NAVIGATION

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NAVIGATION

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

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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

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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

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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

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Magnetic and True North
MAG
TRUE
14?
VARIATION
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Pole Migration
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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

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Units and Conventions
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Navigation

• Lines of Position

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Navigation

• Position Fix

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Navigation

• Position Fix Geometry

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Requirements for an Air Navigation System

• Accuracy(Allowable Error)
• Integrity
• Availability
• Continuity

These all depend on the phase of flight
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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!!

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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

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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

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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

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Availability

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

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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)

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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

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Relative Navigation Systems
Airway Structure between Ottawa and Toronto
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Examples of Relative Navigation Systems

• Nondirectional Beacon/Automatic Direction Finder
  (NDB/ADF)
• VOR (VHF Omnirange)
• TACAN (Tactical Air Navigation)
• DME (Distance Measuring Equipment)

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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

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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

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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

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ADF Antenna Patterns
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ADF

ADF Bearing Indicator
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ADF

Old ADF Antenna Installation
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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

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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.

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Crossed Loop ADF
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Crossed Loop ADF
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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)

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ADF Disadvantages

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

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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.

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VOR (VHF Omnirange)

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

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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

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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

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VOR
VOR ANTENNA PATTERN
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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)
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VOR SIGNAL GENERATION
Note the 1020Hz identifier
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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

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ANTENNA ARRAYS
Two Element Example
l/2
Antenna Pattern
Transmitter
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ANTENNA ARRAYS
Two Element Example
l/2
Antenna Pattern
90deg
Transmitter
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VOR ANTENNA
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VOR TRANSMITTER
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VOR RECEIVER
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VOR RECEIVER
HSI (HORIZONTAL SITUATION INDICATOR)
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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

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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

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DOPPLER VOR
EFFECT OF APERTURE
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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 .

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DOPPLER VOR
vwr
fRfCv/c
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DOPPLER VOR
Note To maintain the correct relationship between
reference and variable signals, the signal
rotation is counterclockwise
fc
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DOPPLER VOR
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VOR as a NAVIGATION AID

• Accuracy 3º
• Availability
• (Two transmitters) 99.9
• Integrity
• Ground - monitors
• Air- receiver measures signal strength and
  modulation depth
• Availability

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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

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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

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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

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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.

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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.

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DME AIRBORNE TRANSPONDER
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DME PULSES
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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.
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SLANT RANGE
Altitude
DME Distance (Slant Range)
Ground Range
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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)
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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
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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.

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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.

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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
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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
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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
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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
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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)
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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
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TACAN
Antenna Installation
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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
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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
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TACAN
The lobe reference point is the NEGATIVE-GOING
ZERO CROSSOVER
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TACAN RECEIVER
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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
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TACAN
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ABSOLUTE NAVIGATION SYSTEMS
Definition An absolute navigation system
provides vehicle position referred to a general
coordinate system. e.g. - Latitude/Longitude -
local Cartesian
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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)
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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

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ABSOLUTE NAVIGATION SYSTEMS

• Importance of Accurate Data Bases
• Mount Erebus

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ABSOLUTE NAVIGATION SYSTEMS
Importance of Accurate Data Bases Mount Erebus
(Antarctica)
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ABSOLUTE NAVIGATION SYSTEMS
Importance of Accurate Data Bases Mount Erebus
(Antarctica)
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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)

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ABSOLUTE NAVIGATION SYSTEMS

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

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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)
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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.

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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

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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)

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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)

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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

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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
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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