Week-1 Module-2 How position is determined by the GNSS - Part-I.pdf

Global Navigation Satellite Systems and Applications
How position is determined by the GNSS? (Part-I)
Dr. Arun K. Saraf,
Professor
Department of Earth Sciences
1

2
Basic principles of satellite navigation
• All GNSS use the same basic principles to estimate position:
• Satellites with a known position transmit a regular time signal.
• Based on the measured travel time of the radio waves
electromagnetic signals travel through space at the speed of light
(299,792,458 metres per second) the position of the receiver is
calculated.
https://www.u-blox.com/sites/default/files/products/documents/GPS-Compendium_Book_%28GPS-X-02007%29.pdf

3
• Imagine that we are in a car and need to determine our position on a long and straight
street.
• At the end of the street there is a radio transmitter sending a time signal pulse every
second.
• The car is carrying a
clock, which is
synchronized to the
clock at the
transmitter.
• By measuring the
elapsed travel time
from the transmitter
to the car we can
calculate our position
on the street.

4
• The distance D is calculated by multiplying the travel time ∆t by the velocity of light c:
D = ∆t x c
• Because the time of the clock on-board, our car may not be exactly synchronized with
the clock at the transmitter and there can be a discrepancy between the calculated
and actual distance travelled.
• In navigation this observed distance referenced to the local clock is referred to as
pseudorange.
• In our example a travel time ∆t of one microsecond (1μs) generates a pseudorange of
300m.

5
• The solution involves using a second synchronized time signal transmitter, for which
the separation (A) to the first transmitter is known.
• By measuring both travel times it is possible to exactly establish the distance (D)
despite having an imprecise on-board clock.
With two transmitters it
is possible to calculate
the exact position despite
time errors.

6
• The solution involves using a second synchronized time signal transmitter, for which
the separation (A) to the first transmitter is known.
• By measuring both travel times it is possible to exactly establish the distance (D)
despite having an imprecise on-board clock.
𝑫 =
∆t𝟏 − ∆t𝟐 ∗ 𝒄 + 𝑨
𝟐

7
• To exactly calculate the position and time along a line one requires two time signal
transmitters.
• From this we can draw the following conclusion: When an unsynchronized onboard
clock is employed in calculating position, it is necessary that the number of time signal
transmitters exceed the number of unknown dimensions by a value of one.
• For example:
• On a plane (expansion in two dimensions) we need three time-signal transmitters.
• In three-dimensional space we need four time-signal transmitters.

8
• Satellite Navigation
Systems use
satellites as time-
signal transmitters.
• Contact to at least
four satellites is
necessary in order
as well as the exact
time.

Satellites
Navigation message includes:
GNSS date and time
Satellite status and health
Satellite ephemeris data, which
allows the receiver to calculate the
satellite’s position.
https://www.e-education.psu.edu/geog862/node/1734
Ephemeris: A set of satellite orbital parameters
that are used by a GNSS receiver to calculate
precise GNSS satellite positions and velocities.
The ephemeris is updated periodically by the
satellite to maintain the accuracy of GNSS
receivers.
National Electrical Manufacturers
Association

10
NMEA-0183 message: GGA
An example of the GBS message string
is:
$GPGGA,172814.0,3723.46587704,N,1
2202.26957864,W,2,6,1.2,18.893,M,-
25.669,M,2.0,0031*4F
GGA message fields
Field Meaning
0 Message ID $GPGGA
1 UTC of position fix
2 Latitude
3 Direction of latitude:
N: North
S: South
4 Longitude
5 Direction of longitude:
E: East
W: West
6 GPS Quality indicator:
0: Fix not valid
1: GPS fix
2: Differential GPS fix, OmniSTAR VBS
4: Real-Time Kinematic, fixed integers
5: Real-Time Kinematic, float integers, OmniSTAR XP/HP or Location RTK
7 Number of SVs in use, range from 00 through to 24+
8 HDOP
9 Orthometric height (MSL reference)
10 M: unit of measure for orthometric height is meters
11 Geoid separation
12 M: geoid separation measured in meters
13 Age of differential GPS data record, Type 1 or Type 9. Null field when DGPS is not used.
14 Reference station ID, range 0000-4095. A null field when any reference station ID is selected and no
corrections are received1.
15 The checksum data, always begins with *

Satellites
Navigation message also includes:
Almanac, which contains information
and status for all GNSS satellites
Almanac: A set of orbital parameters that
allows calculation of approximate GNSS
satellite positions and velocities. The
almanac is used by a GNSS receiver to
determine satellite visibility and as an aid
during acquisition of GNSS satellite signals.
Note that the almanac is the same for all satellites
whereas the ephemeris is unique to each satellite.
TLM = Telemetry
HOW = Handover Word

Reception
• Receivers need at least 3 satellites to obtain 2D position and 4 satellites for
3D position. If more are available, these additional observations can be
used to improve the position solution
• GNSS signals are modulated by a unique pseudorandom digital sequence,
or code. Each satellite uses a different pseudorandom code
• Pseudorandom means that the signal appears random, but actually repeats
itself after a period of time
• Receivers know the pseudorandom code for each satellite. This allows
receivers to correlate (synchronize) with the GNSS signal to a particular
satellite
• Through code correlation, the receiver is able to recover the signal and the
information they contain

13
• Every navigation satellite is equipped with an atomic clock that keeps time with
exceptional accuracy.
• Similarly, every GNSS receiver also includes a clock.
• The time kept by these clocks is used to determine how long it takes for the
satellite’s signal to reach the receiver.
• More precisely, GNSS satellites broadcast “pseudo-random codes” which contain
the information about the time and orbital path of the satellite.
• The receiver then interprets this code so that it can calculate the difference
between its own clock and the time the signal was transmitted.

14
• When multiplied by the
speed of light, the difference
in times can be used to
determine the distance
between the satellite and
receiver.
• Generally, GNSS
constellations are configured
to have signals from
minimum four satellites
everywhere on Earth.

• For each satellite tracked, the receiver determines the propagation time
• The above figure shows the transmission of a pseudorandom code from a
satellite. The receiver can determine the time of propagation by comparing
the transmit time to the receive time
Reception
https://giphy.com/gifs/-kickoff-coverages-history-of-the-32-in-32--eWuNDuFMQZ1Xq

Computation
• For each satellite tracked, the receiver
calculates how long the satellite signal took
to reach it, which in turn, determines the
distance to the satellite:
• Propagation Time = Time Signal Reached Receiver
– Time Signal Left Satellite
• Distance to Satellite = Propagation Time * Speed of
Light
• Receiver now knows where the satellite was
at the time of transmission through the use
of orbit ephemeries.
• Through trilateration, the receiver calculates
its position.

17
Computation
• GNSS is often compared to
triangulation, which is actually not
entirely correct. More correct would
be trilateration.
• Trilateration is based upon distances
rather than the intersection of lines
based on angles.
• In a terrestrial survey, there would
probably be a minimum of three control
stations, and from them would emanate
three intersecting distances, i.e., L1, L2,
and L3.
• Instead, they are measured to satellites
orbiting in nearly circular orbits at a
nominal altitude of about 20,200 km
above the earth.

18
• Both techniques rely exclusively on the measurement of distances to fix
positions.
• One of the differences between them, however, is that the distances (ranges),
are not measured to control points on the surface of the earth.
• This is very similar to what's done with GNSS, except instead of the control
points being on the surface of the Earth, they are orbiting the Earth.
• The GNSS satellites are the control points orbiting about 20,200 km above the
Earth.
Computation

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• There's another difference; instead of there being three lines intersecting at the
unknown point, there are four.
• Four are needed because there are four unknowns - X, Y, Z, and time - that need to
be resolved.
• There are also some similarities between terrestrial surveying and the GNSS
solution. The distances need to be paired with their correct control points in both
cases.
• Another is that the distances are measured electronically based upon the speed of
light and the amount of time that the signal takes to go from the control point to the
unknown point.
Computation

20
Computation
https://www.quora.com/in/Why-are-four-GPS-satellites-required-to-locate-my-position
• Time measurement is essential to
GNSS surveying in several ways.
• For example, the determination of
ranges, like distance
measurement in a modern
trilateration survey, is done
electronically.
• In both cases, distance is a
function of the speed of light, an
electromagnetic signal of stable
frequency and elapsed time.

21
Computation
https://www.quora.com/in/Why-are-four-GPS-satellites-required-to-locate-my-position
• Both GNSS surveys and trilateration surveys begin from control points.
• In GNSS, the control points are the satellites themselves; therefore, knowledge of
the satellite's position is critical.
• The ranges are measured with signals that are broadcast from the GNSS satellites to
the GNSS receivers in the microwave part of the electromagnetic spectrum; this is
sometimes called a passive system.
• GNSS is passive in the sense that only the satellites transmit signals; the users simply
receive them.
• The time is one of the unknowns that needs to be resolved to provide a position on
the Earth using GNSS.

22
Computation
A GNSS signal must somehow
communicate to its receiver:
1. What time it is on the satellite?
2. The instantaneous position of a
moving satellite
3. Some information about
necessary atmospheric
corrections; and
4. Satellite identification system to
tell the receiver where it came
from and where the receiver may
find the other satellites.

23
Computation
• One aspect is the time on the satellite, because, of course, the elapsed time that the
signal spends going from one place to the other is the basis of the distance
measurement - ranging.
• Therefore, it is important to know the time on the satellite the instant that the signal
sent.
• Secondly, the position of the moving satellite at an instant is critical.
• The coordinate of the satellite at that moment of measurement is important so that
it can be used to derive the position of the receiver.

24
Computation
• In a terrestrial survey, instantaneous position hardly comes into it because the
instrument on the control point is stationary on the Earth's surface.
• Satellites, on the other hand, are moving at a pretty tremendous rate of speed
(14,000 km/h) relative to the GNSS receiver, so the ephemeris needs to provide the
coordinates of the satellites at an instant of time.

25
Computation
• The GNSS signal is going through a good deal more of the atmosphere.
• The first component of the atmosphere that the GNSS signal encounters is the
ionosphere. The ionosphere has some characteristics that differ from the next
atmospheric layer the signal encounters, the troposphere.
• In any case, the signal can be attenuated rather dramatically during its trip. It follows
that it is important to have some representation of the atmosphere through which
the signal is passing communicated to the GNSS receiver from the satellite.
• This is so that the resultant delays can be introduced into the calculation of the
GNSS derived position of the receiver.

26
Computation
Further, satellite identification system is also required. Each distance that the receiver
measures from each satellite must be correlated to that satellite.
Since the receiver will need to have at least four distances from at least four different
satellites, it needs to be able to assign the appropriate range, to the correct satellite.
It needs to identify the origin of each signal.
This is just some of the information that needs to come down on that signal from the
satellite to the receiver. It's quite a list and is actually even a little bit longer than this.

Week-1 Module-2 How position is determined by the GNSS - Part-I.pdf

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Week-1 Module-2 How position is determined by the GNSS - Part-I.pdf