High integrity safety-critical GNSS applications on the railways 1 HIGH INTEGRITY SAFETY- CRITICAL GNSS APPLICATIONS ON THE RAILWAYS PAUL CROSS DEPARTMENT

High integrity safety-critical GNSS applications on the railways 1

HIGH INTEGRITY SAFETY-CRITICAL GNSS APPLICATIONS

ON THE RAILWAYS

PAUL CROSS

DEPARTMENT OF GEOMATIC ENGINEERINGUNIVERSITY COLLEGE LONDON


SUMMARY

• GNSS Applications on the railways

• Safety critical quality measures

• Role of track data bases

• Error budgets

• Multipath

• Future experiments


EXPANDING GNSS RAILWAY APPLICATIONS

• Construction– Channel Tunnel link, West coast mainline

• Control of specific operations (e.g. doors)• Track maintenance• Mapping (3D model)• Information control (e.g. balise function)• Information for passengers (arrival and LBS?)• Freight logistics• Odometer calibration• Signalling• etc

Some are potentially safety critical


• Accuracy is the degree of conformance between the estimated or measured position/velocity and its true position/velocity

• Integrity is the measure of trust – the probability of displaying hazardously misleading navigational or positional information

• Continuity is the probability that the specified system performance will be maintained for the duration of a phase of operation

• Availability is the ability of a navigation system to provide the required function and performance at the initiation of the intended operation

REQUIRED NAVIGATION PERFORMANCE FOR SAFETY CRITICAL APPPLICATIONS


Phase of Operation

Accuracy Integrity Continuity

AvailabilityAccuracy (2σ) Alert Limits Integrity Risk TTA

Continuity Risk

En-route2 nm (L)N/A (V)

Oceanic/low density4 nm (L)N/A (V) 1E-7/h 5 min

1E-4 /h – 1E-8/h

0.99 – 0.99999

Continental2 nm (L)N/A (V)

En-route, Terminal0.4 nm (L)

N/A (V)1 nm (L)N/A (V)

1E-7/h 15 s1E-4 /h – 1E-

8/h0.99 –

0.99999

Initial approach, Intermediate approach, NPA, Departure

220 m (L)N/A (V)

556 m (L)N/A (V)

1E-7/h 10 s1E-4 /h – 1E-

8/h0.99 –

0.99999

APV-I16 m (L)20 m (V)

40 m (L)50 m (V)

2E-7/150 s 6 s 8E-6/15 s0.99 –

0.99999

APV-II16 m (L)8 m (V)

40 m (L)20 m (V)

2E-7/150 s 6 s 8E-6/15 s0.99 –

0.99999

Cat-I16 m (L)4 m (V)

40 m (L)10 m (V)

2E-7/150 s 6 s 8E-6/15 s0.99 –

0.99999

Cat-II6.9/6.1 m (L)2.0/1.4 m (V)

17.3/17.9 m (L)5.3/4.4 m (V)

1E-9/15 s 2 s 4E-6/15 s0.99 –

0.99999

Cat-IIIa6.2/3.6 m (L)2.0/1.0 m (V)

15.5/10.4 m (L)10.0/2.6 m (V)

1E-9/15 s 2 s 4E-6/15 s0.99 –

0.99999

Cat-IIIb6.2/3.6 m (L)2.0/1.0 m (V)

15.5/10.4 m (L)10.0/2.6 m (V)

1E-9/30 s (L)1E-9/15 s (V)

2 s2E-6/30 s (L)2E-6/15 s (V)

0.99 – 0.99999

Surface Movement (SM) – Surveillance 7.5 mUnder development

TLS Risk = 3E-9Update rate: 1 s

Under development

SM – Routing

Under development

TLS Risk = 1E-9

Under development

SM – Guidance TLS Risk = 3E-9

SM – ControlTLS Risk = 3E-

9PMD<0.001

SOME AVIATION RNPs


Least Squares Estimation

Based on a single epoch least squares approach to the GNSS navigation solution

1 , CWxF

xFbxAdv

xdxx

WbAWAAxd

xFbx

FA

TT

ˆˆˆ

ˆˆ

ˆ

,

0

1

0 Functional model Stochastic model

CROSS P A, D J HAWKSBEE and R NICOLAI (1994) Quality measures for differential GPS Positioning. Hydrographic Journal, No 72, p17- 22


DESCRIPTION OF ACCURACYAccuracy is quality with respect to random errors. It describes the way that random measurement errors propagate through the positioning solution.

120ˆ ˆ

WAAC T

x

2

2

2

2

2

2

2

2

ˆ

TTHTNTE

HTHHNHE

NTNHNNE

ETEHENE

TTZTYTX

ZTZZYZX

YTYZYYX

XTXZXYX

xC

To describe precision in direction

212222 sincos2sincos ENEN


STASTICAL TESTING• Overall model testing via unit variance

• Outlier detection (slippage testing) via w-tests

Commonly used value

2mn

vWvE

mn

vWv TT

ˆˆ ,1 ˆˆ 2

020

mn

tt

worWeWCevWe

AWAAAWC

ivTii

Ti

TTv

1

01.0 , ˆ

ˆ

2

12

112

1

2

1

ˆ

1120ˆ

iv

iv

ˆ

ˆ

Simple form for uncorrelated data


57.201.0 a

57.2a

01.0

RELIABILITYrelates to the impact of undetected outliers

is commonly used


,f

3.41=,

84.020.0

57.201.0

f

b

a

Commonly used in non-safety critical applications

8.19α,βf

0.00000001when β


RELIABILITY INTEGRITY

Reliability measured via max effect of marginally detectable error

2

1

ˆ,

ivTi

ui WeWCef

iTTu

i WeAWAAMax1

Externalreliability


How many satellites are needed?• Classically four satellites are needed

– May be accurate but will be totally unreliable

• Five will enable some level of fault detection– But can’t distinguish which satellite is at fault

• Six will give some level of fault detection and exclusion (FDE)

• More will give improved reliability• For height aiding it’s one less• For track aiding it’s two less

GRAIL experiments


Basic GNSS positioning equation

usususu ctzzyyxx 2/1222 ])()()[(

User position in Cartesian coordinates Receiver clock offset

xF


Dealing with straight paths


Track aiding equations

We have also developed the equations for curved tracks


Current user position

Approximate position based on previous position and a simple velocity estimate

General Strategy

Area of possible solution centred on closest point on track to approximate position


Numerical verification

x (m) y (m) z (m) Pseudorange (m)

S17 16411645.7050 20913839.0560 -4307717.8190 26077857.5003

S21 14230972.4050 -6562961.2610 -21483601.490 29148754.2764

x (m) y (m) z (m) t (s)

3976515.1540 -9379.8710 4970126.7300 0.0001

x (m) y (m) z (m)

3976500.000 -9391.586918 4970138.752

3976584.963 -9325.900 4970071.351

1X

2X

x (m) y (m) z (m) t (s)

3976515.1538 -9379.871155 4970126.730.000099999

9997


No.of visible satellite

0

2

4

6

8

10

12

00:0

0

01:3

0

03:0

0

04:3

0

06:0

0

07:3

0

09:0

0

10:3

0

12:0

0

13:3

0

15:0

0

16:3

0

18:0

0

19:3

0

21:0

0

22:3

0

Epoch

No

. o

f sate

llit

es

Number of visible satellites

IMPACT OF A TRACK DATA BASE ON ACCURACY AND INTEGRITY

Open area in the London region (10 degree mask angle)


URE budgets for GPS pseudo-ranges (standard deviations)

Elevation angles (o) 10 20 30 40 50 60 70 80 90

GPS URE (m) 2.35 2.11 2.07 2.06 2.06 2.05 2.05 2.05 2.05

Along Track Alarm Limit

Across Track Alarm Limit

Probability of a missed detection

Probability of a false alarm

Mask Angle (o)

20 m 20 m 0.000000001 0.01 10

SOME TEST SPECIFICATIONS

Standard deviation of track data base: 1m in all directions


Standard Deviation of Parameters

00.5

11.5

22.5

33.5

4

00:0

0

01:3

0

03:0

0

04:3

0

06:0

0

07:3

0

09:0

0

10:3

0

12:0

0

13:3

0

15:0

0

16:3

0

18:0

0

19:3

0

21:0

0

22:3

0

Time

σ (

m)

Along Across Height

Standard Deviation of Parameters (Track Known)

00.5

11.5

22.5

00:0

0

01:3

0

03:0

0

04:3

0

06:0

0

07:3

0

09:0

0

10:3

0

12:0

0

13:3

0

15:0

0

16:3

0

18:0

0

19:3

0

21:0

0

22:3

0

Time

σ (

m)

Along Across Height

Mean standard deviationof user position

Along Across

GPS (m) 1.18 1.03GPS+Track data (m) 1.07 0.57


Maximum possible error in position that is undetectable with specified probability

0

20

40

60

80

00

:00

01

:45

03

:30

05

:15

07

:00

08

:45

10

:30

12

:15

14

:00

15

:45

17

:30

19

:15

21

:00

22

:45

Time

Ma

x δ

(m)

Along Across Height


(Track known)

05

10152025

00

:00

01

:45

03

:30

05

:15

07

:00

08

:45

10

:30

12

:15

14

:00

15

:45

17

:30

19

:15

21

:00

22

:45

Time

Ma

x δ

(m)

Along Across Height

External reliability

Along Across

GPS (m) 44.67 23.29

GPS+Track data (m)

18.18 11.49



Along (m) Across (m)

GPS alone 1.18 1.03

GPS + 1m data base 1.07 0.57

GPS + 0.1m data base 1.05 0.22


Along (m) Across (m)

GPS alone 44.67 23.29

GPS + 1m data base 18.18 11.49

GPS + 0.1m data base 17.64 12.49

Does the accuracy of the track data base matter?


Satellite visibility (London Region)

0123456789

Epoch

No

. o

f sate

llit

es


Along Across

GPS (m) 1.71 1.45

GPS+Track data (m)

1.32 0.60Standard Deviation of Parameters

0

2

4

6

8

10

12

00:0

0

01:3

0

03:0

0

04:3

0

06:0

0

07:3

0

09:0

0

10:3

0

12:0

0

13:3

0

15:0

0

16:3

0

18:0

0

19:3

0

21:0

0

22:3

0

Time

σ (

m)

Along Across Height

TESTS WITH REDUCED VISIBILITY

Standard Deviation of Parameters (Track Known)

012345

00:

00

01:

30

03:

00

04:

30

06:

00

07:

30

09:

00

10:

30

12:

00

13:

30

15:

00

16:

30

18:

00

19:

30

21:

00

22:

30

Time

σ (

m)

Along Across Height



Along Across

GPS (m) 2957.45 () 1568.09 ()

GPS+Track data (m) 160.78 22.22


(Track known)

0

50100

150

200

00

:00

01

:45

03

:30

05

:15

07

:00

08

:45

10

:30

12

:15

14

:00

15

:45

17

:30

19

:15

21

:00

22

:45

Time

Ma

x δ

(m)

Along Across Height


0

1000

2000

3000

4000

00

:00

01

:45

03

:30

05

:15

07

:00

08

:45

10

:30

12

:15

14

:00

15

:45

17

:30

19

:15

21

:00

22

:45

Time

Ma

x δ

(m)

Along Across Height


Impact on RAIM availability

RAIM Availability (London Region)

GPS only GPS+Track data

Along Across Along Across

Full constellation 88% 95% 100% 100%

Reduced constellation 49% 54% 82% 97%


Space Segment Errors Clock errors

Ephemeris errors

Propagation Errors Ionospheric delay

Tropospheric delay

Local Errors Multipath

Receiver noise

Common Mode

Strong Spatial Correlation

Weak Spatial Correlation

No Spatial Correlation

GNSS ERROR SOURCES


SV23 ~20o

SV23 ~65o

CODE MULTIPATH AT A TYPICAL GNSS BASE STATION

constf

cL

f

cLCM P

22

1111 0915.30915.4

1m

0.25m


Data gathering in Wales


Severn Valley Railway results

Longitude lattitude plot for Severn valley railway

52.360

52.365

52.370

52.375

52.380

52.385

52.390

52.395

52.400

52.405

52.410

52.415

52.420

52.425

52.430

52.435

52.440

52.445

52.450

Longitude (degrees)

Lat

titu

de

(deg

rees

)

Longitude lattitude plot for Severn valley railway

52.360

52.365

52.370

52.375

52.380

52.385

52.390

52.395

52.400

52.405

52.410

52.415

52.420

52.425

52.430

52.435

52.440

52.445

52.450

Longitude (degrees)

Latti

tude

(deg

rees

)

•Long/Lat plot fits well over OS map

•Tunnel can be clearly seen on data

•Heavily forested areas show as breaks

•More missing L2 data than L1, due to weaker signal


50 Epoch minimum


20 Epoch minimum


IMPACT OF POWER LINES?


LOCASYS – A MAJOR DATA GATHERING AND EVALUATION EXERCISE

• NSL in collaboration with UCL and Bangor– Funded by RSSB

• Two trains on the Litchfield to Redditch line– Passing through Birmingham New Street– Data collected on every journey– Recorded on board and collected later

• Will begin in next two months– Operate for a full twelve months

• Fully instrumented– Standard GPS, Dual frequency phase GPS– Full inertial system, axle revolution counter

• Data itself will be used to deliver the track data base


GNSS Availability - courtesy of

265000

270000

275000

280000

285000

290000

295000

300000

305000

310000

315000

400000 405000 410000 415000

Location of outages greater than 2s

>5s

>10s

>50s

>20s

>100s

>200s

Sutton Tunnel

Birmingham

New St

285000

286000

287000

405000 406000 407000 408000 409000 410000

Church Road Tunnel

New St Station

New St South TunnelBath Row, Granville Street, Canal and Holliday Tunnels

Journey Time: 11:56:27 to 13:14:57

Samples: 4711Outages: 501 GNSS availability 89.36%


GNSS Signals - courtesy of

Satellite Visibility

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7 8 9

Number of Satellites

Perc

en

tag

e o

f T

ime

2¾ hours data at 1Hz, 80% of time 6 or more satellites


GNSS Outages - courtesy of

Analysis of 22 Recorded Positioning Outages (<4 SV or HDoP > 4)

0

10

20

30

40

50

60

70

80

1s>outage<=5s 5s<outage<=10s 10s<outage<=20s 20s<outage<=50s 50s<outage<=100s 100s<outage<=200s outage>200s

Per

cen

tag

e o

f O

uta

ges

Aiding processes ? Coasting sensors ?

22 position outages

Additional Systems?


QUESTIONS TO BE ADDRESSED

• What is typical level of GNSS availability?– Accuracy and integrity

• Realistic assessment of GNSS errors– Through comparisons with truth and other sensors

• How much can a track data base really help?• How does INS help?

– Is a full system necessary?• Prediction of improvement with new GNSSs

– Sky visibility will be obtained from GPS history• Optimal on-board package?

– Most cost effective solution


THE END!

Documents

High integrity safety-critical GNSS applications on the railways 1 HIGH INTEGRITY SAFETY- CRITICAL GNSS APPLICATIONS ON THE RAILWAYS PAUL CROSS DEPARTMENT