GPS Signals(c)

7/27/2019 GPS Signals(c)

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Understanding GPS Signals &Pseudo Ranging

S.D.P.J. Dampegama

Senior Lecturer / Superintendent of SurveysInstitute of Surveying & Mapping

Diyatalawa -Sri Lanka


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1/29/2005 10:23:11 PM GPSSignals by Dampe 2

Contents

Some Basic Concepts

Wave Equation

Electro Magnetic Waves propagate through

vacuum at a rate of about 300,000 km./sec.(C)This propagation can be expressed by the wave

equation,

C= f

f- Frequency of the Wave

- Wave length


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Energy of a Wave

The energy of an electro magnetic wave is

directly proportionate to the frequency.

E = h fWhere E -Energy


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Wave Modulation

In order to send a wave through long

distances the energy of the wave should be

increased. But this distort the frequency.

One remedy is to load the wave onto a wavewith higher energy known as carrier wave.

This loading is known as modulation and

can be done in many ways.


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Wave Modulation

Different types of Modulation

Amplitude Modulation

Frequency Modulation

Phase Modulation


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GPS Signal Structure

L1 Carrier

P-Code P-CodeC/A Code

L2 Carrier Data Message


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Satellites Atomic Clock gives fundamental frequency 10.23 Mhz.

Two Carrier frequencies L1 & L2

L1= 10.23x154=1575.42 MHz (=19 cm.) L2= 10.23x120=1227.60 MHz (=24 cm.)

Two Code frequencies. Precise Code (P-Code) & Coarse

Acquisition Code (C/A Code). The codes were encrypted on to

the carrier waves by phase modulation.

L1 with P-Code & C/A Code

L2 with P-Code


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GPS Signal StructureC/A code and P code are designed to carry information

from the satellite to the receiver. They are also

impressed on to the carrier frequencies L1 whichcarries both P code & C/A code and L2 carries P code

only.

The Phase modulation used by GPS receivers are

known as binary biphase modulation. Each zero & one

of the binary code is known as code chip. The phase of

the carrier wave (L1 or L2) will change by 180 torepresent each binary code. There for the frequency and

the amplitude of the carrier wave remain unaltered

during the phase modulation.


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As L1 carrier has to carry both P code and C/A code throughthe same phase modulation the codes could be mixed up.

This problem was solve by transmission in quadraturve. The

C/A code modulation in L1 carrier is phase shifted by 90from the P code modulation on the Same Carrier.

C/A Code frequency 1.023 million bits per second (=300

m) repeated in every Millie second. Each satellite broad castsunique C/A code on its L1 frequency.


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P Code frequency 10.23 M/S (=30 m) repeated in every 37

weeks. There fore the chirping rate of P code is ten timesfaster than C/A code. This also defines the satellite uniquely.

Each satellite was given one week portion of P-Code and this

week number is known as the satellites identity. (Space

Vehicle Number or SV number)

Pseudo Random Noise (PRN):

P code & C/A code are so complicated and appear to be noiseas first. But these code can be read in order to grab the

information associated.


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GPS Signal StructureStandard Positioning Service (SPS)

C/A code is designed for most civilian applications. Whichis low in terms of accuracy. ( 100 m.)

Precise Positioning Service (PPS)

P code is designed to get higher degree of accuracy in

positioning and is restricted to users authorized by the

DoD

Selective Availability (SA)

Selective availability is the intentional degradation of

codes.


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Navigation Message:

The navigation message is a 50Hz signal on L1& L2

containing data that describes many parameters required

for the processing.The message is 1500 bits long and divided in to five sub-

frames with 300 bits in each. The time-tagged sub frames

are marked with the time they transmitted by the Satellite.One data frame will get transmitted in 30 seconds.


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Types of GPS Observations

There are two main types of methods to determine position in

GPS.

Pseudo Range observations

Carrier beat phase

Pseudo Range Observations:

Pseudo range observations provide instantaneous positions

and relatively low accuracy when compared with carrierphase measurements. Pseudo range is based on time

measurements. The time difference d is the time taken for

the electro magnetic wave to travel from the satellite to the

receiver.


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How To Measure Time


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Pseudo Range Observations

A position on three dimensional space consists of threeparameters. (x,y,z) Determination of position is equivalent to

solve for three unknowns in mathematics. There for it is

necessary to create three independent equations. In pseudoranging each equation is represented by distance (range) from

a satellite to the receiver.

The range = c x d


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1st Range

(Eqn. 1)

2nd Range

(Eqn. 2)

3rd Range

(Eqn. 3)

Three equations to solve forthree parameters.

(X,Y,Z)UnknownKnown(X,Y,Z)


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Problem:

But the above technique is not practically possible due to errors

associated with the receiver clock. It is impossible to use

precise atomic clock in the receiver due to the price and the

size.

Solution:

By treating the error of the receiver clock as another unknown

the clock error can be computed and corrected.


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1st Range

(Eqn. 1)

2nd Range

(Eqn. 2)3rd Range

(Eqn. 3)

Four equations to solve forfour parameters.Receiver

clock error can be eliminated.

4th Range(Eqn. 4)

(X,Y,Z dt)Unknown(X,Y,Z,dt)Known


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Accuracy of Pseudo Ranging

Pseudo range can be resolved for about 1% of the accuracy ofthe code being used by using good receiver.

For C/A code ( = 300 m.) accuracy = 3 m.

For P code ( = 30 m) accuracy = 30 cm.

Various types of systematic errors are also associated with

GPS observations. In order to reach highest accuracy thesesystematic errors are also to be considered. But with selective

availability the accuracy of positions can be reduced even up

to 100 m.


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How to Reach Better Accuracy

A single receiver observing four or more satellites on its

own to find a position is subjected to various errors and asmentioned earlier the errors can be large as 100 m in

horizontal . ( 160 m in vertical) This accuracy level is not

good enough for most applications.By comparison positions generated by simultaneous data,

most of the systematic errors will get cancelled out and

could reach much better accuracy levels when comparedwith positions obtained by single receiver. This method is

known as differential GPS technology.


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Differential GPS Observations

Error =Computed - ObservedCompute Position

(Contaminated by errors)

Correct the computed positions

by applying error corrections

Base

Rover

Compute Position

(Contaminated by errors)

Unknown Point (X,Y,Z)

Known Point (X,Y,Z)


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Differential Corrections

The base station and rover should receive signals from sameset of satellites in order to apply the differential correction

successfully. This will reduce the errors by substantial

amount.

By applying differential correction to code, positions can be

obtained to an accuracy of0.5-2 m. This is a suitable

accuracy range for most applications.


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GPS Range Error Sources

Error Source Range Error DGPS Range Error

SV Clock 1.0 m.

SV Ephemeris 1.0 m.

Troposphere 1.0 m.

Ionosphere 10.0 m.Pseudo Range Noice 1.0 m 1.0 m.

Multipath 0.5 m. 0.5 m.

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