gps loop mm12_slides

7/29/2019 GPS Loop Mm12_slides

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DANISHGPSCENTER

Carrier Tracking Loop;

Loop FilterGPS Signals And Receiver Technology MM12

Darius Plauinaitis

[email protected]


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DANISH GPS CENTERTodays Subjects

Demodulation of the GPS signal Tracking loop introduction

Carrier tracking

Phase Lock Loop (PLL)

Frequency Lock Loop (FLL)

Loop filters

2009 2Danish GPS Center


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DANISH GPS CENTER

Demodulation

Or how to turn the radio waves back into the data

message that we are interested in



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DANISH GPS CENTERDemodulation

The transmitted signal from satellite k is:

)2cos())()((2

)2sin())()((2

)2cos())()((2)(

22

11

1

tftDtPP

tftDtPP

tftDtCPtS

L

kk

PL

Lkk

PL

L

kk

c

k

+

+

= L1 C/A signal

L1 P(Y) signal

L2 P(Y) signal

D data

C C/A code

P P(Y) code



5/40


The transmitted signal from satellite k is:

After an RF front-end (L1 only):

The signal from one satellite after the ADC(narrow filters and low sampling frequency):

)2cos())()((2

)2sin())()((2)2cos())()((2)(

22

111

tftDtPP

tftDtPPtftDtCPtS

L

kk

PL

L

kk

PLL

kk

c

k

+

+=

)()cos()()()( nennDnCnS ifkkk

+=

)sin())()((2)cos())()((2)( 1 ttDtPPttDtCPtS IFkk

PLIF

kk

c

k +=



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The signal from two satellites after the ADC:

The code phase and the intermediatefrequency of the carrier wave should be

known parameters to demodulate thenavigation data from e.g. satellite 1.

)()cos()()()cos()()()( 222

1

11nennDnCnnDnCnS ifif ++=



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Convert the signal down to baseband:

)()cos()cos()()(

)cos()cos()()()cos()(

12

22

11

11

1

nennnDnC

nnnDnCnnS

ifif

ififif

+

+=

)()cos()cos()()(

)2cos()()()()()cos()(

12

22

11

2111

21

1

nennnDnC

nDnCnDnCnnS

ifif

ifif

+

++=

cos(a)*cos(b) = cos(a+b) + cos(a-b)

)()cos()()(

)cos()()(

)2cos()()()()()cos()(

12

22

21

12

22

21

11

2111

21

1

nennDnC

nnDnC

nDnCnDnCnnS

ifif

ifif

ifif

+++

+

+=



8/40

DANISH GPS CENTERDemodulation Visualized

fIF



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Code wipe off:

After low-pass filtering (integration):

Received signal amplitude vs. tracking errors

Conclusion: perfectly aligned code and carrierreplicas are required to do demodulation.These replicas can be tracked using twotracking loops.

)()2cos()()()()cos()( 1211

211

1 nenDnDnCnnS ifif ++=

)()()()cos()(1

211

1 nenDInCnnS if +==

iiii

i

ii eDR

N

S

Tf

TfI +

= )cos()(2

)(

)sin(

0



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DANISH GPS CENTER

Tracking Loop

A way to generate exact copy of the received signal



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DANISH GPS CENTERWhat does tracking do and

why?

The main goal is to receive the GNSS signalas clear and loud as possible the local

carrier and spreading code must be well

aligned with the ones in the signal

GNSS adds one more requirement: to tracksignal arrival (time) as precise as possible

Advanced receivers can detect multipath to

some extent Additional task can be signal quality

monitoring



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DANISH GPS CENTERThe Tracking Loop Idea

Generate a local signal Correlate it with the received signal

Measure (time/code-phase, frequency, phase)

error between the local and the received

signals

Steer local signal generators to minimize the

error

Pass demodulated data bit value stream to thedata processing task

Repeat procedure



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DANISH GPS CENTERMain Parts Of A Tracking Loop

F(s)

Filter

Kd

K0

/s

VCO

1(s)

2(s)

e(s)

Tracked

signal

Generated

signal

Error

measurement unit

(called error

detector or

discriminator)

The error measurement Scaling of error used to control

sensitivity to the tracking error

Filter has two

main tasks:To filter noise in

the error

measurements

(due to noise in

the tracked signal)

To shape thetracking loops

response to the

tracking errorSignal generator generates

replica of the tracked signal

?



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DANISH GPS CENTERTypes Of Tracking Loops

There are 3 main types of the tracking loopsdepending on the tracked property of the

tracked signal:

Phase lock loop (PLL)

Frequency lock loop (FLL) Delay lock loop (DLL)

There are few error detectors for each type of

the tracking loop with different properties

Variations of filter parameters will shape the

filter response and amount of noise filtering



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DANISH GPS CENTERPlan For The Tracking Topic

PLL (FLL) and DLL are explained in sectionson carrier and code tracking

Each section will also cover a set of error

detectors applicable in a given tracking loop

Tracking loop filter is explained in a separatesection as the same theory is used for all

types of tracking loops



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DANISH GPS CENTER

The Carrier Tracking Loop

The Phase Locked Loop (PLL)



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DANISH GPS CENTERCarrier Tracking Loop

The goal of the Carrier Tracking Loop is to produce aperfectly aligned carrier replica. The most commonway is to use a PLL:

)cos( +nif)cos()( nnD if

)sin( +nif

Quadrature-

phase arm

In-phase arm



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The demodulation in the In-phase (I) branch:

The demodulation in the Quadrature-phase (Q)

branch:

The I signal:

The Q signal:

)2cos()()cos()()cos()cos()(21

21 ++=+ nnDnDnnnD ififif

)cos()(21 nDI=

)2sin()()sin()()sin()cos()(21

21 ++=+ nnDnDnnnD ififif

)sin()(21 nDQ =



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Costas loop:

)cos()(21 nDI=

)cos( +nif

)cos()( nnD if

)sin( +nif

)sin()(21 nDQ =



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To find the phase error:

Phase

delay

-2)tan(

)sin()(

)cos()(

21

21

==

nD

nD

I

Q

)cos()(

)sin()(tan

21

21

1

nD

nD

=

I

Q1tan=

Q

I

2



21/40


The Costas loop is independent on the phase shifts

caused by the data bits

Phasor diagram: An output example:

-8000 -6000 -4000 -2000 0 2000 4000 6000 8000

-4000

-2000

0

2000

4000

Discrete-Time Scatter Plot

I prompt

Qprompt

Q

I



22/40


Different kinds of phase lock loop discriminators:

Arctan

Much time consuming (not a big problem today)

The output is the real phase error

Sign product

Fast method

The discriminator output is proportional to sin()

I

QD 1tan=

)(IsignQD =



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Different kinds of phase lock loop discriminators:



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Costas loop:

)cos()(21 nDI=

)cos( +nif)cos()( nnD if

)sin( +

nif

)sin()(21 nDQ =

Q

I1tan=



25/40


The signal energy in I and Q when PLL has locked on

the signal:



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DANISH GPS CENTER

The Carrier Tracking Loop

The Frequency Locked Loop (FLL)



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DANISH GPS CENTERFrequency Lock Loop

The discrimators are a bit different than inPLL. They measure change in carrier phase

over an interval of time.

Less noise sensitive than PLL it can track at

lower SNR The tracking loop has more noise than PLL

Can be used for the re-acquisition or pull-in

states due to bigger frequency lock range



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DANISH GPS CENTER

Loop Filters


Wh Th Filt I N d d


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DANISH GPS CENTERWhy The Filter Is Needed

Anyway?

The error measurement is there, so justcorrect the generator frequency and job is

done, right?

The answer is NO:

There is an error measurement noise (even at goodSNR)

There is a stady state error caused by Doppler



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DANISH GPS CENTERThe Typical Tracking Loop

Phase error detector has

gain Kd. The transfer

function is showed in

figure a)

The VCO has a center

frequency 0 and gainK0. The transfer function

is showed in figure b)

The filter coefficients

depend on Kd and K0

F(s)

Phase detector Filter

Kd

K0/s

VCO

1(s)

2(s)

e(s)

u

0

ud

e

a) b)

+


An Example Of Filter Output


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DANISH GPS CENTER

There is an initial

frequency between

tracked and generated

signals (27Hz here)

Figures show:

The filter accumulates

offset over time and keeps

it

The result of damping

different convergence

times

An Example Of Filter Output

vs. Input

0.05 0.1 0.15 0.2 0.25 0.3

-20

-10

0

10

20

30

Time (s)

Amplitude

Filtered PLL discriminator

0.05 0.1 0.15 0.2 0.25 0.3

-0.2

-0.1

0

0.1

0.2

Time (s)

Amplitude

Raw PLL discriminator



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DANISH GPS CENTER

The C1 and C2 depend

on loop noise bandwidthBL, VCO and PD gainsand loop damping factor.

Damping factor controlshow fast the filterreaches its settle point

Noise bandwidthcontrols the amount of

allowed noise in thefilter

A Simple Digital Loop Filter

2

0

1)(44

81

TT

T

KKC

nn

n

D

++=

z-1

c2

c1

Filterinput

Filteroutput

2

2

0

2)(44

)(41TT

TKK

Cnn

n

D

++=

14

82 +

=

Ln

B



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DANISH GPS CENTER

2008 Danish GPS Center 33

Determines how much

the loop filter resiststo the control signal: On one hand how fast

the loop will fix thetracking error

On other hand howmuch the loop willovershoot 0 error point

A compromise value isused or few values are

used for differentreceiver modes

Damping Factor

Different loop responses

depending on the damping factor(first 20ms are due to loop filter initialization)

0

20

40

60

80

minatoroutput[]

= 0.

= 0.

= 0. = 0.

= 1.1


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DANISH GPS CENTERNoise Bandwidth

Narrow noise bandwidth decreases noise inthe tracking loop, AND response speed

At 100ms the loop noise bandwidth is

switched from about 100Hz to 15Hz

0 100 200 300 400 500-2600

-2580

-2560

-2540

-2520Carrier frequency offset

Time (ms)

Frequency

offset(Hz)

0 100 200 300 400 500-90

-45

0

45

90PLL discriminator

Time (ms)

Phaseoffs

et[degrees]



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DANISH GPS CENTERNoise Bandwidth

Loop noise

bandwidth also

determines

maximum

Doppler offset

and ratestolerated by the

loop

Figures show a

case of too biginitial frequency

error in

acquisition

0 50 100 150 200 250 300 350 400 450 500-90

-45

0

45

90PLL discriminator

Time (ms)

0 50 100 150 200 250 300 350 400 450 500-101

-100

-99

-98Carrier frequency offset

Time (ms)

Frequency

offset(Hz)



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DANISH GPS CENTER

2008 Danish GPS Center 36

The filter is a first order

filter

The tracking loop

(excluding filter) is a

first order system,

therefore the trackingloop is second order

Higher order filters

approximate the error

dynamics better (e.g. tobe used for ships etc.)

Loop Order

z-1

c2

c1

Filter

input

Filter

output


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DANISH GPS CENTERAn Example Of A PLL

=20/0.7845; T=0.02; k1= 2.4 *

k2= (1.1 * ^2)/20

k3= ^3/20

=20/0.53; T=0.02; k1= 1.414 *

k2= ^2/20 k3= 0


This slide

contents is only

available to the

listeners of our

courses


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DANISH GPS CENTER2-nd Order Loop Responce



39/40

DANISH GPS CENTER3-rd Order Loop Responce



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DANISH GPS CENTER

Questions and Exercises

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