GPS and Navigation
Subject Topics:
Geography, Geometry and Trigonometry
GPS and Navigation
How have humans navigated their world, in the
past, and in the present?
What does GPS stand for?
How do you think GPS works? What is
involved?
Early Greek Contributions to Navigation
There’s a lot that goes into GPS. Here are
some of the organizations involved:
Click on each symbol or banner to go to their websites to learn more.
The home of the
discovery of GPS and
research operations for
the Navy.
Department of Defense
The Nat. Geodetic Survey is responsible for maintaining
the National Spatial Reference System and the
Continuously Operating Reference Station network.
US Naval Observatory
The US Geodetic Survey Runs the Continuously Operating
Reference Station (CORS) network across N. America.
Our Nearest
Stations Are:
Can you find your
nearest CORS
Location?
Click Here to Find
Them.
What Satellites are Overhead Right Now?
Click the satellite picture to find out.
How Do Satellites and GPS units
communicate?
•31 satellites
•Radio Waves (mechanical waves)
•Pseudo Random Code (PRC)
•Atomic clocks and accurate time
•Geodesy (accounting for the uneven
features of the Earth’s surface)
•Mathematical equations
•What else?
How long does it take a radio signal from a
satellites to reach your GPS unit?
Distance (D)= time it takes the satellite radio wave to travel (T)
x Speed of light (300 km/ms)
or D=T x (300/ km/ms)
What is the difference between satellites using
triangulation and trilateration?
c
a
b
Triangulation
Trilateration
GPS and Navigation
Triangulation: Where in the World?
90° latitude (+)
Longitude and Latitude
0° latitude
90° latitude ()
http://oceanservice.noaa.gov/education/lessons/plot_course.html
There are 60 minutes per degree of longitude
or latitude, written as ('), and there are 60
seconds per minute (").
If you were looking at the top of the Earth, from
the North Pole, much like looking down at the
face of a clock, fill in the degrees of longitude on
the diagram below starting with the prime
meridian (0°) at 6 o’clock.
Convert degrees of longitude and latitude into precise
minutes and seconds:
Decimal x 60 = minutes (') remaining decimal x 60 = seconds (")
EXAMPLE: Longitude of 77.023
Remember: Degrees remain the same
.023 x 60 = 1.38, so 1 becomes the minutes 77°1'
.38 x 60 = 22.7994 becomes the seconds so 77⁰ 1' 22.7994"
Convert degrees of longitude with minutes and seconds
back into degrees only:
Degrees + (minutes/60) + (seconds/360)
Click here for the National Geodetic Society Online Converter
for degrees into minutes and seconds.
Practice Converting
Degrees of Longitude and
Latitude into Minutes and
Seconds and Then Find
and Label the Locations on
Student Map 1.
What is the significance of
each location?
Location
US Navy Yard
USNA
Memorial
Washington
Memorial
US Naval
Observatory
National
Gallery of Art
Longitude
(degrees)
38.889°
GPS Units
(Longitude)
Latitude (degrees)
77.009°
38.8723°
76.995°
38.889°
77.049°
38.920°
77.066°
38.891°
77.0199°
GPS Units
(Latitude)
How are the
streets in
Washington
DC laid out?
How are the
streets labeled
and
numbered?
How is a road
number
determined?
What are the
quadrants?
Can you find
the state
circles?
Why would
this system be
useful for
navigation?
When Measuring Distances with GPS What Are
Confidence Intervals? WAAS Values?
Distance (d) measured using GPS
from point to point
Shortest possible distance
confidence interval (Sd):
D - 2(WAAS value)= Sd
Longest possible distance
confidence interval (Ld):
D + 2(WAAS value)= Sd
Calculate the confidence interval for the shortest possible distance and longest possible
distance from the steps of the US Capitol to the National Gallery of Art. You measured the
distance on your GPS to be 800 m, your WAAS is 10 m.
Shortest possible distance
confidence interval (Sd):
D - 2(WAAS value)= Sd
Longest possible distance
confidence interval (Ld):
D + 2(WAAS value)= Sd
Confidence intervals are written as:
(Sd) ≤ d ≤ (Ld) or d € (Sd , Ld)
Longest Possible Confidence Interval = _______ m
Distance (d)= _______ m
_____ m
National
Gallery of
Art, GPS
Position
_____ m
Shortest
Possible
Confidence
Interval =
_______ m
US Capitol,
GPS Position
Navy Fitness and GPS Challenge Scenario:
Location
Point 1
2nd Street & Independence Ave. SW
Point 2
2nd Street & Constitution Ave. NW
Midpoint (W) Midpoint of Mall 2nd St. between
Independence and Constitution Ave.
Point 3
14th Street & Constitution Ave. NW
Point 4
14th Street & Independence Ave. SW
Midpoint (E) Midpoint of Mall 14th St. between
Independence and Constitution Ave.
Long.
38°53'15.17"N
38°53'31.01"N
Lat.
77° 0'12.67"W
77° 0'12.61"W
38°53'23.21"N
38°53'31.29"N
38°53'15.09"N
77° 0'12.67"W
77° 1'54.90"W
77° 1'55.03"W
38°53'23.17"N
77° 1'54.90"W
Confidence Intervals (What was your WAAS Value Again?)
Distance (d)
Length (m)
Point 1 to Point 2 (a)
487 m
Point 2 to Point 3 (b)
2,465 m
Point 3 to Point 4 (a)
490 m
Point 4 to Point 1 (b)
2,462 m
Midpoint W to Midpoint E
2,464 m
Confidence Interval
To meet the standards in the Navy’s scenario the Mall must be a rectangle and not a
parallelogram, meaning it must have 90° angles at the corners. Check for right angles
using the Pythagorean Theorem to find the lengths of the two diagonals:
c2 = a2 + b2 or c=√ a2 + b2
Rectangle
or
Parallelogram?
b
c
a
But Wait! How do we account for the variability of
our data and confidence values when calculating
angles?
To account for data variability and range of error you have to use
calculus to account for the WAAS value which was 6m total
(represented by ∆). The equation would be:
∆a=6 m
∆b=6 m
Calculate for ∆c
∆c = (a x ∆a + b x ∆b)
√ a2 + b2
Why would ∆c be larger than your WAAS value?
Wrap Up:
• Name and explain the role of the different organizations that contribute to the
maintenance of GPS satellites, coordinates, accuracy, and accurate time keeping.
• What is the difference between triangulation and trilateration? Explain how they
are used by GPS units and satellites.
• What are some factors that might affect successful GPS measurements? Explain.
• When measuring distances between two points, what are confidence values and
how do they affect how individuals find their locations?
• Discuss how GPS technology might be useful when creating records of naval
navigation, crime scenes, tracking animal populations, or even archaeology.
Cartographer
Tracking Marine
traffic
(click on the image to visit
this site)
•provide any advantage to speed and reaching your destination!
Plotting a Course and Velocity Made Good (VMG)
Ground Track
Boat Speed
Start
Point
NAVIGATION TERMINOLOGY
•
Knot (kt)
•
Speed Over Ground (SOG)
•
Course Over Group (COG)
•
Rhumb Line
•
Velocity Made Good (VMG)
•
Course Offset
•
Cross Track Error (XTE)
XTE
VMG
Rhumb Line
DEFINITION
Destination
VELOCITY MADE GOOD TABLE
Angle
5
10
15
20
25
30
35
40
45
50
55
60
65
70
%
.4%
1.5%
3.5%
6.4%
10.3%
15.5%
22.1%
30.5%
41.4%
55.6%
74.3%
100%
136.6%
192.4%
2
2
2
2.1
2.1
2.2
2.3
2.4
2.6
2.8
3.1
3.5
4
4.7
5.8
2.5
2.5
2.5
2.6
2.7
2.8
2.9
3.1
3.3
3.5
3.9
4.4
5
5.9
7.3
3
3
3
3.1
3.2
3.3
3.5
3.7
3.9
4.2
4.7
5.2
6
7.1
8.8
3.5
3.5
3.6
3.6
3.7
3.9
4
4.3
4.6
4.9
5.4
6.1
7
8.3
10.2
4
4
4.1
4.1
4.3
4.4
4.6
4.9
5.2
5.7
6.2
7
8
9.5
4.5
4.5
4.6
4.7
4.8
5
5.2
5.5
5.9
6.4
7
7.8
9
10.6
5
5
5.1
5.2
5.3
5.5
5.8
6.1
6.5
7.1
7.8
8.7
10
5.5
5.5
5.6
5.7
5.9
6.1
6.4
6.7
7.2
7.8
8.6
9.6
6
6
6.1
6.2
6.4
6.6
6.9
7.3
7.8
8.5
9.2
10.5
6.5
6.5
6.6
6.7
6.9
7.2
7.5
7.9
8.5
9.2
10.1
7
7
7.1
7.2
7.4
7.7
8.1
8.5
9.1
9.9
10.9
7.5
7.5
7.6
7.8
8
8.3
8.7
9.2
9.8
10.6
8
8
8.1
8.3
8.5
8.8
9.2
9.8
10.4
C= (X-Y)
C= (Y-X)
Rhumb Line
Draw and label:
• Course over ground above
the rhumb line (COG).
• Angle between your COG
and true North (Y).
• Angle between the rhumb
line and true North (X).
C= Course offset
X= Angle between magnetic north and the Rhumb line
Y= Course over ground angle (COG)
Rhumb Line
Draw and label:
• Course over ground below
the rhumb line (COG).
• Angle between your COG
and true North (Y).
• Angle between the rhumb
line and true North (X).
Click here to
view a
slideshow
about the Naval
Research
Laboratory
Arctic Research
Initiative.
Click here to
visit the Naval
Postgraduate
School Arctic
Modeling Effort
ARCTIC ICE NAVIGATION
CHALLENGE
On the map draw a star
at your starting point at
the Eastern most
entrance of the
Northwest Passage. Also
label Baffin Bay and the
Gulf of Boothia.
Wrap Up:
• Explain how GPS is used to track marine traffic and shipping trade and
how this information might be used.
• Explain a rhumb line and course offset angles and how they are used in
navigation.
• What is velocity made good?
• Describe how to use GPS to calculate velocity made good and course
offset angles.
• How can GPS technology be useful to scientists when studying climate
change?