Reliability Characteristics of Reliability Characteristics of Differential GPS TransmissionDifferential GPS Transmission
Cezary Specht
Institute of Navigation and Maritime Hydrography
Naval University in [email protected]
•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.
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