Gps measurements

TRANSMITTING FREQUENCY

C/ A and P(Y) codes

P(Y) codes

Vrince Vimal,CSED BAHIR DAR
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•Very accurate ,reference is atomic frequency standard
•The reference frequency is off by−4.567 × 10−3 Hz to

take the relativistic effect into consideration.
•Reference frequency used by the satellite is

10.229999995433 MHz
•Doppler frequency shift produced by the satellite
motion at L1 frequency is approximately ±5KHz

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•The C/ A and P(Y) code in the L1 are in quadrant
phase of each other and can be written as:

Where,
SL1 = signal at L1 frequency
Ap = the amplitude of the P code
P(t) =±Phase of P code
D(t) =±data code
Ø
= the initial phase
Ac
=the amplitude of the C/ A code
C(t) =±phase of C/A code

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Codes
There are basically two types of codes:-

•Coarse (or clear)/ acquisition (C/ A)
•Precision (P) codes
•Coarse / acquisition (C/ A)
•Bi-phase modulated with a chip rate of 1.023 MHz
•chip is about 977.5 ns (1/ 1.023 MHz) long
•C/ A code contains the main lobe and several sidelobes
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• C/ A code is 1 ms long i.e 1,023 chips last 1 ms and
repeats after every ms

•Every satellite has its own C/A code
Data Format

1st row shows a C/ A code with 1,023 chips;
2nd row shows a navigation data bit;

5th row shows a page

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Precision (P) codes
•Bi-phase modulated at 10.23 MHz

•Chip length is about 97.8 ns (1/ 10.23 MHz)
• It is generated from two pseudorandom noise (PRN)

codes with the same chip rate.
•One has 15,345,000 chips an other has 15,345,037
chips

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•There are no common factors between them i.ecode
length
generated by these two codes is 23,017,555.5 (1.5 ×
15,345,037)
seconds, which is slightly longer than 38 weeks.
•Navigation data rate carried by the P code through
phase
modulation is at a 50 Hz rate

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IONOSPHERIC DISPERSION EFFECTS
•The ionosphere generally region with altitude of

50 to 1000 km with free electrons
•GPS signals, propagating through an ionized
medium, are affected by the non-linear
dispersion characteristics of this medium

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The change in path length due to the ionosphere is

Where,
ρ=Change in path length
n=Index of Refraction
GPS codes are dependent upon the group inx of refraction
∴ ionospheric group delay is

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& ionospheric phase delay is

Where,

ng group index of refraction = vg / c.
np phase index of refraction = vp / c,
NT total no of electrons in electrons/m2

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TROPOSPHERIC EFFECTS
•Troposphere is regions up to 80 km in altitude

•Troposphere is not dispersive for frequencies below30 GH
•Tropospherich Refraction may be conveniently separated
into 'dry' and 'wet' components.
•The dry component can be approximated by
DTC = 2.27 • 10-3 P0
P0 is thesurface pressure (in mbar)
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•The dry term contains approximately 90% of the total
zenith range error

•The wet component depends on the atmospheric
• Conditions all along the signal path Some of factors

effecting are the water vapour content, temperature,
altitude,the elevation angle of the signal path

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RINEX format
•It is a internationally accepted data exchange format

& is in the standard ASCII format
•A RINEX file is a translation of the receiver.s own
compressed binary files.
•A draft version of the RINEX format was introduced in
1989 followed by a number of updates to
accommodate more data types
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•The current RINEX version 2.10 defines six
different RINEX files:-

(1) Observation data file,
(2) navigation message file

(3) meteorological file
(4) GLONASS navigation message file
(5) geostationary satellites
(6) satellite and receiver clock data file
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The naming convention for RINEX files is “ssssdddf.yyt.”
•ssss-represent the station name

•ddd-represent the day of the year of first record
•f-represents the file sequence number within the day

•yy-represent the last two digits of the current year
•t-represent the file type

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LINEAR COMBINATIONS OF OBSERVATIONS

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•Certain combinations of the basic code pseudo-range,
or carrier beat phase observables are required for different
type of application and the level of accuracy one
seeks from GPS,
•Many different differencing combinations are possible
1. first between receivers,
2. then between satellites,
3.

lastly between epochs.
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The notation we use for taking these differences is:•Δ denotes differences between two receivers

•▽ denotes differences between two satellite
•Δ denotes differences between two epochs

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BETWEEN-EPOCH (DOPPLER) SINGLE
DIFFERENCES

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•Frequency at GPS receiver is different than frequency
transmitted by the satellite this is due to the

Doppler effect.
•The basic GPS Doppler observable is essentially the

change of phase between two epochs
•The corresponding between-epoch single
difference (Doppler) equation is

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We get,

Some techniques,
1. Intermittently Integrated Doppler (IID)
2. Consecutive Doppler Counts (CDC)
3. Continuously Integrated Doppler (CID)

Q.1. carrier phase Vs IID
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BETWEEN-RECEIVER SINGLE DIFFERENCES

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•2 stations observing the same satellite, the
mathematical model for a between-receiver single

difference pseudo-range observable obtained
from P- or C/A-code
•It can be derived by differencing two simultaneous
pseudo-ranges as

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We get,

•This greatly reduce the effects of errors associated
with the satellites:
•satellite clock errors,
•orbit errors and atmospheric delays

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BETWEEN-SATELLITE SINGLE DIFFERENCES

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•Between -satellite single difference is formed by
differencing the observations of two satellites by

single receiver
•The mathematical model of the between-satellite
single range difference

We get

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RECEIVER-TIME DOUBLE DIFFERENCES

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•It is the change from one epoch to the next, in the
between-receiver single difference for the same satellite.

The equation for the receiver-time double difference
carrier beat phase observable is

•This allows an easier editing of cycle slips

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RECEIVER-SATELLITE DOUBLE DIFFERENCES

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The receiver-satellite double difference can be
constructed either by:

• taking 2 between-receiver single difference observables,
involving the same pair of receivers but different satellites

• taking2 between-satellite single difference observables,
involving the same pair of satellites but different receivers
The two results, i.e., Δ▽(.) and ▽Δ(.), are identical.

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•The receiver-satellite double difference observation
equation, for pseudo-range measurements is

Double differences remove, the effects of
•Errors due to misalignment between the 2receiver clocks
•Errors due to misalignment between the satellite clocks
Q.2RECEIVER-SATELLITE TRIPLE DIFFERENCES
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CYCLE SLIPS
If the satellite signal is blocked in any way, it can’t be
tracked anymore, When signal is lock again, the fractional
part of the measured phase would still be the same as if
tracking had been continuous.The integer cycle however is
discontinuous this is cycle slip

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There are couple of approaches to dealing with this
problem

•Manually
•Piecewise continuous polynomial
•Between-receivers, satellites, and time triple difference

•Q3. Clock errors

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Gps measurements

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Gps measurements