will be operational by 2008. Thus by

2008 the world will have two operational global

navigation satellite systems (GNSS), the modernized GPS

system and Galileo. What will be the availability and

reliability improvements attained by augmenting the

modernized GPS system with Galileo? The answer to this

question is the focus of this paper. Since Galileo is still in

the planning stages, the availability and reliability

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Oceanic Navigation using advanced GPS

A Haider . Scientist State University of New York

A Haider [email protected]



improvements will be estimated through software

simulations. Before the results are presented, the Galileo

constellations used for the analysis are described,

followed by a brief discussion of reliability theory. Since

Galileo will be a world wide system, the simulations are

conducted for users all over the globe, under benign and

extreme masking conditions.

GALILEO CONSTELLATIONS

The Galileo system will consist of a constellation of eithermedium earth orbiting (MEO) satellites or a combination

of MEOs and geostationary (GEO) satellites. Both of

these constellations are considered baseline

configurations for Galileo (Lucas and Ludwig, 1999, and

Wolfrum et al., 1999). Within each baseline configuration

there are various altitude, orbital plane, and satellite

spacing possibilities. The following four potential Galileo

constellations were discussed in Lucas and Ludwig

(1999) and Wolfrum et al. (1999):

1) 24 MEOs in three orbital planes, with an altitude

of 24,000 km, inclination of 55º, augmented with

three GEOs2) Same as (1), but at an altitude of 19,500 km

3) Same as (1), but at an altitude of 24,126 km,

with nine GEOs for world wide coverage using a

Walker 24/3/2 constellation.

4) 30 MEOs in three planes, with an altitude of

24,000 km

Taking these different constellation configurations into

account, the two constellations given in Table 1 were

chosen for the simulations.

Table 1 Galileo Satellite Constellations

# MEOs Altitude i Walker GEOs

1 24 24,126 km 55º 24/3/2 9

2 30 24,126 km 55º 30/3/2 0

Figure 1 shows the locations of the MEO satellites within

their orbital planes for the two Galileo constellations. For

more information on the Walker constellation definitions

see Walker (1978) and Spilker (1994).

Galileo #1 contains nine geostationary satellites equally

spaced around the globe at the following longitudes

-160° E, -120° E, -80° E, -40° E, 0° E, 40° E, 80° E,

120° E, 160° E. Geostationary satellites provide excellent

visibility at low latitudes, however, as the user’s latitude

increases, the elevation angle steadily decreases. Figure 2

shows the elevation angles for a geostationary satellite at

0° longitude using color contours drawn in 5° increments.

At mid to high latitudes the geostationary satellite can be

easily blocked by obstructions.

- 1 8 0 - 9 0 0 9 0 1 8 0

- 1 8 0

- 1 5 0

- 1 2 0

- 9 0

- 6 0

- 3 0

0

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

Longitude of the Assending Node

A u g u m e n t o f

L a t i t u d e

24 MEO + 9 GEO

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

- 1 8 0 - 9 0 0 9 0 1 8 0

- 1 8 0

- 1 5 0

- 1 2 0

- 9 0

- 6 0

- 3 0

0

3 0

6 0

9 0

1 2 0

1 5 0

1 8 0

30 MEO

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 1 Galileo Constellations

Elevation Angle0 10 20 30 40 50 60 70 80 90

Longitude

L a t i t u d e

180oW 120

oW 60

oW 0

o60

oE 120

oE 180

oW

90oS

60oS

30oS

0o

30oN

60oN

90oN

Figure 2 Geostationary Satellite Elevation Angle

Figure 3 plots the number of visible geostationary

satellites using Galileo #1, assuming an isotropic mask

angle of 30°. The locations for the nine geostationarysatellites are displayed as red squares on the equator. At

least two satellites are visible within ±45° latitude.However, at higher latitudes the number of visible

satellites quickly drops to one and then zero. This figure

illustrates the main drawback of geostationary satellite

augmentations, the poor visibility at high latitudes. Thus

Galileo #2 which does not contain any geostationary

satellites should outperform Galileo #1 at high latitudes

under moderate to extreme masking conditions.

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Number of Visible GEOs0 1 2 3 4 5

Longitude

L a t i t u d e

180oW 120

oW 60

oW 0

o60

oE 120

oE 180

oW

90oS

60oS

30oS

0o

30oN

60oN

90oN

Figure 3 Number of Visible Geostationary Satellites

with a 30°°°° Isotropic Mask Angle

RELIABILITY THEORYReliability refers to the ability to detect blunders in the

measurements and to estimate the effects of undetected

blunders on the navigation solution. Reliability can be

sub-divided into internal and external reliability. Internal

reliability quantifies the smallest blunder that can be

detected in each observation through statistical testing of

the least squares residuals. Once the internal reliability

has been determined, external reliability quantifies the

impact that an undetected blunder can have on the

navigation solution.

In order to detect a blunder using an epoch by epoch least

squares approach, a statistical test must be performed onthe residuals. Hence, redundancy must exist in order to

detect the blunder. An unknown blunder vector, ∇, will

bias the least squares residuals r̂ according to:

∇∗−=∇∗∗−= − RCCr̂ 1lr̂ (1)

where r̂C is the covariance matrix of the residuals

lC is the covariance matrix of the observations

1lr̂CCR −= and is the redundancy matrix

Assuming that one blunder can occur at a time, the

blunder vector ∇ contains only one non-zero element.Using local residual checking, each standardized residual

is tested according to:

21

iir̂

i nC

r̂α

−≥ (2)

The underlying assumption is that the residuals are

normally distributed, and that a blunder, while biasing the

residual, does not change its variance. Two types of errors

can be made whenever a statistical test is performed.

1) A Type I error occurs whenever a good

observation is rejected. The probability

associated with a Type I error is denoted α.

2) A Type II error occurs whenever a bad

observation is accepted. The probability

associated with a Type II error is denoted β.

By selecting values for α and β the bias in thestandardized residual called the non centrality parameter

δo can be calculated, [Leick, 1995]. Once the reliabilityparameters have been specified, the smallest blunder that

can be detected through statistical testing of residual “i” is

computed by substituting equation (1) into (2) and letting

0

21

n δ=α−

:

ii

iiii

r̂

lo

ii

r̂o

iC

C

R

C ∗δ=

∗δ=∇ (3)

This is called the Marginally Detectable Blunder (MDB).

Each observation has a different MDB since each

residual’s covariance matrix ( iir̂C ) is different. Once all

of the MDBs have been calculated, the impact of each

MDB on the parameters is assessed separately using:

o1

lT1 CANˆ ∇∗∗∗−=δ −− (4)

where A is the design matrix

ACAN 1-l

T ∗∗= is the normal matrix

∇o is a column vector containing all zero’s

except for the MDB in the ith

position.

The horizontal position error (HPE) corresponding to

each MDB is calculated using δ̂ from equation (4). The

largest HPE from all of the MDBs represents the external

reliability for that epoch.

For a more detailed treatment of reliability theory see

Vaníček and Krakiwsky (1986), Leick (1995), and Koch

(1999).

SOFTWARE SIMULATION

The reliability and precision improvements obtained by

augmenting DGPS with the two Galileo constellations as

well as with a height and a clock constraint were

evaluated under isotropic masking conditions and in a

constricted waterway / urban canyon.

The simulations were conducted over 24 hours in 60

second increments, using the GPS almanac from June 6,

2000. The following reliability parameters were used: α =

0.1%, β = 10%, and δo = 4.57, the reliability algorithm

assumed that the residual testing was performed epoch by

epoch using no apriori knowledge of the trajectory. DGPS

(28 satellites available) was augmented with the two

Galileo constellations, a height constraint and a clock

constraint. Taking all of these combinations into account,

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the following three different satellite constellation

combinations were simulated:

1) DGPS

2) DGPS + Galileo #1 (MEO + GEO)

3) DGPS + Galileo #2 (MEO)

For each satellite constellation combination, the following

four types of constraints were employed:

1)

No Constraints – “N”2) Height Constraint – “H”

3) Clock Constraint – “C”

4) Both Height and Clock Constraints – “B”

Each of these 12 positioning methods were simulated over

24 hours at each of the computation points shown in

Figure 4. 118 computation points were used to represent

the world.

12 0o

E 1 8 0o

W

6 0

o

N

1 80o

W 1 2 0o

W 6 0o

W 0o

6 0o

E

3 0o

N

9 0o

N

0o

9 0o

S

6 0o

S

3 0o

S

Long i t ude

L a t i t u d e

Figure 4 Computation Points

A measurement variance of 1 m2 was assumed for allsatellite observations (GPS and Galileo). This can be

achieved in two ways:

1) differential GPS and differential Galileo

2) single point positioning using dual frequency

civilian signals with accurate broadcast orbits

and clocks, which may be possible with the

modernized GPS system and Galileo

Variances of 4 m2

and 1 m2

were used for the height and

clock constraints respectively. The height constraint

variance allows for tidal variations, swells, and waves.

The clock constraint assumes that a good quality ovenizedquartz oscillator is being used.

The isotropic mask angle simulations were performed for

the following five mask angles 0º, 10º, 20º, 30º, and 40º.

The constricted waterway / urban canyon simulations

were performed using the channel shown in Figure 5

oriented in a North / South direction. This channel was

then rotated 180o

in 30o

increments to simulate various

channel orientations. A total of six different constricted

waterways / urban canyons were simulated and analyzed.

The shape of the constricted waterway defines the shape

of the resulting masking profile, however, the scale of the

masking profile must still be specified. Figure 6 shows the

masking profile for the North / South orientation.

N

E

C h a n n e l R o ta t e d

1 8 0 o i n 3 0 o S te p s

Figure 5 Constricted Channels / Waterways

0 4 5 90 1 3 5 1 8 0 2 2 5 2 7 0 3 1 5 3 6 00

10

2030

40

50

60

70

80

90

M ax 56 .3

M a

s k A n g l e ( D e g )

A z i m u t h ( D e g )

Figure 6 Mask Angle Profile

The maximum mask angle was set to 56.3º. While this is a

very realistic simulation for down town urban canyons,

general marine navigation in most constricted waterways

will experience much lower masking angles. However,

hydrographic surveys conducted near cliff walls willsometimes encounter these extreme masking conditions.

Thus these simulations are applicable to both marine and

land applications.

Isotropic Mask Angles Simulations

If all of the isotropic mask angle simulation data were to

be presented, a six dimensional figure would be required

(computation point latitude, computation point longitude,

positioning method, isotropic mask angle, time, and

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HDOP / HPE). Instead of presenting any time series, the

95th

percentile HDOP / HPE were calculated for:

1) each computation point

2) all 118 computation points batched together to

generate world values

In addition to calculating the 95th

percentile values, the

percentage of time that the HDOP ≤ 2 and the

HPE ≤ 10 m were also calculated for the two cases listed

above. These limits were chosen since for many marine

navigation applications the position is only considered

available if the HDOP ≤ 2, and the required positional

accuracy is usually 10 m. The percentage of available /

reliable positions quoted in the following sections are in

the context of these values.

Availability Results

A summary of the isotropic mask angle availability results

for the world are given in Figure 7 and Figure 8. The

results are presented in graphical form with the 12

positioning methods on the x-axis grouped according to

the satellite constellations employed. Within each groupare the four constraints. Figure 7 plots the overall world

95% HDOP, while Figure 8 plots the overall world

percentage of HDOPs ≤ 2.

N H C B N H C B N H C B0

1

2

3

4

56

7

8

9

1 0

H D O P

D G PS + M E O+ G E O M E O

01 02 03 04 0

Figure 7 95% HDOP, for the World, Isotropic Mask

These results show that unaugmented DGPS provides

available navigation for the benign masking conditions of

0º and 10º with 95% HDOPs of 1.0 and 1.4 respectively.

Even for the 20º mask case, the 95% HDOP is 2.8 with an

availability of 87% (percentage of HDOP ≤ 2).

Augmenting DGPS with either a height or clock

constraint improves the 95% HDOP to 2.0 and 1.9

respectively. Thus for the 20º mask case no additional

satellite navigation system is required to meet the

availability requirements. This is not the case however for

the two higher mask angles.

For the 30º mask case, DGPS + both constraints has a

95% HDOP of 4.8 with a corresponding availability of

71%. DGPS and constraints do not provide available

navigation, Galileo is required. Once DGPS is augmented

with either Galileo constellation the 95% HDOP

decreases to ≤ 1.8 and the availability increases to ≥ 97%.Adding both constraints increases the availability to

≥ 99%. At the highest isotropic mask case of 40º, the 95%

HDOP is > 10 with an availability is < 21% for DGPS +

both constraints. Augmenting with Galileo and both

constraints reduces the 95% HDOP to < 3.5 and increases

the availability to 80%. Thus Galileo greatly improves the

availability under the worst case masking conditions.


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 00

P e r c e n t a g e o f H D O P s < 2

D G P S + M E O+ GE O M E O

01 0

2 03 04 0

Figure 8 Percentage of HDOPs ≤≤≤≤ 2, for the World

Isotropic Mask

When the results for both Galileo constellations are

compared, there is very little difference in the overall

world performance. Galileo #2 (MEO only) produces

slightly better availability performance over Galileo #1

(MEO + GEO), however, both greatly improved the

navigation availability under the extreme maskingconditions.

The summary results provide a world view of the

availability performance, but mask any regional

differences. The regional differences first become

apparent for the 30º mask case using DGPS + height.

Figure 9 is a contour graph of the 95% HDOP using the

individual computation point values. The overall 95%

HDOP is 5.7 with a 65% availability. However, there are

large variations in the 95% HDOP with locations ranging

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from a low of 1.6 to a high of > 10. Unavailability bands

are found in the 30º-75º latitudes. Although on the world

scale DGPS + height for the 30º mask case does not

provide available navigation, some locations still have

acceptable availabilities.

95% HDOP0 2 4 6 8 10

120oE 180

oW

60oN

180oW 120

oW 60

oW 0

o60

oE

30oN

90oN

0o

90oS

60oS

30oS

Longitude

L a t i t u d e

Figure 9 HDOP 95%, DGPS + Height

30°°°° Mask Angle

Unfortunately the converse is also true, methods with

good world availabilities will have availability holes. For

example the overall world performance for DGPS +

Galileo #1 (30º mask case) is extremely good with a 95%

HDOP of 1.7 and 97.2% availability. However, as shown

in Figure 10 the minimum and maximum 95% HDOP

over the world are 1.1 and 3.7 respectively. These

availability holes are again found around ±60º latitude.These variations are not as problematic as in Figure 9,

however there are variations based on the user’s locations.

Figure 10 HDOP 95%, DGPS + Galileo #1,


The following statistics were generated for the 95%

HDOP values for the 118 computation points (30º mask

case) for each positioning method:

1) minimum value (0%)

2) median value (50%)

3) 95% value (95%)

4) maximum value (100%)

Figure 11 shows the results of this analysis, the maximum

and minimum values are the red lines with red trianglemarkers. The median value is the dark green line with

dark green “o” markers. The 95% value is the light green

shaded area. When DGPS is only augmented with

constraints, there are large variations between the

minimum and maximum values. Even when Galileo #1 is

added, there are still variations (1.1 to 3.7). Galileo #2

tends to moderate the results reducing the maximum

values while slightly increasing the median values over

Galileo #1.


12

3

4

5

6

7

8

9

1 0

H D

O P

M i n

M e d i a n

M a x

D G P S + M E O + G E O M E O

Figure 11 Statistics for Computation Points’

95% HDOP, 30°°°° Mask Angle

Reliability Results

The reliability results will be presented in a similar

manner to the availability results. A summary of the

isotropic mask angle reliability results for the world aregiven in Figure 12 and Figure 13, for the 95% HPE and

the percentage of HPEs ≤ 10 respectively. DGPS with

constraints showed available positioning for the 0º, 10º,

and 20º masking cases. However, reliable navigation is

only possible for the 0º and 10º masking cases. For the

20º mask case, unaugmented DGPS has a 95% HPE of

> 100 m with a corresponding reliability of 54%

(percentage of HPE ≤ 10 m). Augmenting DGPS with

both constraints improves the 95% HPE to 21.1 m and

95% HDOP

0 2 4 6 8 10

120oE 180

oW

60oN

18 0oW 120

oW 60

oW 0

o60

oE

30oN

90oN

0o

90oS

60oS

30oS

Longitude

L a t i t u d e

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increases the reliability to 85%. This still does not meet

the desired reliability of ≥ 95%. However, augmenting

DGPS with either Galileo constellation decreases the 95%

HPE to 4.1 m and increases the reliability to 100%.

At the higher masking angles of 30º and 40º, DGPS with

both constraints have 95% HPE > 100 m, with reliabilities

of 38% and 5% respectively. This is well below the

desired reliability level of ≥ 95%. For the 30º mask case

augmenting DGPS with either Galileo constellation andone constraint produces 95% HPE < 8 m and reliabilities

> 97%. In this case reliable navigation is achieved.


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

H P E

( m )


01 02 03 04 0

Figure 12 95% HPE, for the World, Isotropic Mask


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

P e r c

e n t a g e o f H P E s < 1 0 m


01 02 03 04 0

Figure 13 Percentage of HPEs ≤≤≤≤ 10 m, for the World

Isotropic Mask

Even the most augmented case for the 40º mask case has a

maximum reliability of 70%. While this is a dramatic

improvement over the DGPS and constraints value of 5%,

it falls short of the 95% reliability goal.

Overall the two Galileo constellations perform almost

identically for all of the mask cases. Only at the 40º mask

case is there a noticeable difference in the 95% HPE

(Figure 12) performance, with Galileo #2 outperforming

Galileo #1. However the reliability results (Figure 13) areagain almost identical. This indicates that Galileo #1 has

larger outliers than Galileo #2.

The regional differences first become apparent for the 20º

mask case using DGPS + height. Figure 14 is a contour

graph of the 95% HPE using the individual computation

point values. The overall 95% HPE is 30.9 m with a 79%

reliability. However, there are large variations in the 95%

HPE with locations ranging from a low of 5.9 m to a high

of > 100 m. Regions of poor reliability are found at ±60º

latitudes. Although on the world scale DGPS + height for

the 20º mask case does not provide reliable navigation,

some locations still have acceptable reliabilities.

95% HPE (m)0 20 40 60 80 100

120oE 180

oW

60oN

180oW 120

oW 60

oW 0

o60

oE

30oN

90oN

0o

90oS

60oS

30oS

Longitude

L a t i t u d e

Figure 14 HPE 95%, DGPS + Height


The results from analyzing the 95% HPE values for the

118 computation points (20º mask case) for each

positioning method is shown in Figure 15. The maximumand minimum values are the red lines with red triangle

markers. The median value is the dark green line with

dark green “o” markers. The 95% value is the light green

shaded area. When DGPS is augmented with constraints

there are large reliability variations between computation

points. The minimum and maximum 95% HPEs are 5.7 m

and 57.8 m respectively for DGPS + both constraints.

However, all of the Galileo augmentations have

maximum 95% HPEs < 10 m. Thus when DGPS is

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95% HPE, 20°°°° Mask Angle

augmented with Galileo for this masking case there are no

regions of poor reliability.

The regional reliability performance differences between

the two Galileo constellations become apparent at the 30º

mask case as shown in Figure 16. Galileo #1 has lower

minimum and higher maximum 95% HPE values

compared with Galileo #2 (MEO only). This matches

with the overall world reliability trends seen in Figure 12.

Thus Galileo #2 tends to moderate the results.


10

20

30

40

50

60

70

80

90

100

H P E ( m )

MinMedianMax

DGPS+ MEO+GEO MEO


95% HPE, 30°°°° Mask Angle

Constricted Waterway / Urban Canyon Simulation

The results for the constricted waterway / urban canyon

simulations are presented using the same format as the

isotropic mask angle results. For each orientation of the

constricted waterway / urban canyon (six orientations)

and for all of the orientations batched together the 95th

percentile HDOP / HPE were calculated:

1) for each computation point2) all 118 computation points batched together to

generate world values

In addition the percentage of time that the HDOP ≤ 2 and

the HPE ≤ 10 m were also calculated for the cases listed

above.

Availability Results

A summary of the constricted waterway / urban canyon

availability results for the world are given in Figure 17

and Figure 18. For each positioning method the 95th

percentile / percentage is plotted for each orientation of

the constricted waterway, resulting in six data points. Theoverall result for all of the orientations is plotted as the

solid magenta line through all of the positioning methods.

When six data points are not identifiable for a specific

case, it is because several points overlap. Figure 17 plots

the overall world 95% HDOP, while Figure 18 plots the

overall world percentage of HDOPs ≤ 2.

N H C B N H C B N H C B

0

1

2

3

4

5

6

7

8

9

1 0

H D O P


Figure 17 95% HDOP, for the World

Constricted Waterway / Urban Canyon

The overall results are similar to the 40º isotropic mask

angle case. DGPS + both constraints has a 95% HDOP

> 10 with a corresponding availability < 12%. Once

Galileo is added, the results improve to a 95% HDOP of

≤ 5.9 with an availability ≥ 53%. However, if the channel


10

20

30

40

50

60

70

80

90

1 00

H P

E

( m

)

M in

M ed i a n

M a x

D G PS + M E O + G E O M E O

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is oriented in the north / south direction the 95% HDOP

increases to 9.6 and the availability decreases to 43%. If

one constraint is also added to the DGPS + Galileo system

all of the channel orientations have similar availability

results.


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

P e r c e n t a g e o f H D O P < 2


Figure 18 Percentage of HDOPs ≤≤≤≤ 2, for the World


In order to examine how the availability results varied

with user location, the 95% HDOP statistics for the 118

computation points with all of the orientations batched

together were analyzed as shown in Figure 19. When

DGPS is augmented with Galileo #1 and constraints the

95% HDOPs ranged from a low of 1.8 to a high of 7.2

with 95% of the locations being ≤ 5.5. When DGPS is

augmented with Galileo #2 and constraints the 95%

HDOPs ranged from a low of 3.0, to a high of 5.5 with

95% of the locations being ≤ 5.0. Again Galileo #2 (MEO

only) produces much more balanced results as compared

with Galileo #1.

Reliability Results

A summary of the constricted waterway / urban canyon

reliability results for the world are given in Figure 20 and

Figure 21. Figure 20 plots the overall world 95% HPE,

while Figure 21 plots the overall world percentage of

HPEs < 10 m.The reliability results are very similar to the 40º isotropic

mask case. DGPS with both constraints has a reliability of

only 4%. By augmenting with Galileo, the reliability can

be increased to 68% and 60% for Galileo #1 and Galileo

#2 respectively. While Galileo #1 + both constraints has

the higher overall reliability there is a 10% reliability

variations between channels, while with Galileo #2 + both

constraints there is only a 3% reliability difference

between channels.


1

2

3

4

5

6

7

8

9

10

H D

O P

MinMedian

Max

DGPS+ MEO+GEO MEO


95% HDOP, Constricted Waterway / Urban Canyon


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

H P E ( m )


Figure 20 95% HPE, for the World


In order to examine how the reliability results varied withuser location, the 95% HPE statistics for the

118computation points with all of the orientations batched

together were analyzed as shown in Figure 22. When


95% HPEs ranged from a low of 10.9 m to a high of

> 100 m with 95% of the locations being ≤ 97.4 m. When


95% HPEs ranged from a low of 25.1 m, to a high of

729



68.6 m with 95% of the locations being ≤ 56.5 m. Again

Galileo #2 (MEO only) produces much more balanced

results.


1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

P e r c e n t a g e o f H P E <

1 0 m


Figure 21 Percentage of HPEs ≤≤≤≤ 10 m, for the World



1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

H P E

( m

)

M in

M e d i a n

M a x



95% HDOP, Constricted Waterway / Urban Canyon

CONCLUSIONS

Standalone DGPS (28 SVs) will meet the availability and

reliability requirements for most applications under

benign masking conditions (≤ 10°). Augmenting DGPS

with constraints improves the availability for the 20°mask case, however even with constraints the availability

is poor for the higher isotropic mask angles. While DGPS

and constraints do not provide reliable navigation for

masking angles ≥ 20°, once Galileo is added most of the

availability and reliability requirements can be met for

isotropic masking angles ≤ 30°. When extreme mask

angles are encountered (≥ 40° isotropic and severe

constricted waterways and urban canyons), DGPS must

be augmented with Galileo as well as the two constraints.

Even then the 95% HPE is in the 30-40 m range. In order

to reliable work under these masking conditions planning

must be performed.

The two Galileo constellations produced very similar

world results for all but the extreme mask conditions.

Under extreme mask conditions Galileo #2 (MEOs only)

moderates the results by reducing the maximum HDOPs

and HPEs and increasing the minimum and median values

as compared with Galileo #1 (MEOs and GEOs).

REFERENCES

Leick, A., 1995, GPS Satellite Surveying, 2nd

Edition,

John Wiley & Sons, Inc. 1995.

Lucas, R. and D. Ludwig, 1999, Galileo: System

Requirements and Architectures, Proceedings of

the ION GPS 99 Conference, Nashville,

Tennessee, September 14-17, 1999.

Office of the US President’s Press Secretary, 2000,

Statement by the President Regarding the United

States' Decision to Stop Degrading Global

Positioning System Accuracy, May 1, 2000.

Koch, K.R,. 1999, Parameter Estimation and Hypothesis

Testing in Linear Models (2nd Edition),

Springer-Verlag, New York, 1999.

Ryan S., and G. Lachapelle, 1999, Augmentation of

DGNSS With Dynamic Constraints for Marine

Navigation. Proceedings of ION GPS 99,

Nashville, TN, September 1999.

Ryan S., M. Petovello, and G. Lachapelle, 1998,

Augmentation of GPS for Ship Navigation in

Constricted Water Ways. Proceedings of ION

NTM 98, Long Beach CA, January, 1998.

Ryan S., J. Stephen, J.H. Keong, G. Lachapelle, and R.

Hare, 1999a, Augmentation of GPS for Hydrographic Application under Signa

Masking. International Hydrographic Review,

LXXVI, 1, pp 105-122, March 1999.

Ryan S., J. Stephen, and G. Lachapelle, 1999b, Testing

and Analysis of Reliability Measures for GNSS

Receivers in the Marine Environment.

Proceedings of ION NTM 99, San Diego CA,

January, 1999.

730



Spilker, J. J. Jr., 1994, Satellite Constellation and

Geometric Dilution of Precision, Chapter 5 in

Global Positioning System: Theory and

Applications Volume I, ed. B. W. Parkinson and

J. J. Spilker Jr., Volume 163 Progress in

Astronautics and Aeronautics, American Institute

of Aeronautics and Astronautics, Washington,

DC, 1996.

Vaníček, P., and E.J. Krakiwsky, 1986, Geodesy: TheConcepts (2

nd Edition), North-Holland,

Amsterdam, 1986.

Walker, J. G., 1978, Satellite Patterns for Continuous

Multiple Whole-Earth Coverage, IEE

Conference Publication No.: 160, pp 119-122,

1978.

Wolfrum, J., M. Healy, J.P. Provenzano, and T.

Sassorossi, 1999, Galileo - Europe’s

Contribution to the Next Generation of GNSS,

Proceedings of the ION GPS 99 Conference,

Nashville, Tennessee, September 14-17, 1999.

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