Reliability Characteristics of Reliability Characteristics of Differential GPS TransmissionDifferential GPS Transmission

Cezary Specht

Institute of Navigation and Maritime Hydrography

Naval University in GdyniaCSpecht@amw.gdynia.pl

•AccuracyAccuracy•Fix rate Fix rate •Capacity Capacity •AmbiguityAmbiguity•Fix dimensionFix dimension•CoverageCoverage•AvailabilityAvailability•ReliabilityReliability•ContinuityContinuity•IntegrityIntegrity

year 2000year 1995year 1990 International Association of Lighthouse,International Association of Lighthouse, European Radionavigation Plan, European Radionavigation Plan, Federal Radionavigation Plan.Federal Radionavigation Plan.

The importance of the navigation systems comparable criteria during the last years

?

Differential GPS transmission methodsDifferential GPS transmission methods

V,2 ,3

SS V4 ,5 ,6

S V1 ,2 , 3

S V4 ,5 ,6

S V1 ,2 ,3

S V4 ,5 ,6

S V1 ,2 ,3

S V4 ,5 , 6

S V1 ,2 , 3

V2 ,, 3

S V7 ,8 ,9

S V4 ,5 ,6

S V7 ,8 ,9

S V4 , 5 ,6

S V7 ,8 ,9

S V4 , 5 ,6

S V7 , 8 ,9

S V4 ,5 ,6

S V7 ,8 ,9

S V4 ,5 , 6

S V1 , 2 ,3

S V1 , 2 , 3

S V1 ,2 ,3

S V1 , 2 ,3

S V1

1

,2 ,3S V1 ,2 ,3

S V1 ,2 , 3

S V1 ,2 ,3

S V7 ,8 ,9

S V7 ,8 ,9

S V7 , 8 ,9

S V7 ,8 ,9

S V4 ,5 ,6

S V4 ,5 , 6

S V4 ,5 ,6

S V4 , 5 ,6

S V1 0 ,1 1 ,1 2

S V1 0 ,1 1 ,1 2

S V1 0 ,1 1 ,1 2

P = 2 . 8 %

P = 9 0 %

P = 7 . 2 %

RTC M no 1

RTC M no 9-3

RTCM no 1 m essages

4-6 satellites

7-9 satellites

10-12 satellites

visibility [%]

0,01 0,042,8

23,55

39,13

27,31

6,77

0,41 0,010

5

10

15

20

25

30

35

40

45

4 5 6 7 8 9 10 11 12Ns

a n d a n d a n d a n da n do r o r o r

Availability of Differential GPS transmission

The availability will be the state in which the age of at least 4 pseudorange corrections related to various satellites is lower than the maximum.

The process of PRCs transmission for NThe process of PRCs transmission for Nss ={7,8,9} ={7,8,9}

consttP h 9/712 sh

consttP h 9/7 sh 2 ...3,2,1s

9/71

9/75

9/76

9/78

9/71 0

9/71 2

9/74

9/73

9/72

tim ekt ,11,1 kt2,1 kt3,1 kt4,1 kt kt ,21,3 kt2,3 kt3,3 kt4,3 kt5,3 kt 1,2 kt2,2 kt3,2 kt4,2 kt5,2 kt

9/77

9/79

9/711

Availability of DGPS transmissionAvailability of DGPS transmissiontthe process of PRCs transmission for Nhe process of PRCs transmission for N

ss ={7,8,9} ={7,8,9} The binary state vectors of the system :

and the functions of their structures

1,34,35,31,23,24,2,13,14,1 ,...,,,,...,,,,...,, kkkkkkkkk xxxxxx xxx1Λ

1,33,34,31,23,24,2,13,14,1 ,...,,,,...,,,,...,, kkkkkkkkk xxxxxx xxx2Λ

,

.........

.........

.........Λ

5

1,3

4

1,2

4

0,1

4

1,2

5

1,3

4

1,2

4

0,1

4

0,1

5

1,3

1,34,35,31,23,24,2,13,14,1

1,23,24,21,34,35,31,23,24,2

,13,14,1,13,14,11,34,35,31

iik

iik

iik

iik

iik

iik

iik

iik

iik

kkkkkkkkk

kkkkkkkkk

kkkkkkkkk

xxxxxxxxx

xxxxxxxxx

xxxxxxxxx

xxxxxxxxx

4

1,3

4

1,2

4

0,1

4

1,2

4

1,3

4

1,2

4

0,1

4

0,1

4

1,3

1,33,34,31,23,24,2,13,14,1

1,23,24,21,33,34,31,23,24,2

,13,14,1,13,14,11,33,34,3

.

.........

.........

.........

iik

iik

iik

iik

iik

iik

iik

iik

iik

kkkkkkkkk

kkkkkkkkk

kkkkkkkkk

xxxxxxxxx

xxx

xxx

xxx

xxxxxx

xxxxxx

xxxxxx2Λ

14

13

12

111 Ω,Ω,Ω,ΩmaxΛ 2

4

2

3

2

2

2

12 Ω,Ω,Ω,ΩΛ max

1

12u

1u

Ω

Ω

P

Pzu

,,

,,1

2

1

1

1

1

k

k

tt

tt

.4321421321432

4314131433242214321

zzzzzzzzzzzzz

zzzzzzzzzzzzzzzzzzztA

4

0,1

5

1,3

iik

iik xx1

1Ω

4

0,1

4

1,3

iik

iik xx2

1Ω

4

1,2

4

0,1

iik

iik xx2

2

1

2 ΩΩ

4

1,2

5

1,3

iik

iik xx1

3Ω

4

1,2

4

1,3

iik

iik xx2

3Ω

5

1,3

4

1,2

4

0,1

iik

iik

iik xxx1

4Ω

4

1,3

4

1,2

4

0,14

iik

iik

iik xxx2Ω

10555 21111 dddd qqqqP 11Ω

.2211111Ω 13958444524 dddddddd qqqqqqqqP

After decomposition:

95454 1111 ddddd qqqqqP 21Ω

95445 11111 ddddd qqqqqPP 22

12 ΩΩ

95445 1111 ddddd qqqqqP 13Ω

8444 21111 dddd qqqqP 23Ω

141095454514 211111Ω dddddddd qqqqqqqqP

AVAILABILITY:

Availability of DGPS transmissionAvailability of DGPS transmissiontthe process of PRCs transmission for Nhe process of PRCs transmission for N

ss ={7,8,9} ={7,8,9}

Transmission availability calculation (1)Transmission availability calculation (1)

DGPS RSDGPS RS signal strength level signal strength level

Noise levelNoise level

SNR=f(BER)SNR=f(BER)

Transmission availabilityTransmission availability zoneszones

Transmission availability calculation (2)Transmission availability calculation (2)

SNR=f(BER)SNR=f(BER)kt ,1 1,1 kt

1,1 kt2,1 kt3,1 kt4,1 kt5,1 kt6,1 kt7,1 kt kt ,21,2 kt

6/41

6/42

2,2 kt3,2 kt4,2 kt5,2 kt6,2 kt7,2 kt

6/43

6/44

kt ,1 1,1 ktkt ,21,2 kt

6/41

6/42

6/43

6/44

kt ,1 1,1 kt1,1 kt2,1 kt3,1 kt4,1 kt5,1 kt6,1 kt7,1 kt kt ,21,2 kt

6/41

6/42

2,2 kt3,2 kt4,2 kt5,2 kt6,2 kt7,2 kt

6/43

6/44

kt ,1 1,1 ktkt ,21,2 kt

6/41

6/42

6/43

6/44

time

Transmission modelTransmission model

Reliability Reliability and Continuity and Continuity of of Differential GPS Differential GPS transmissiontransmission

t

t''0Z

'1Z

'2Z

1X1Y 2Y

tA

2X 3X

''1Z ''

2Z

t

''0Z

'1Z

'2Z

1X1Y 2Y

tA

2X 3X

''1Z ''

2Z

0

1

Availab ility

t

t''0Z

'1Z

'2Z

1X1Y

2Y2X 3X

''1Z ''

2Z

,tR

t

''0Z

'1Z

'2Z

1X1Y 2Y2X 3X

''1Z ''

2Z

0

1

,tRReliability

any moment in timeany moment in time time periodtime period

failure rate -

renewal rate -

tR

kt 1kt vkt 1vkt2kt

p1

k1

1 2 2 2 21 1 t

tR

kt 1kt vkt 1vkt2kt

p1

k1

1 2 2 2 21 1

Reliability functionReliability function

some comparative analyses ...

1

2

2

1

A

110 110 21 0 21 0 310 310

B E R

1 0 0 %

5 0 %

R=100 bps1

R=200 bps2

R=100 bps2

R=200 bps1

B E R

110 110 21 0 21 0 310 310

1 0 0 %

5 0 %

The increase in the number of satellites, for which the reference station transmits pseudorange corrections by message RTCM type 9-3, improves the availability

Type of the message, bit rate vs BER

P O L IS H A C A D E M Y O F S C IE N C E S

P O L IS H N AV IG AT IO N F O R U M

ANNUALof

NAVIGATION

N o 5 2 0 0 3

1. The aim of this presentation has been to develop a mathematical model of availability, reliability and continuity of differential GPS transmission based on probabilistic approach.

2. The problem was important because of the lack of methods, which would enable the parameter prognosis with regard to the process of navigation. In this light, the problem reliability characteristics constitutes one of the fundamental issues for multi-criteria assessment of modern systems at the stage of system testing and exploitation as well.

3. The theory the author worked out has been referred to the probabilistic characteristics of navigation systems functioning such as expected value, variance, or standard deviation.

Conclusions

Specht C., (2003) Availability, Reliability and Continuity of Differential GPS Transmission, Annual of Navigation, no 5/2003, Polish Academy of Sciences, Gdynia, 2003, 85 pages.