Processing in Geostationary Orbit

photohomoeopathAI and Robotics

Nov 24, 2013 (3 years and 7 months ago)

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1


Comparison of acquisition
Techniques for GNSS Signal
Processing in Geostationary Orbit

B.Chibout, ENAC/TesA

C.Macabiau, ENAC

A
-
C.Escher,ENAC

L.Ries, CNES

J
-
L.Issler, CNES


S.Corrazza,ThalesAleniaSpace



2

Introduction


GPS is optimised for an earth use.


The use of GNSS for geostationary positioning is
possible with specific constraints.
In particular, the
geostationary satellites have to process signals with low
C/No (<25dBHz) to ensure that at least 4 satellites can
be used to compute its position


Our aim is to design an autonomous geostationary
receiver


In geostationary orbit, the receiver faces long spell
without the possibility to demodulate the data for each
satellite. This fact lays a problem to compute its position
autonomously.


To solve this problem, a reduction of the data
demodulation threshold is envisaged to increase the
number of GPS satellites with valid ephemeris.

3

Introduction


Three differents acquisition techniques are then
presented.

-
1+1ms FFT acquisition method

-

Half Bit acquisition method

-

Double Block Zero Padding Method


Their performances in geostationary orbit with the
specific constraint (number of useable satellites) are
compared over a 24 hours period


A peak acquisition extrapolation technique is also
presented to improve the accuracy of the positioning

4

Outline


GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER


REDUCTION OF THE DATA DEMODULATION
THRESHOLD


ACQUISITION

ALGORITHMS


1
+
1
ms

FFT

acquisition

method


Half

Bit

acquisition

method


Double

Block

Zero

Padding

Method


GEOSTATIONARY

ACQUISITION

RESULTS


5

Outline


GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER


REDUCTION OF THE DATA DEMODULATION
THRESHOLD


ACQUISITION ALGORITHMS


1+1ms FFT acquisition method


Half Bit acquisition method


Double Block Zero Padding Method


GEOSTATIONARY ACQUISITION RESULTS


6

GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER

Geostationary

Orbit

GPS Orbit

Earth

GPS 1

GPS 2

S’

S

45
°

S’’’

Teta GEO

S’’

GPS


main lobe

main and secondary lobes

main lobe only



For a geostationary receiver, the
usefull GPS satellites are mainly
those located on the «

opposite

»side
of the earth


The GPS satellites located in the S’’
area are masked by the earth.
Masking Earth encompasses the Iono


The free space losses are 5 to 10dB
higher

than for an earth user


High DOP value (from 15 to more
than 50)


The gain of the transmitting antenna
decreases drastically when signals
are emitted through side lobes



The design of the receiver must be
adapted to that geometry

7

GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER

Receiver antenna pattern: 9 dB
from 0
°

to 30
°

and decreasing
value after

In red: theoreticall pattern

In blue: receiver pattern well
suited to GEO condition.

The received C/No decreases with the off
boresight angle of the GEO antenna.

C/No are mainly between 18 and 27 dBHz

The acquisition techniques have to deal with
these low values

Main lobe only receiver Antenna pattern

8

GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER

2
4
6
8
10
12
14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
PROBABILITY TO SEE AT LEAST n SATELLITES WITH C/No >20
NUMBER OF SATELLITES
PROBABILITYY
1
2
3
4
5
6
7
8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
PROBABILITY TO SEE AT LEAST n SATELLITES WITH C/No >25
NUMBER OF SATELLITES
PROBABILITYY


The simulations are conducted with the nominal 24 satellites GPS constellation

The number of useable satellites increases while the processing threshold decreases.

More than 65% of the time, the GEO receiver sees 4 satellites and almost every time 2
satellites with C/No>25 dBHz.

For 100% of the time, the GEO receiver sees 6 satellites with C/No>20 dBHz

A 20 dBHz processing threshold should be sufficient to provide continuous
positioning



9

GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER

0
5
10
15
20
25
0
50
100
150
200
250
300
350
400

To be autonomous and get precise position, the receiver must be able to
demodulate the data of each PRN so as to get their ephemeris.



The C/NO of the received signals have long spell under the classic data
demodulation threshold: 27 dBHz.

PRN number

Time

(min)

TOTAL VISIBILITY DURATION WITH C/NO>27dBHZ OVER 1DAY

10



TOE1

TOE2

Validity period for ephemeris
broadcasted with TOE1

Validity period for ephemeris
broadcasted with TOE2

t

t
-
2h

t+2h

t+4h

Ephemeris
broadcasted with
TOE1

Ephemeris
broadcasted
with TOE2

Once an ephemeris set is demodulated, its
validity is 4h. A new set of ephemeris is broadcast
every 2hours.

As long as the C/NO of a GPS satellite is above
the Data Demodulation Threshold (i.e 27 dBHz),
the ephemeris is known for the next 4hours in the
best case

GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER




the ephemeris demodulation cannot always be achieved (inspite of their 4 hours




validity)



the number of useable satellites to compute the GEO satellite position decreases

0
5
10
15
20
15
20
25
30
35
40
45
TIME (h)
C/NO(DBHZ)
C/No for PRN 1
0
5
10
15
20
15
20
25
30
35
40
45
C/NO(DBHZ)
TIME (h)
C/No for PRN 20
Data Demodulation
threshold

More than
15hours

Maximum 4 hours
ephemeris validity after
last data demodulation

11

Outline


GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER


REDUCTION OF THE DATA DEMODULATION
THRESHOLD


ACQUISITION

ALGORITHMS


1
+
1
ms

FFT

acquisition

method


Half

Bit

acquisition

method


Double

Block

Zero

Padding

Method


GEOSTATIONARY

ACQUISITION

RESULTS


12

REDUCTION OF THE DATA
DEMODULATION THRESHOLD




A reduction of the Data Demodulation Threshold (DDT) increases the BER but
increases the average number of visible satellites with valid ephemeris.



A trade off must be found between those two properties



The data needed to compute an accurate GEO receiver position are:



-

Ephemeris data (encoded by 600 bits in subframes 2&3)


-

the clock correction (62 bits)

The probability to demodulate the
entire ephemeris with no error is
too weak

with a 24 dBHz DDT



24 dBHz is not retain
for the Data Demodulation
Threshold

Minimum C/No

for the Data demodulation
threshold

Corrresponding

BER

Probability to demodulate
the entire ephemeris with no
error

(1
-
BER)
662

27dBHz

6.10
-
6

0.996

26dBHz

5.10
-
5

0.967

25dBHz

2.10
-
4

0.88

24dBHz

10
-
3

0.52

13

REDUCTION OF THE DATA
DEMODULATION THRESHOLD


0
5
10
15
20
25
1
2
3
4
5
6
7
8
9
Time(h)
Number of visible satellite
NUMBER OF VISIBLE PRN WITH VALID EPHEMERIS, C/NO>20DBHZ, AND DDT=27DBHZ
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
Time(h)
Number of visible satellite
0
5
10
15
20
25
0
1
2
3
4
5
6
7
8
9
10
Time(h)
Number of visible satellite



NUMBER VISBLE SATELLTE WITH VALID EPHEMERIS C/NO>20 DBHZ


Data Demodulation Threshold=27 dBHz


Data Demodulation Threshold=26 dBHz

Data Demodulation Threshold=25 dBHz



With a DDT=27dBHz, more than 3 hours with only 2 or 3 satellites
useable to compute a position.


With a DDT=25dBHz, less than 50min with less than 4 satellites to
compute a position. The average number of usable satellites is 6.1

14

REDUCTION OF THE DATA
DEMODULATION THRESHOLD


GPS satellites are considered
usable

when:

-
The Line Of Sight between them and the GEO satellite
is not obstructed,

-
The received C/No is above 20 dBHz
(processing threshold)

-
The ephemeris is valid
(with regards to the 25 dBHZ DDT)


The 3 algorithms will be tested under these

constraints

15

Outline


GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER


REDUCTION OF THE DATA DEMODULATION
THRESHOLD


ACQUISITION

ALGORITHMS


1
+
1
ms

FFT

acquisition

method


Half

Bit

acquisition

method


Double

Block

Zero

Padding

Method


GEOSTATIONARY

ACQUISITION

RESULTS


16

ACQUISITION ALGORITHMS


1+1ms FFT acquisition method

FFT

FFT

FFT

IFFT


IFFT

conj

( )²

( )²

T

Q

I

Block A

:

1ms of

signal

Block B

:

1ms of

signal

1ms of

local code

1ms of zero
padding

FFT

FFT

IFFT

conj

Block 0


Block C


This technique follows a
classic acquisition scheme.

The correlation scheme consist in:


2ms of signal in a buffer (First In First Out)


1ms of local code +1ms of zeros


FFT correlation between the 2 blocks

Results: keep only the 1rst ms of the correlation






ˆ
2
cos

e
I
kT
f




ˆ
2
sin

e
I
kT
f
)
(
e
kT
c
f
s

M
17


Half Bit acquisition method

ACQUISITION ALGORITHMS

Set 1

Set 1

Set 1

Set 2

Set 2

Set 2

10ms

Data Bit
transition

Method based on two sets of 10 ms of signal coherently integrated

The initial signal is divided into two sets:


Set2: to=10 t1=30 t2=50

Set1: to=0 t1=20 t2=30

Only Set 1 is affected by the data bit transition
losses.

This technique allows long coherent integration
without the knowledge of the data bit integration
time

This method has a heavy computational cost

18

ACQUISITION ALGORITHMS

1

2

3



j

j+1



M

1

2

3



j

j+1



M


m m m


points points points


2 m 2m 2m

points points points

1

2

3



j

j+1



M


m m m

points points points


m m m m m m m m m


2 m 2m 2m


points points points

Data

C/A

code

1

2

3

j

M







Double

Block

Zero

Padding

Method




This

method

uses

correlation

over

less

than

1
ms

of

signal
.




No

acquisition

matrix



Method

very

fast

and

low

computational

cost


The

signal

is

divided

into

M

blocks

of

m

samples

each





Construction of the extended
data and extended local code


extended Data


extended C/A code

19

ACQUISITION ALGORITHMS

1

2

3



j

j+1



M


2 m 2m 2m


points points points

1

2

3

j

M








extended Data




FFT correlation




extended C/A Code







Correlation result

1

2

3



j

j+1



M

M
-
point FFT on the ith point of each block


Double Block Zero Padding Method

i

i

i

i

i



Extended data and
extended C/A code are FFT
correlated block by block


The M
-
point FFT
corresponds to M doppler
bins


The M
-
point FFT is carried
on the m possible point of
each block


We get M x m vectors


Maximum amplitude research: vect_max(i,M)


Code is synchronised for this maximum


Delay:i


Doppler:bin where vect_max is maximum


20

Outline


GPS SIGNAL CHARACTERISTICS FOR A
GEOSTATIONARY ORBIT RECEIVER


REDUCTION OF THE DATA DEMODULATION
THRESHOLD


ACQUISITION

ALGORITHMS


1
+
1
ms

FFT

acquisition

method


Half

Bit

acquisition

method


Double

Block

Zero

Padding

Method


GEOSTATIONARY

ACQUISITION

RESULTS


21

GEOSTATIONARY ACQUISITION
RESULTS

Signal strength

Coherent

acquisition

(ms)

Non
-
Coherent

acquisition

Signal Duration

(s)

C/No>30

1

100

0.1

30>C/No>26.5

1

200

0.2

26.5>C/No>24

5

200

1

24>C/No>22

10

150

1.5

C/No<22

10

250

2.5

Signal strength

Coherent

acquisition

(ms)

Non
-
Coherent

acquisition

Total Signal

Duration (s)/

Signal set duration

C/No>30

10

20

0.2/0.1

30>C/No>26.5

10

40

0.4/0.2

26.5>C/No>24

10

150

1.5/0.75

24>C/No>22

10

250

2.5/1.25

C/No<22

10

350

3.5/1.75


Signal strength

Signal Duration

(ms)

C/No>30

100

30>C/No>26

500

26>C/No>22

1000

C/No<22

1500

The

simulations

are

conducted

over

24

hours
.

The

GPS

signals

are

simulated

under

MATLAB
.


The

search

of

the

Delay
-
Doppler

is

done

by

detecting

the

maximum

of

the

Acquisition

matrix
.

For

different

signal

strengh,

the

number

of

coherent

and

non
-
coherent

integration

is

fixed
.


1+1ms FFT acquisition method parameters


Half Bit acquisition method parameters

The double block zero padding method
does not requires coherent or non
coherent integration time. We only
define the total signal duration

double block zero padding method parameters

22

Probability of

misdetection

Pmd with all

visible

Satellite

Pmd with

satellites

with valid

ephemeris

1
st

method

0.005

0

2
nd

method

0.007

0.003

3
rd

method

0.23

0.14

GEOSTATIONARY ACQUISITION
RESULTS

Probability of misdetection

Total integration time chosen to ensure that the receiver is able to
compute a position at a maximum of epoch inspite of the low number
of usable satellite at some epoch.


It explains the choice of long signal duration


Pmd is very low for the first two
methods which have similar results


The results are really degraded for
the double block zero padding
acquisition method

23

GEOSTATIONARY ACQUISITION
RESULTS

0
5
10
15
20
-200
0
200
TIME(H)
ERROR(M)
ALONG TRACK ERROR
0
5
10
15
20
-2000
0
2000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
-200
0
200
TIME(H)
ERROR(M)
CROS TRACK ERROR
0
5
10
15
20
-2000
-1000
0
1000
2000
TIME(H)
ERROR(M)
CLOCK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
ALONG TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
CROS TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
CLOCK ERROR
average position error:
-

48.7m along track





-

350 m radial track





-

52.2 m cross track

average position error
:
-

101.1m along track



-

742 m radial track



-

67.8 m cross track

1+1ms FFT acquisition method positioning results

Position computed with all visible satellites (C/No>20dBHz)

Position computed with visible satellites with valid ephemeris (C/No>20dBHz)





The resolution of the delay is only ½ chip due to the sample frequency


The pseudorange resolution is limited by 150 m

The radial track error is the biggest because of the geometry of the GPS satellites wrt the GEO

24

GEOSTATIONARY ACQUISITION
RESULTS

average position error:
-

50.5 m along track




-

359 m radial track



-

50.8 m cross track

average position error
:
-

102.4 m along track




-

745 m radial track




-

69.3 m cross track

Half Bit acquisition method positioning results

5
10
15
20
-200
-100
0
100
200
TIME(H)
ERROR(M)
ALONG TRACK ERROR
5
10
15
20
-2000
0
2000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
-200
0
200
TIME(H)
ERROR(M)
CROS TRACK ERROR
5
10
15
20
-2000
0
2000
TIME(H)
ERROR(M)
CLOCK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
ALONG TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
CROSS TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
CLOCK ERROR
Position computed with all visible satellites (C/No>20dBHz)

Position computed with visible satellites with valid ephemeris


(C/No>20dBHz)

The results in term of position accuracy are similar to the previous method

25

GEOSTATIONARY ACQUISITION
RESULTS

0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
ALONG TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
CROS TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
CLOCK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
ALONG TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
RADIAL TRACK ERROR
0
5
10
15
20
25
-500
0
500
TIME(H)
ERROR(M)
CROS TRACK ERROR
0
5
10
15
20
25
-4000
-2000
0
2000
4000
TIME(H)
ERROR(M)
CLOCK ERROR
average position error:
-

95.1 m along track






-

703.6 m radial track





-

80.9 m cross track

average position error:
-

211.7m along track





-

1659.8 m radial track





-

136.4 m cross track

Position computed with all visible satellites (C/No>20dBHz)

Position computed with visible satellites with valid ephemeris


(C/No>20dBHz)

Double block zero padding positioning results

The accuracy of the position is decreased compared to the two other method

Many epochs with no position computed due to lack of acquisition success

26

Percentage of time
where the receiver is
able to compute its
position

(all satellites)

Percentage of time
where the receiver
is able to compute
its position

(satellites with
valid ephemeris)

Average number

of visible

Satellites with

C/No>20dBHz


Average number

of visible satellites

with valid

ephemeris and

C/No>20dBHz

Average number of

Successful

acquisition with

every sat

Average number of

Successful

acquisition with

valid ephemeris

only

1
st

Method

100%

97%

10.2

6.1

10.1

6

2
nd

Method

99.6%

96.8%

10.2

6.1

10.1

6.06

3
rd

Method

98%

88%

10.2

6.1

7.8

5.1

GEOSTATIONARY ACQUISITION
RESULTS

Number Of Successful acquisitions and number of
successful position calculations


Performances in term of accuracy and availability of the measurements for
the double block zero padding method are really inferior compared to the two
other methods


But, computational cost really lower and computational time more than 20
times faster under Matlab

27

GEOSTATIONARY ACQUISITION
RESULTS

Peak Acquisition extrapolation technique

The accuracy of the estimated positions are not good due to the resolution of the

estimated delay (1/2 chip)





extrapolation technique to improve the accuracy of the estimated delay


½ chip

½ chip

y = ax+c

Estimated tau

Extrapolated tau

tau
-
1/2 chip

Tau+1/2 chip

y =
-

a.x+b


assumption:
the autocorrelation function of
the code is a perfect triangle with opposite
slope on both side of the peak



Comparison of the amplitude of the sample
on both side of the peak


The slope «

a

» of the straight line between
the peak and the lowest sample is the
biggest


A straigth line passing by the highest
sample with a slope

a is drawn


Intersection between the two straight line
gives the extrapolated tau

28

GEOSTATIONARY ACQUISITION
RESULTS

New Position results with extrapolated delay

This method only works for the first two methods as it uses delay
-
doppler acquisition matrix

Position error with all
satellites (
improvement
compared without
extrapolation)

Position error with satellites
with valid ephemeris
(improvement compared
without extrapolation)

1+1ms
method


-

27m along track
(43%)


-

210m radial track
(40%)


-

25.5 m cross track
(50%)

-

68m along track
(32%)

-

539 m radial track
(27%)

-

37 m cross track
(44%)

Half Bit
Method


-

22.5m along track
(55%)


-

163 m radial track
(54%)

-

19.5m cross track
(61%)

-

62m along track
(39%)

-

465 m radial track
(37.5%)

-

39.9 m cross track
(42%)

29

Conclusion


Three acquisition techniques in geostationary environment have been studied


The number of usable GNSS satellites is increased by lowering the Data
Demodulation Threshold


To obtain almost continuous positioning, i.e to successfully acquire at least 4 usable
satellites at any time, the duration of the signals to be processed during the acquisition
must be very long for the first two methods
(1+1ms method and Half Bit method):
up to 3
seconds. The double block zero padding method needs less signal


The 1st two methods have heavy computational cost and duration due to the duration
of the signal processed. The double block 0
-
padding method is more than 20 times
faster


The accuracy of the positions are similar with the first two methods. Lower accuracy
with the double block zero padding method.


The average position error is large (>750m) because of the large DOP and the
resolution of the pseudoranges at the output of the acquisition process (only 1/2 chip)


An extrapolation peak acquisition technique reduces the mean error to around 500m