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NAVIGATION

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Title: NAVIGATION


1
NAVIGATION
  • The science of determining the position of a
    vehicle relative to the position of its
    destination

2
NAVIGATIONUnits and Conventions
  • Distance Nautical Mile (NM) 1852m exactly
  • Speed Knot (kt) 1 NM/hour
  • Angle degrees measured Clockwise from North and
    is always expressed as three digits e.g. 090,
    006. Note zero is pronounced zero

3
North
  • Two main North references
  • True (T) the geographical North Pole(the point
    at which the earths spin axis intersects the
    earths surface in the Northern hemisphere)
  • Magnetic (M) the North magnetic pole
  • VARIATION is the differencebetween True and
    Magnetic North

4
North
  • Conversion from Magnetic to True and Vice Versa
  • Variation is usually given as West or East
    depending on whether the Magnetic Pole appears to
    be West or East of the True Pole
  • East Variation is considered positive ()
  • True direction Magnetic direction Variation

5
Magnetic and True North
MAG
TRUE
14?
VARIATION
6
Pole Migration
7
Units and Conventions (Continued)
  • Heading The angle between the longitudinal axis
    of a vehicle and the North reference (can be
    either Magnetic or True)
  • Relative Bearing The angle between the
    longitudinal axis of the vehicle and a line
    joining the vehicle and the point in question

8
Units and Conventions
9
Navigation
  • Lines of Position

10
Navigation
  • Position Fix

11
Navigation
  • Position Fix Geometry

12
Requirements for an Air Navigation System
  • Accuracy(Allowable Error)
  • Integrity
  • Availability
  • Continuity

These all depend on the phase of flight
13
Phases of Flight
  • Enroute least restrictive
  • Usually at cruising altitude - no
    obstaclesstable situation, no conflicting
    traffic
  • Terminal Area more restrictive
  • Lower altitude possible obstaclesless stable
    situation, probable conflicting traffic
  • Approach and Landing most restrictive
  • Very low altitude obstacles present
  • on collision course with the ground - must make
    sure it is the runway!!

14
Accuracy
  • Two main types of ERROR
  • Flight Technical ErrorThe difference between the
    actual position of the aircraft and the required
    position given by the navigation system
  • System ErrorThe difference between the position
    given by the navigation system and the true
    position

15
Requirements for Accuracy (95)
  • Enroute
  • 12.4NM (Oceanic), 2.0 NM (Continental)
  • Terminal Area
  • 0.4 NM
  • Landing
  • Category I (Limits of 200Ft ceiling and ½ NM
    visibility)
  • 16. m laterally and 8 m vertically

16
Integrity
  • The ability of the system to warn the pilot when
    an out-of-tolerance condition is detected
  • Enroute
  • 5 minutes
  • Terminal Area
  • 30 seconds
  • Landing
  • Category I - 6 seconds
  • Category II and III 1 second

17
Availability
  • The probability that the required navigation is
    usable
  • All Modes
  • .99 to .99999

18
Continuity
  • The probability that the required navigation is
    available for the duration of a procedure once
    the procedure has been started
  • Enroute/Terminal
  • 10-5/hr
  • Landing
  • 10-6/15sec (Cat I)

19
Relative Navigation Systems
  • These systems allow an aircraft to determine its
    position relative to a ground-based station
    (usually called a facility)
  • Most provide a bearing to (or from) the facility
  • They are almost always used as intermediate
    points enroute
  • Thus the aircraft is usually flying directly
    toward or away from the facility

20
Relative Navigation Systems
Airway Structure between Ottawa and Toronto
21
Examples of Relative Navigation Systems
  • Nondirectional Beacon/Automatic Direction Finder
    (NDB/ADF)
  • VOR (VHF Omnirange)
  • TACAN (Tactical Air Navigation)
  • DME (Distance Measuring Equipment)

22
Nondirectional Beacon
  • The oldest (and simplest) navigation system in
    general use a simple transmitter radiating in
    an omidirectional radiation pattern
  • Frequency of Operation 200 to 500 kHz
  • Power 20 W to several kW
  • Modulation 1020Hz tone Morse Code Identifier
  • Propagation Ground Wave

23
Automatic Direction Finder (ADF)
  • The airborne part of the system is the ADF
  • Its purpose is to provide the pilot with a
    relative bearing from the aircraft to the NDB
  • This is done using the directional property of a
    loop antenna

24
ADF (1)
  • The loop antenna is mounted so that it can rotate
    about the vertical axis and its orientation is
    controlled by a servomotor
  • The antenna is rotated until the receiver detects
    the null after which the null is tracked
  • The relative angle of the antenna is transmitted
    to the cockpit via a synchro system

25
ADF Antenna Patterns
26
ADF

ADF Bearing Indicator
27
ADF

Old ADF Antenna Installation
28
ADF (2)
  • The rotating loop antenna installation is large
    and causes excess drag and icing problems
  • It is also mechanical which reduces its
    reliability
  • Thus most modern ADF systems use a crossed loop
    system

29
Crossed Loop ADF
  • A ferrite loop antenna consist of a bar of
    ferrite material about which is wound many turns
    of fine wire
  • The ferrite concentrates the RF magnetic field
    and allows a sensitive antenna to be constructed
    in a small space.

30
Crossed Loop ADF
31
Crossed Loop ADF
32
ADF Advantages
  • Cheap
  • Reliable
  • Available (over 500 installed in Canada)
  • Commercial AM radio stations can be used in an
    emergency (positions of stations are given in
    aeronautical publications)

33
ADF Disadvantages
  • Only Relative Bearing Available
  • Difficult to Automate
  • Susceptible to Low Frequency propagation effects.
    (skip, refraction, sky wave interference)

34
ADF as a Navigation System
  • Accuracy 4.5 degrees
  • Availability 99.9
  • Integrity Receiver monitors RF level flag
    on indicator shows if level drops too low.

35
VOR (VHF Omnirange)
  • Frequency 108-112MHz (even tenths) 112-118MHz
    (every 0.1 MHz)
  • RF Power Level Output (Ground Station)
  • 100W

36
Bearing Systems
  • General Principle
  • Need two signals
  • 1. One whose phase varies with bearing from (or
    to) the transmitter
  • 2. A reference signal whose phase is constant
    regardless of bearing
  • Lighthouse example

37
VOR
  • In VOR, the variable signal is provided by a
    limacon antenna pattern which rotates clockwise
    at 30Hz.
  • Note a limacon has the equation
  • Thus an observer at any point measures an RF
    signal , amplitude modulated at 30 Hz

38
VOR
VOR ANTENNA PATTERN
39
VOR REFERENCE SIGNAL
The Reference Signal is radiated in an
omnidirectional pattern. It is amplitude
modulated by a 9960Hz subcarrier. This, in turn,
is frequency modulated at 30Hz The FM (reference)
modulation is in phase with the variable pattern
when the observer is North of the station (can be
referenced to Magnetic or True)
40
VOR SIGNAL GENERATION
Note the 1020Hz identifier
41
ANTENNA ARRAYS
  • It is often impossible to generate a desired
    antenna pattern with just one antenna
  • Using two or more antenna elements provides the
    designer with more design variables e.g.
  • Number of elements
  • Physical arrangement of elements
  • Amplitude and Phase of input signals

42
ANTENNA ARRAYS
Two Element Example
l/2
Antenna Pattern
Transmitter
43
ANTENNA ARRAYS
Two Element Example
l/2
Antenna Pattern
90deg
Transmitter
44
VOR ANTENNA
45
VOR TRANSMITTER
46
VOR RECEIVER
47
VOR RECEIVER
HSI (HORIZONTAL SITUATION INDICATOR)
48
VOR ERRORS
  • Since the system depends on the antenna pattern,
    any distortion of the pattern will cause errors
  • Internal sources of error
  • antenna or feed mismatch
  • External sources of error
  • Reflections from buildings, terrain, trees, etc

49
DOPPLER VOR
  • Sometimes a particular site has too many
    reflecting objects to permit the operation of a
    standard VOR
  • In this case, a Doppler VOR is installed.
  • This permits a large aperture antenna array to be
    used,i.e. an antenna array covering a large
    area.
  • A large antenna array uses space diversity

50
DOPPLER VOR
EFFECT OF APERTURE
51
DOPPLER VOR
  • If an antenna, radiating a signal at a carrier
    frequency fC , is placed on the edge of a
    platform which rotates at an angular rate w, a
    receiver at a distance will observe that the
    carrier is frequency modulated at the angular
    frequency w.
  • This is due to the Doppler shift caused by the
    relative motion of the antenna and receiver .

52
DOPPLER VOR
vwr
fRfCv/c
53
DOPPLER VOR
Note To maintain the correct relationship between
reference and variable signals, the signal
rotation is counterclockwise
fc
54
DOPPLER VOR
55
VOR as a NAVIGATION AID
  • Accuracy 3º
  • Availability
  • (Two transmitters) 99.9
  • Integrity
  • Ground - monitors
  • Air- receiver measures signal strength and
    modulation depth
  • Availability

56
DME (Distance Measuring Equipment )
  • Frequency Band
  • Airborne 1025 MHz 1150 MHz
  • Ground 63 MHz below Tx frequency 1025 1087
    MHz 63 MHz above Tx frequency 1088 1150 MHz
  • This gives 126 channels but two codings are used
    (X and Y) which doubles the capacity

57
DME
  • As the name implies , DME provides information on
    the distance from the aircraft to the ground
    station
  • Used to establish position along an airway and
    also to establish hold points

58
DME
  • Frequency Band
  • Airborne 1025 MHz 1150 MHz (L band)
  • Ground 63 MHz below Tx frequency 1025 1087
    MHz 63 MHz above Tx frequency 1088 1150 MHz
  • This gives 126 channels but two codings are used
    (X and Y) which doubles the capacity

59
DME
  • General Principle
  • Airborne transceiver transmits a pair of pulses
  • (spaced at 12µs for mode X and 30µs for mode Y)
  • Ground transmitter receives the pulses, waits
    50µs and then transmits another pair of pulses
    back to the aircraft
  • Airborne transceiver measures the time between
    transmission and reception, subtracts the 50µs,
    multiplies by the speed of light and divides by
    2.

60
DME
  • This is very simple but gets more complicated
    when we want to service more than one aircraft
  • We need a method of distinguishing among the
    signals from up to 100 aircraft.
  • This is done essentially by generating a random
    set of pulses and correlating with the replies to
    determine the correct ones.

61
DME AIRBORNE TRANSPONDER
62
DME PULSES
63
DME OUTPUTS
  • Distance
  • Speed
  • Time to Station

Notes 1. The last two are valid only if the
aircraft is going directly towards or away from
the ground station. 2. The DME measures SLANT
RANGE to the station.
64
SLANT RANGE
Altitude
DME Distance (Slant Range)
Ground Range
65
DME Ground Station
The ground station simply receives a pulse pair,
inserts the 50 µs delay and retransmits it. To
reduce the effects of reflections it will not
reply to another interrogation for about 60 µs
(dead time)
66
DME Ground StationSQUITTER
The ground station transmits 2700 pulse pairs per
second regardless of the number of aircraft
interrogating. The extra pulse pairs are called
squitter If there are not enough interrogations
to make up 2700 pulse pairs, the ground receiver
increases its sensitivity until noise pulses
trigger enough replies to make up the
difference If there are too many interrogations,
the receiver decreases its sensitivity so that
the weakest interrogations get ignored
67
DME Ground StationSQUITTER
  • Using squitter has the following advantages
  • The transmitter average output power is constant
  • The receiver AGC has a constant average signal to
    work with
  • The ground receiver sensitivity is maintained at
    the optimum level
  • In the case of overload, the aircraft farthest
    from the station are dropped off first.

68
DME
  • Using squitter has the following advantages
  • The transmitter average output power is constant
  • The receiver AGC has a constant average signal to
    work with
  • The ground receiver sensitivity is maintained at
    the optimum level
  • In the case of overload, the aircraft farthest
    from the station are dropped off first.

69
DME as a Navaid
Accuracy The ICAO specification for DME is 0.5NM
or 3 of distance Tests done on Canadian DMEs
show that their errors are less than
30m. Integrity DME ground stations are equipped
with monitors which can detect erroneous delays
and out-of-tolerance power output levels. These
shut the system down if and error is detected
70
DME as a Navaid
Availability As with most systems there is a
standby transmitter which takes over when the
main one fails. availability is well above 99.9
71
DME as a Navaid
Availability As with most systems there is a
standby transmitter which takes over when the
main one fails. availability is well above 99.9
72
TACAN (TACTICAL NAVIGATION SYSTEM)
General TACAN is a military system combining
the bearing capability of VOR with the distance
measuring capability of DME It is also designed
to be transportable so that it can be used in
combat areas, hence the name tactical
73
TACAN (TACTICAL NAVIGATION SYSTEM)
Principle TACAN is based on DME in that it uses
the DME antenna and the DME pulse format. Thus
the distance measuring is inherent
74
TACAN
Bearing Function
Two concentric drums are placed around the DME
antenna The parasitic elements distort the DME
antenna pattern The drum structure is rotated at
900 rpm (15 Hz)
75
TACAN
Bearing Function
The resulting pattern has one main lobe caused by
the inner parasitic element, and 9 secondary
lobes caused by the outer elements
76
TACAN
Antenna Installation
77
TACAN
Thus the TACAN signal consists of 2700
pulse-pairs/second whose amplitude is modulated
by a 15Hz signal and a 135 Hz signal These
constitute the variable part of the TACAN signal
78
TACAN
The reference part of the TACAN signal consists
of coded sets of pulses called reference groups
(or bursts) The MAIN reference group (MRG)
consists of 24 pulses with alternate spacings of
12 and 18µs. This is transmitted when the antenna
pattern main lobe reference point passes the
North reference The AUXILIARY reference group
(ARG) consists of 12 pulses with of 30 µs
spacing. This is transmitted when each of the
auxiliary lobe reference points passes the North
reference
79
TACAN
The lobe reference point is the NEGATIVE-GOING
ZERO CROSSOVER
80
TACAN RECEIVER
81
TACAN
Since TACAN is not a civilian system it does not
have to conform to normal aviation
requirements However, since military aircraft
use the same airway structure as civilian
aircraft, there are TACANS collocated with VORs
on most airways. and these conform with the
civilian standards for VORs These facilities are
called VORTACs
82
TACAN
83
ABSOLUTE NAVIGATION SYSTEMS
Definition An absolute navigation system
provides vehicle position referred to a general
coordinate system. e.g. - Latitude/Longitude -
local Cartesian
84
ABSOLUTE NAVIGATION SYSTEMS
Waypoints The straight segments of a route are
usually called legs In relative navigation the
endpoints of legs are defined by a facility (VOR,
NDB, TACAN) In absolute navigation there are no
such facilities and so legs are defined by
waypoints A waypoint is simply an imaginary
point in space defined in the coordinate system
being used Can be 2 or 3-dimensional)
85
ABSOLUTE NAVIGATION SYSTEMS
  • Special Requirements for Absolute Navigation
  • Accurate survey of ground stations (if used, e.g.
    LORAN C)
  • Accurate survey of Airway waypoints
  • Accurate data base of airway waypoints, facility
    locationsSize of data base depends on area of
    operation- updated every 28 daysGood
    Configuration Control is MandatoryMany
    opportunities for error

86
ABSOLUTE NAVIGATION SYSTEMS
  • Importance of Accurate Data Bases
  • Mount Erebus

87
ABSOLUTE NAVIGATION SYSTEMS
Importance of Accurate Data Bases Mount Erebus
(Antarctica)
88
ABSOLUTE NAVIGATION SYSTEMS
Importance of Accurate Data Bases Mount Erebus
(Antarctica)
89
ABSOLUTE NAVIGATION SYSTEMS
  • Advantages
  • Unlimited freedom to define airway structures
  • Fewer ground-base facilities less cost
  • Greater flexibility for flight-planning but
    greater complexity for ATC (Air Traffic Control)

90
ABSOLUTE NAVIGATION SYSTEMS
  • Absolute Navigation Systems in Use Today
  • LORAN C
  • INS (Inertial Navigation)
  • GPS (Global Positioning System)
  • Multi-DME,

91
LORAN C
Long RAnge Navigation version C Originally a
marine navigation systemBecame feasible for
aircraft navigation with the introduction of
microprocessors Frequency of Operation 100kHz
(all stations)
92
LORAN C
  • A HYPERBOLIC SYSTEMi.e. lines of position are
    hyperbolas
  • This results from the fact that the lines of
    position are determined by measuring the
    DIFFERENCE in distance from two points.

93
LORAN C

One station is referred to as the Master and the
others as Slaves
94
LORAN C
  • At least two lines of position are required for a
    position fix thus more than one slave is required

95
LORAN C
  • A useful property of the hyperbola is that its
    tangent at any point bisects the angle subtended
    by the line joining the two foci
  • Exercise Use this property to determine where
    the best geometry occurs (LOP at 90º)

96
LORAN C
  • How do we determine the time difference?
  • Each station, starting with the Master, transmits
    a series of pulses with the following shape

This pulse has a bandwidth of about 20kHz
97
LORAN C
  • Each station transmits a series of eight of these
    pulses
  • Pulse separation is 1000µs (1ms)
  • Note In most chains the master transmits a ninth
    pulse after 2000µs. This can be used to indicate
    the status or integrity of the chains signals

98
LORAN C
  • How do we identify the pulses from each station?
  • The stations transmit their signals in sequence.
    The delay between signals from each station is
    such that the signal from the previous
    transmission is out of the coverage area before
    the next is sent.
  • Thus they always appear in the same order

99
LORAN C Chains
  • A group consisting of a Master and up to four
    slaves is called a chain
  • Each chain is identified by a Group Repetition
    Rate (GRI) which is the time between
    transmissions from the master.

100
LORAN C Chains
  • Each slave transmits its pulse train at a
    specified interval after the master has
    transmitted.
  • This is called the emission delay (ED) and is
    made up of the master-slave time (MS) and a
    coding delay (CD)

101
LORAN C Transmitters
  • Due to the long distances covered by each LORAN C
    chain, the power transmitted must be high (0.5
    to 4 MW)
  • Propagation is by ground wave and thus has to be
    vertically polarized
  • Antenna therefore is a vertical mast (ideally a
    quarter wavelength long (3km) (10,000 ft.)
  • Not very practical!!

102
LORAN C Antennas
  • Antennas are typically about 400m high
  • To improve the current flow, many are top
    loaded
  • They are still not very efficient (10)

103
LORAN C Antennas

Top loaded antenna with ground plane
104
LORAN C Receivers
  • Receivers require a data base which provides
  • the location (Lat/Lon) of the Master and Slave
    stations
  • the GRI of the chains to be used
  • the Time Delays for the individual stations
  • The LORAN C signal travels both by ground wave
    and sky wave
  • ground wave gives stable, reliable timing
  • sky wave does not due to the variable nature of
    the ionosphere
  • ground wave is attenuated more and hence is
    weaker and can be contaminated by the sky wave

105
LORAN C Receivers
  • Since sky wave is always delayed by a minimum of
    30µs, the positive-going zero crossover of the
    third cycle of the ground wave is used for timing

106
LORAN C Receivers
  • Problems to be solved by receiver
  • Signals strength may vary by 120dB
  • Large dynamic range required
  • Noise at LF can be very high due to long range
    propagation of interference (e.g. lightning in
    tropics)
  • Signal to noise ratio can be 20 dB

107
LORAN C Receivers
  • Receiver Operation
  • Searches for Master pulses using known GRI
  • PLL locks on to carrier to generate master clock
  • Locks on to slave pulses
  • Measures Master/slave time interval and subtracts
    the Emission Delay (ED)
  • Calculates the distances and position

108
Phase Locked Loops (PLLs)

109
LORAN C Accuracy

Error Sources Variation in propagation speed
(land vs water, type of terrain) Changes in
signal strength
  • Absolute Accuracy depends on geometry
  • 0.1 to 0.25NM
  • Repeatability
  • 20 to 100m

110
LORAN C
  • Integrity
  • Monitors are installed throughout the LORAN C
    coverage area
  • These monitors adjust the transmitter timing to
    compensate for changing propagation conditions
  • If excessive errors are detected, the master
    transmitter is commanded to blink the ninth
    pulse off and on to indicate which station is
    unreliable
  • For airborne use, this can be done within 10
    seconds of detection

111
LORAN C Coverage

112
Multi-DME

Multi-DME uses the measured ranges from two or
more DME stations to determine position
113
Multi-DME

Two configurations
114
Multi-DME
  • Problem
  • Multiple DME transceivers are expensive
  • Early frequency-hopping receivers had to acquire
    and lock on to each station. This took time
    (3s/station)
  • Required another system to navigate between fixes
  • Usually Inertial (expensive)

115
Multi-DME

Solution Modern DMEs use multiple (usually
three) processing channels Each channel keeps
track of one DME station i.e. it holds the
tracking gate position while the other stations
are being tuned and thus reacquisition is not
required typical update rate 26 times/second
116
Multi-DME

Accuracy 30m Integrity,Availability and
Continuity Slightly less than stand-alone DME
117
GPS

Global Positioning System otherwise known as
NAVSTAR NAVigation System with Timing And Ranging
118
GPS

General Principle
If we know our distance from n known points, we
can determine our position in n dimensions
119
GPS
  • Three Segments
  • Space Segment
  • The satellites
  • Control Segment
  • Special US military facilities
  • User Segment
  • Everybody with a GPS receiver

120
GPS
  • Space Segment
  • Satellite Constellation
  • Nominally 24 satellites (21 3 active spares)
  • Actually (today 17 Jan) - 28 usable
  • Current satellites designated Block IIA
    (original) and IIR (replacement)
  • Next set designated Block IIF (Follow-on)

121
GPS
  • Current Satellites
  • Block IIR-M (first one launched 25 Sep 2005)

Mass 1133 kg Nav Signals 1.572.42 GHz
(L1) 1.227.6 GHz (L2) Comm Signals1.783.7
GHz(Uplink) 2.2275 GHz (Downink) Design
Life 10 years Clocks 3 Rubidium (1x10-11)
122
GPS Constellation Status 23 Jan 2008
123
GPS

Space Segment
  • Orbit Characteristics (6 parameters required to
    define)
  • semimajor axis a 26,609 km (12 hour
    period)
  • eccentricity (non circularity) 0 (circular)
  • argument of perigee variable
  • inclination at reference time 55º (nominal)
  • mean anomaly at reference time variable
  • longitude of ascending node variable (60º incs)

124
GPS

Space Segment
125
GPS

Control Segment
  • Tracking Stations (Hawaii, Ascension Island,
    Diego Garcia, Kwajalein, Colorado Springs)
  • measure satellite positions
  • some (underlined) transmit orbital data to
    satellites
  • Master Control Station (Falcon AFB, Colorado)
  • calculates orbital parameters
  • performs orbital corrections when necessary

126
GPS

Distance Measurement and Clock Adjustment
127
GPS

Measurement of Satellite Position Satellite
position depends on its orbital parameters
(ephemeris, plural ephemerides) detailed
earlier. Each satellite transmits its own
ephemeris information as part of the Navigation
Message described later. It also depends on a
very accurate knowledge of TIME. We shall see
that the time measurement depends on knowing
satellite position. Thus we have a chicken and
egg situation. Fortunately this can be resolved
using iteration Rough time gives reasonable
position Reasonable position gives better time
etc. etc.
128
PERIGEE and ARGUMENT OF PERIGEE

Reference (x) axis in orbit is the Line of Nodes
129
LINE OF NODES/INCLINATION

Line of Nodes is the intersection of the Orbital
Plane and the Equatorial Plane
130
GPS

Measurement of Satellite Position in Orbital Plane
The navigation message includes the position of
the satellite at a given point in time in the
form of an angle relative to the Line of
Nodes. The receiver must then deduce the current
angle based its estimate of the current
time. This is complicated by the fact that the
orbit is not perfectly circular and the angle is
not a linear function of time
131
GPS

Measurement of Satellite Position in Orbital Plane
xrcos(?) yrsin(?)
if eccentricity (es)?0, ? is not a linear
function of time
132
GPS

Measurement of Satellite Position in Orbital Plane
Need to find a relation which is linear with time.
M (mean anomaly) is linear with time Mn(t-tp) n
is mean motion or average angular velocity
M is related to the angle E through ME- essin(E)
which cant be solved explicitly but can be by
iteration.
133
GPS

Measurement of Satellite Position in Orbital Plane
Once E has been found, ? can be found from
and r is calculated from ras(1- escos(E))
134
GPS Satellite Position

Once the position of the satellite has been
determines in the orbital coordinate system, it
must be translated into a coordinate system which
can be used for navigation
135
GPS Satellite Position
  • This is done by a series of coordinate
    transformations
  • From orbital plane to equatorial plane (x axis
    along Line of Nodes)
  • Rotate x axis to present position of the
    Greenwich Meridian (this involves knowing time
    since the Greenwich Meridian is moving with the
    Earths rotation)

136
GPS Satellite Position

Greenwich Meridian
137
GPS Satellite Position

138
Satellite Distance
  • Now we know the position of the satellite
  • The next thing we need to know is the distance
    from the satellite to the receiver
  • This is done by measuring the time it takes the
    signal to travel from the satellite to the
    receiver.
  • This time is then multiplied by the speed of
    light to get the distance

139
Satellite Distance
  • Note that the signal must travel through the
    ionosphere.
  • The speed of the signal through the ionosphere is
    less than that through space so that the signal
    is delayed by an amount equivalent to several
    meters
  • The thickness and density of the ionosphere are
    highly variable so the this delay is a random
    quantity and is the largest single error source

140
GPS Signal Format
  • Spread Spectrum Signals
  • Originally developed for military communications
  • Two objectives
  • Low probability of intercept
  • Less vulnerability to jamming (intentional
    interference)
  • Two main techniques
  • Frequency Hopping (FH)
  • Direct Sequence (DS) (Used in GPS)

141
Spread Spectrum
  • Pseudorandom Signals
  • Both techniques use pseudorandom (PR)
    codes(otherwise known as pseudonoise (PN))
  • These codes appear to be random to an observer
  • They are actually deterministic and their format
    is known to the transmitter and receiver
  • They are also periodic

142
Direct Sequence
  • In the direct sequence (DS) technique, the signal
    is multiplied by a pseudorandom (PR) also called
    pseudonoise (PN) sequence of binary digits (known
    as the code)
  • The receiver knows the sequence and, by
    multiplying the received signal by the same
    sequence, can recover the message

143
Direct Sequence
144
Direct Sequence
  • The coding bits are called chips.
  • tC is the chip period and its inverse is the chip
    rate
  • The spectrum of the signal is determined by the
    chip rate as follows

145
Autocorrelation
  • Thus the product is integrated for every offset
    between the two functions and the thus the
    correlation is a function of the offset between
    the two
  • Autocorrelation is the correlation between the
    function and itself
  • Obviously, the autocorrelation function is going
    to have an infinite value at zero offset if the
    integration is from plus to minus infinity
  • In practice, the integration is done over a
    limited set of values

146
Spreading Codes
  • GPS uses what is know as the CDMA technique.
  • This stands for Code Division, Multiple Access.
  • Multiple Access means that many transmitters may
    use a particular communications channel
  • Code Division means that a spreading code is used
    to allow the receivers to select the signals they
    want to receive
  • There must be one unique code for each
    transmitter in the system

147
Spreading Codes
  • Other techniques used are
  • FDMA (Frequency Division Multiple Access)in
    which the transmitters transmit on different
    frequencies
  • TDMA (Time Division Multiple Access)in which a
    time slot is assigned to each transmitter.

148
Spreading Codes
  • With CDMA it is necessary to design codes which
    have
  • good autocorrelation so that the receiver can
    lock on easily
  • Negligible cross correlation so that the receiver
    does not lock on to a code used by any other
    transmitter in the system
  • Note cross-correlation is the correlation between
    two codes

149
Spreading Codes
  • A purely random code is infinite, and, we shall
    see, would be almost impossible to lock on to.
  • In order to facilitate signal acquisition, short,
    periodic codes are used.

150
Code Generation
  • GPS uses two codes
  • C/A (Clear/Acquisition) and
  • P/Y
  • C/A codes are short (1ms long) and their
    structure is public knowledge
  • P/Y codes are for military use and are very long
    (1 week) and the Y code is encrypted. Thus they
    are very difficult to lock on to.

151
GPS Signal Format
  • GPS satellites transmit navigation signals on two
    frequencies
  • 1.57542 GHz (called L1)
  • and 1.2774 GHz (called L2)
  • Civilian receivers (with a very few exceptions)
    can use only the L1 signal.
  • NOTE
  • A third frequency (L3) at 1.17645 GHz is being
    added to permit better ionospheric correction for
    civilian receivers

152
GPS Signal Format
  • The L1 signal is BPSK (binary phase shift key)
    modulated with the C/A code multiplied by the
    Navigation Data Message.
  • In addition it is BPSK modulated (in quadrature)
    by the P/Y code

153
GPS Signal Format
  • The L2 signal is BPSK modulated with the P/Y code
    only (except for Block IIR-M)
  • Note Two carrier frequencies are used by
    military receivers to reduce errors introduced by
    the ionosphere.

154
Navigation Data Message
  • The navigation data message provides receivers
    with
  • current ephemeris for the transmitting satellite
    (or SV (space vehicle))
  • timing information
  • almanac (rough ephemerides for all other SVs in
    the constellation)

155
Navigation Data Message
  • The Data Message is transmitted at 50 bits/s
  • A frame of 1500 bits is transmitted as 5
    subframes
  • Each subframe begins with a Telemetry Word (TLM)
    and a Handover Word(HOW)

156
Navigation Data Message
157
Navigation Data Message TLM
  • The TLM starts with a Barker code (bits 10001011)
    which permits the receiver to determine the
    correct polarity of the data bits
  • The start of the TLM is the timing reference
    point in the message

158
Navigation Data Message HOW
  • The HOW was originally intended to provide the
    receiver with information to allow it to lock on
    to the P/Y code
  • The first 17 bits contain the number of 1.5
    second periods (300 bits x 20ms) from the start
    of the GPS week (midnight Saturday) to the start
    of the next subframe (TLM)
  • Bits 21 to 23 contain the ID of the current
    subrame

159
GPS Position Calculation
The basic equations for the position fix are
where x,y,z are the position coordinates and t is
the clock error
160
GPS Position Calculation
The basic equations are nonlinear and not easy to
solve so they are linearized (see notes) to
produce
xn , yn , zn and tn are the coordinates of a
nominal (initially arbitrary) position Rni is the
distance from the nominal position to SVI ?Ri is
the difference between Rni and the measured
pseudorange
161
GPS Position Calculation
Note that the coefficients of the variables are
the Direction Cosines of the vector from the
nominal position to the satellite
Unit Vector
162
GPS Position Calculation
  • Procedure
  • Assume a nominal position (could be 0,0,0,0)
  • Calculate the delta positions
  • Add these to the nominal position to get a new
    one
  • Recalculate delta positions
  • Repeat 3 and 4 until the RHS of equation is less
    than a prespecified value

163
GPS Receivers
  • Antennas
  • Circularly polarized
  • Signal level -130dBM
  • Low signal level requires a built-in Low Noise
    Amplifier (LNA) to avoid excessive signal to
    noise ratio

164
GPS Receivers
Typical GPS Receiver RF Processing
165
GPS Receivers
  • Receivers must (1 and 2 must be done at the same
    time)
  • Find and lock on to the spreading code from the
    desired SV
  • Lock on to the Doppler-shifted RF carrier
  • Demodulate the Navigation Data Message
  • Measure the signal delay for each satellite
  • Calculate the position

166
GPS Errors
Various Sources give different errors The
following are typical
The Root Sum Square of these errors is 6m
167
DOPs
At the beginning of the Navigation section we
mentioned the idea of good and bad geometry when
considering a position fix. In GPS a numerical
measure of geometry has been developed GDOP,
Geometrical Dilution of Precision
Where Vx, Vy and Vz, are the variances of the x,
y, z components of position error and Vt is the
variance of time error
168
DOPs
The GDOP is derived from the relative positions
of all of the satellites PDOP is Position
Dilution of Precision and does not include
time HDOP is Horizontal DOP VDOP is Vertical
DOP
169
DOPs
Note Position Error is determined by multiplying
the satellite range error by the appropriate
DOP e.g. if the estimated satellite range error
is 6 m, and the HDOP is 2.5, then the error in
horizontal position is 6 x 2.5 15m
170
DOPs
Satellites in View 1450, Wednesday 21 Jan 2009
171
GPS Augmentation Systems
For some applications, (in particular aircraft
approach and landing), it is desirable to reduce
or eliminate some of these errors Also, some form
of integrity is necessary since GPS by itself
does not provide it These requirements have given
rise to two types of GPS augmentation
systems Each uses reference stations to measure
the errors and then transmit the corrections to
users.
172
GPS Augmentation Systems
  • Local Area Differential GPS
  • A GPS receiver is installed at a position whose
    coordinates are known to a high degree of
    accuracy
  • The receiver calculates its distance to each
    satellite and subtracts this value from its
    measured pseudorange
  • The resulting corrections are then transmitted on
    a data link (e.g. VHF communications)

173
GPS Augmentation Systems
6m
2 to20cm
174
GPS Augmentation Systems
LADGPS Advantages Increased accuracy Ability to
introduce integrity Disadvantages Requires a
separate data link Limited coverage Accuracy
Decreases with increased distance from reference
175
GPS Augmentation Systems
  • Wide Area Augmentation System (WAAS)
  • Objective To provide precision (horizontal and
    vertical guidance) approach capability at any
    airport in US without having to install local
    equipment

176
GPS Augmentation Systems
  • Wide Area Augmentation System (WAAS)
  • In WAAS, several reference stations are installed
    across North America with separations of about
    500NM
  • The stations measure the GPS range errors as in
    the case of the Local Area Differential System
    but instead of broadcasting them they transmit
    them to a master station (presently at Atlantic
    City NJ)

177
GPS Augmentation Systems WAAS
178
GPS Augmentation Systems WAAS
The master station then calculates the errors for
a grid of points across the coverage area. This
information then is coded and transmitted up to a
geostationary INMARSAT satellite The satellite
then transmits the information to the coverage
area In addition, the geostationary satellite
signal is spread with a Gold code and can be used
for ranging
179
GPS Augmentation Systems WAAS
180
GPS Augmentation Systems WAAS
The receiver selects the corrections for the four
grid points surrounding its position,
interpolates them and applies the result to
refine the computation of its position. Note
The receiver can also use the range from the
INMARSAT satellite to compute its position
181
GPS Augmentation Systems WAAS
  • Advantages
  • Corrections are available over a large area
  • The geostationary satellites add to the GPS
    constellation
  • No extra equipment required to get corrections
  • Provides integrity to Cat I requirements (6
    seconds)
  • Disadvantage
  • Not as accurate as LAGPS ( about 2m)

182
GPS Installation Considerations
  • Obviously the antenna should be on the top of the
    fuselage
  • If the aircraft has a T tail, shadowing could be
    a problem, thus the antenna should be as far
    forward as possible
  • The antenna should be as close to the receiver as
    possible since the signal level is very low at
    the antenna and long antenna cables (plus
    connectors) introduce attenuation
  • Airline type receivers are usually computer cards
    installed in the Flight Management System
  • Light Aircraft receivers are usually panel mounted

183
Other GNSS (Global Navigation Satellite Systems)
  • Glonass (Russia)
  • Galileo (European Union)
  • Compass (China)

184
Glonass
  • Similar to GPS and developed about the same time
  • Suffered from poor quality satellites with short
    life spans
  • Effectively ceased to exist until recently
  • Satellites transmit same codes but on different
    frequencies
  • (FDMA)
  • Presently being rebuilt with improved satellites
  • Expected to reach 24 satellites by the end of
    2009
  • Satellites are launched three at a time.

185
Galileo
  • European Unions answer to GPS
  • First civilian Satellite Navigation System
  • 30 satellites in three planes at 56 degrees
    inclination
  • 10 signals in three frequency bands are to be
    used
  • CDMA coding as with GPS

186
Galileo
  • Five levels of service
  • Open Service three frequencies no integrity
  • Safety of Life transport integrity provided
  • Commercial service higher accuracy than Open
    Service - encrypted, pay for use
  • Public Regulated Service police, fire, customs
    etc. encrypted
  • Search and Rescue location of accidents,
    communication with distress beacon

187
Galileo
  • Status
  • Two Galileo In Orbit Validation (GIOVE)
    satellites in orbit
  • Procurement for operational system has started
  • Contracts expected in mid to late 2009.
  • Four more IOV satellites planned for 2010
  • Full 30 satellite constellation scheduled for
    2013

188
Compass
  • Design
  • 5 Geostationary
  • 30 Medium Earth Orbit (MEO) (21,500 km)
  • 10 levels of service
  • 8 carrier frequencies, various modulations/codes
  • Status
  • Four experimental satellites launched since 2000
    (2 operational as of April 2007).
  • Regional coverage was planned for 2008 but no
    further news about launches available

189
Inertial Navigation
  • Advantages
  • instantaneous output of position and velocity
  • completely self contained
  • all weather global operation
  • very accurate azimuth and vertical vector
    measurement
  • error characteristics are known and can be
    modeled quite well
  • works well in hybrid systems

190
Inertial Navigation
  • Disadvantages
  • Position/velocity information degrade with time
    (1-2NM/hour).
  • Equipment is expensive (250,000/system) - older
    systems had relatively high failure rates and
    were expensive to maintain
  • newer systems are much more reliable but still
    expensive to repair
  • Initial alignment is necessary - not much of a
    disadvantage for commercial airline operations
    (12-20 minutes)

191
Inertial Navigation Basic Principle
  • If we can measure the acceleration of a vehicle
    we can
  • integrate the acceleration to get velocity
  • integrate the velocity to get position
  • Then, assuming that we know the initial position
    and velocity we can determine the position of the
    vehicle at ant time t.

192
Inertial Navigation The Fly in the Ointment
  • The main problem is that the accelerometer can
    not tell the difference between vehicle
    acceleration and gravity
  • We therefore have to find a way of separating
    the effect of gravity and the effect of
    acceleration

193
Inertial Navigation The Fly in the Ointment
  • This problem is solved in one of two ways
  • Keep the accelerometers horizontal so that they
    do not sense the gravity vector This is the
    STABLE PLATFORM MECHANIZATION
  • Somehow keep track of the angle between the
    accelrometer axis and the gravity vector and
    subtract out the gravity componentThis is the
    STRAPDOWN MECHANIZATION

194
Inertial Navigation STABLE PLATFORM
  • The original inertial navigation systems (INS)
    were implemented using the STABLE PLATFORM
    mechanization but all new systems use the
    STRAPDOWN system
  • We shall consider the stable platform first
    because it is the easier to understand

195
Inertial Navigation STABLE PLATFORM
  • There are three main problems to be solved
  • The accelerator platform has to be mechanically
    isolated from the rotation of the aircraft
  • The aircraft travels over a spherical surface and
    thus the direction of the gravity vector changes
    with position
  • The earth rotates on its axis and thus the
    direction of the gravity vector changes with time

196
Inertial Navigation Aircraft Axes Definition
  • The three axes of the aircraft are
  • The roll axis which is roughly parallel to the
    line joining the nose and the tail Positive
    angle right wing down
  • The pitch axis which is roughly parallel to the
    line joining the wingtipsPositive angle nose
    up
  • The yaw axis is verticalPositive angle nose to
    the right

197
Inertial Navigation Aircraft Axes Definition
ROLL
PITCH
YAW
198
Inertial Navigation Platform Isolation
  • The platform is isolated from the aircraft
    rotation by means of a gimbal system
  • The platform is connected to the first (inner)
    gimbal by two pivots along the vertical (yaw)
    axis. This isolates it in the yaw axis
  • The inner gimbal is the connected to the second
    gimbal by means of two pivots along the roll
    axis. This isolates the platform in the roll
    axis.
  • The second gimbal is connected to the INU
    (Inertial Navigation Unit) chassis by means of
    two pivots along the pitch axis. This isolates it
    in the pitch axis.

199
Inertial Navigation Platform Isolation
Now the platform can be completely isolated from
the aircraft rotations
200
Inertial Navigation Gyroscopes
  • To keep the platform level we must be able to
  • Sense platform rotation and
  • Correct for it
  • To do this we mount gyroscopes on the stable
    platform and install small motors at each of the
    gimbal pivots.
  • The gyroscopes sense platform rotation in any of
    the three axes and then send a correction signal
    to the pivot motors which then rotates the
    relevant gimbal to maintain the platform at the
    correct attitude

201
Inertial Navigation Alignment
  • Before the INS can navigate it must do two
    things
  • Orient the platform perpendicular to the gravity
    vector
  • Determine the direction of True North
  • Also it must be given
  • Initial Position Input by the Pilot (or
    navigation computer)
  • Velocity This is always zero for commercial
    systems

202
Inertial Navigation Orientation
  • In the alignment mode the INU uses the
    accelerometers to send commands to the pivot
    motors to orient the platform so that the output
    of the accelerometers is zero.
  • Note that the earth (and therefore the INU) is
    rotating so that it will be necessary to rotate
    the platform in order to keep it level.

203
Inertial Navigation Gyrocompassing
  • The rotation of the platform to keep it level is
    used to determine the direction of True North
    relative to the platform heading.

204
Inertial Navigation Gyrocompassing
205
Inertial Navigation Gyrocompassing
The platform is being rotated around the X and Y
axes at measured rates RXOcosFcosa RYOcosFsina
Since O is known (15.05107 º/hour) we have two
equations in two unknowns and can calculate F
(Latitude) and a (platform heading)
206
Inertial Navigation Navigation
  • Once the INU has been aligned it can be put into
    NAVIGATE mode .
  • In navigate mode, the outputs of the
    accelerometers are used to determine the
    vehicles position and the gyroscopes are used to
    keep the platform level.
  • This involves
  • compensating for the earths rotation
  • compensating for travel over the earths
    (somewhat) spherical surface

207
Inertial Navigation Schuler Oscillation
To compensate for the travel over the surface of
the earth the platform must be rotated by an
amount d/R where d is the distance travelled and
R is the radius of curvature of the earth
R
s
?
208
Inertial Navigation Schuler Oscillation
This leads to a phenomenon know as Schuler
oscillation At the end of the alignment procedure
the accelerometers are almost never perfectly
level.
209
Inertial Navigation Schuler Oscillation
Assume for now that the aircraft remains at
rest The measured acceleration causes the INU to
compute a velocity and hence a change in
position. This in turn causes the gyros to rotate
the platform
210
Inertial Navigation Schuler Oscillation
Assume for now that the aircraft remains at
rest The measured acceleration causes the INU to
think that it is moving an it computes a velocity
and hence a change in position. This in turn
causes the gyros to rotate the platform
211
Inertial Navigation Schuler Oscillation
The direction of the rotation tends to level the
accelerometer but when it is level, the computer
has built up a considerable speed and thus
overshoots. (this is like pulling a pendulum off
centre and letting it go)
212
Inertial Navigation Schuler Oscillation
Characteristics of the oscillation a-gsin? or
g? for small angles ? s/R where R is the
radius of curvature
differentiating twice
213
Inertial Navigation Schuler Oscillation
This is a second order differential equation
whose solution is ? ?0cos(?t) where ?0 is the
initial tilt angle and
The period of this oscillation is 84 minutes
214
Inertial Navigation Accelerometers
  • Requirements
  • high dynamic range (10-4 g to 10g)
  • low cross coupling
  • good linearity
  • little or no asymmetry
  • Exacting requirements dictate the use of
    Force-Rebalance type of devices

215
Inertial Navigation Accelerometers
  • Types
  • Pendulum
  • floating
  • flexure pivot
  • Vibrating String or Beam
  • MEMS (micro electromechanical systems)

216
Inertial Navigation Accelerometers
Floated Pendulum
217
Inertial Navigation Accelerometers
Flexure Pivot Pendulum
218
Inertial Navigation Accelerometers
Vibrating Beam
219
Inertial Navigation Accelerometers
MEMS
220
Inertial Navigation Gyroscopes
Three main types Spinning Mass Ring Laser MEMS
221
Inertial Navigation Gyroscopes
Spinning Mass Rigidity in Space A spinning mass
has a tendency to maintain its orientation in
INERTIAL space Its rigidity (or resistance to
change) depends on its moment of inertia and its
angular velocity about the spin axis (INU gyros
spin at around 25,000 RPM) Precession If a
torque t is applied perpendicular to the spinning
mass it will respond by rotating around an axis
90 degrees to the applied torque. I.e. ? t
222
Inertial Navigation Gyroscopes
Construction
223
Inertial Navigation Gyroscopes
  • Spinning Mass Gyros
  • Disadvantages
  • sensitive to shock during installation and
    handling (Pivots can be damaged)
  • requires several minutes to get up to speed and
    temperature
  • expensive

224
Inertial Navigation Gyroscopes
  • Ring Laser Gyro (RLG) in service since 1986
  • Advantages over spinning mass gyros
  • more rugged
  • inherently digital output
  • large dynamic range
  • good linearity
  • short warm up time

225
Inertial Navigation Gyroscopes
  • Ring Laser Gyro (RLG) in service since 1986
  • General Principle

226
Inertial Navigation Gyroscopes
  • Ring Laser Gyro (RLG) in service since 1986
  • General Principle

227
Inertial Navigation Gyroscopes
  • Ring Laser Gyro
  • Problems
  • Lock-in at low rotation rates due to weak
    coupling between the two resonant systems
    (coupling due to mirror backscatter)
  • Analagous to static friction (stiction) in
    mechanical systems
  • Causes a dead zone
  • Alleviated by dithering the gyro at a few
    hundred Hz
  • Random loss of pulses at the output ( causes
    drift)

228
Inertial Navigation Gyroscopes
  • Fibre Optic Gyro
  • Similar concept to RLG except that amplification
    is not usesd
  • Two strands of optical fibre are wound in
    opposite directions on a coil form
  • Laser light is sent from a single source down
    both fibres
  • The outputs of the two fibres are combined at a
    photodiode
  • Rotation of the coil around its axis causes the
    two paths to have different lengths and the
    output of the photodiode provides a light dark
    pattern. Each cycle indicates an increment of
    angular rotation

229
Inertial Navigation Gyroscopes
  • Fibre Optic Gyro
  • Has the advantage of being rugged and relatively
    cheap
  • Sensitivity increases with length of fibre
  • Unfortunately, the longer the fibre, the lower
    the output signal.
  • Used on low performance systems

230
Inertial Navigation Gyroscopes
  • MEMS Gyro
  • All gyros to date have been quite large
  • in fact the sensitivity of spinning mass gyros
    and RLGs are a direct function of their size.
  • Efforts are being made to apply MEMS technology
    to gyros as well as to accelerometers

231
Inertial Navigation Gyroscopes
  • MEMS Gyro
  • The MEMS gyro uses the Coriolis Effect
  • In a rotating system (such as the earth) moving
    objects appear to deflected perpendicular to
    their direction of travel.
  • The ef
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