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Introduction to Navigation Systems
Joseph Hennawy
Computer Engineer
Table of Contents
 History of Navigation Systems.
 Accelerometer Sensors Technologies (Body Speed &
Acceleration).
 Gyr...
Inertial Navigation History
Inertial Guidance System of SAGEM used in the Air-Surface Medium-
range missile
Dead Reckoning
Early Compasses
Surveyor’s Compass--1820
Jean Bernard Léon Foucault
Originator of the Foucault pendulum
1819-68
Foucault's gyroscope (1851)
Mechanical Dead Reckoning Computer: Early 20th century
SG-66 Guidance System for the V-2
(1944)
Charles Stark Draper
Gyroscopic Apparatus - Spinning Gyroscope
Born 2 October 1901
Died 25 July 1987
First Successful All-Inertial Navigator (1954)
Professor Arnold Nordiseck Holding Early Electrostatically Suspended
Gyroscope (1959)
Honeywell Advertisement for Electrostatically Suspended Gyroscope,
1962
Warren Macek of Sperry Circa 1963 Demonstrating the Ring Laser Gyro
Concept
Laser Gyro
Tactical Grade Closed-Loop FOG
• Tactical FOG IMU funded by USAF
• HG1800 FOG IMU is pin-for-pin
compatible with HG1700 RL...
INERTIAL NAVIGATION HISTORICAL EVENTS
• Newton’s second law: circa 1688
• Leon Foucalt: demonstration of earth rotation us...
INERTIAL NAVIGATION HISTORICAL EVENTS(2)
•Various: First inertial navigation systems in commercial aircraft late 60’s
• RL...
Accelerometers
FORCER VERTICAL
PIVOT
PICKOFF
AMPLIFIER
Simple Pendulum Accelerometer
Torque Balance Pendulous Accelerometer Schematic
EMERGING ACCELEROMETER TECHNOLOGY APPLICATIONS
MEMS/MOEMS
Mech.
Silicon
Quartz
WSN-7 Accelerometer
Physical
•Weight 1.54 pounds (700 grams)
•Size 3.5 inches (8.9 cm) diameter by 3.35 inches (8.5 cm) high
•Power 10 watts s...
Accelerometer Name $2K(1)
Part of System Name $2Ksystem(1)
Where Found IMU Performance vs. Cost
Velocity Random Walk 0.60 ...
Accelerometer Name $20K
Part of System Name $20K
Where Found IMU Performance vs. Cost
Velocity Random Walk 0.03 (meters/se...
Velocity Random Walk 0.0003 (meters/sec)/√(rt-hr)
Bias 100 micro-g
Misalignment 3 arcsec
Scale Factor 100 ppm
Second Order...
Gyroscopes
INERTIAL ROTATION SENSOR TECHNOLOGY
E;CoursesGyros
INERTIAL SENSOR APPLICATION
1 5 25 125 625 3125
1e-005
0.0001
0.001
0.01
0.1
1
10
WEIGHT
SENSORPERFORMANCE(deg/hr)
TACTICA...
Inertial Sensor Technology Comparison
Inertial Acronym Definitions
ESG Electrostatic Gyro
FOG – Fiber Optic Gyro
HRG – Hem...
Honeywell Gyro Technology Heritage
1920 1960 1970 1980 2000 202020101990
Iron Gyros Optical Gyros MEMS
Optical Gyros
 Rin...
IMU Product Evolution Overview
RLG FOG MEMS
• EGI • GGP • Future
• MAPS • PSN Growth
• Digital
Laser
Gyro
• HG1700 • HG180...
Rate Gyro Principles and Designs
Type Principle
Rotor 1 and 2
2
1
Constancy of
Angular Momentum
Sagnac Effect 1
1
Preserva...
CURRENT GYRO TECHNOLOGY APPLICATIONS
Sagnac Effect
Active Approach Passive Approach
RING LASER FOG
INTERFEROMETER
OPTICAL GYRO TECHNOLOGIES
∆ƒ = (4Α/λΡ)Ω
∆Φ = ...
Suitability of RLG for Strapdown
•Wide Dynamic Measuring Range
•Direct Digital Output
•Excellent scale factoring Linearity...
GG 1320 Digital Ring Laser Gyro
• Characteristics
— < 5.5 cubic inches
— < 1 lb
— < 2.5 watts
— DC power in (+ 15 and +5 V...
Honeywell Ring Laser Gyros
(RLGs)
Ring Laser Gyro Operation
The Fiber Optic Gyro
• Consists of:
1. Semiconductor laser
diode as light source.
2. Beam splitter.
3. Coil of optical fib...
Tactical Grade Closed-Loop
FOG• Tactical FOG IMU funded by USAF
• HG1800 FOG IMU is pin-for-pin
compatible with HG1700 RLG...
Types/Characteristic Applications Ex. Manufacturer Accuracy
(deg/hr)
Maturity Cable
Length
(meters)
Commercial Grade Autom...
 SAGNAC Effect (Phase Shift Measured in
Nano Radians)
 Computer Maintains Spatial Reference
 Uses Large Coil LD Product...
IMU Product Evolution Summary
• RLG IMUs and RLG systems are a growth industry with proven
track records in the field
• FO...
Coordinate Systems
Coordinate Frames
AXIS 1 AXIS 2 AXIS 3
Inertial(I) (vernal equinox (in equatorial plane) (polar)
Aries)
ECEF(E) (through (...
AXIS 1 AXIS 2 AXIS 3
Wander(WA) (α counterclockwise (α counterclockwise
from north) from east)
(α chosen such that )
Body ...
Coordinate Systems Use
Navigation quantities, eg, Position, Velocity, Acceleration,
Jerk…. are three dimensional vectors a...
GEODESY, DATUMS
Conceptual Reasons for Studying
Geodesy
• Three main reasons for studying
Geodesy/Astronomy related to inertial
navigation...
The Ellipsoid of Rotation
Z
P
P’
Equatorial
Plane
a
a
F O F’
b
X
a
a
22
ba +
12
2
2
2
=+
b
Z
a
X
Shape of the Earth
WGS-84 & WGS-72 Defining Parameters
For WGS-84 Ellipsoid
WGS-84 Derived Geometric
Constants
CONSTANT NOTATION VALUE
Flattening(ellipticity) f 1/298.257223563
Semiminor Axis b 6356...
Different datums may use different ellipsoids. Datums may also differ by the location
of the center and orientation of the...
Simply put, a datum is the mathematical model of the Earth we use to calculate the coordinates on
any map, chart, or surve...
Gravity Disturbance Effects
On INS
TLV = True Local Vertical
Perpendicular to Geoid
Actual Gravity Vector
Astronomic Vertical
REV = Reference-Ellipsoid Verti...
APPROACHES TO GRAVITY COMPENSATION
STORED MAP APPROACH
PATROL AND PRELAUNCH PHASE USE
DEFLECTION/GEOD MAPS
TARGET OFFSETS ...
Gravity Compensation Techniques
GRAVITY COMPENSATON EMBODIES
• MAP UTILIZATION/INTERPOLATION AND/OR
• REAL-TIME MEASUREMEN...
INS Error Analysis
Causes of Inertial Navigation Errors
• Initial Conditions
– An inertial needs three dimensional position, velocity,
and at...
Causes of Inertial Navigation Errors
(cont’d)
• Inertial Sensor Assembly Misalignments
– Each sensors orientation may be m...
GPS/INS Systems
Inertial
Navigation
System
Aiding
Sources
Optimal
Processor
Corrected
Navigation
Output
(Includes Models of
INS errors, ai...
Inertial
Navigation
System
Aiding
Sources
Inertial
Error
Estimates
Corrected
Inertial
Outputs
Kalman
Filter+
-
Inertial + ...
Loosely Coupled GPS/INS
Integration ArchitectureRF / IF / A/D
MULTI-CHIP
CORELATOR
CARRIER
DISCRIMINATOR
90°
I & D
IE
IP
Q...
Tightly Coupled GPS/INS
Integration ArchitectureRF / IF / A/D
MULTI-CHIP
CORELATOR
CARRIER
DISCRIMINATOR
90°
I & D
IE
IP
Q...
Intimately Coupled GPS/INS Integration
Architecture
RF / IF / A/D
MULTI-CHIP
CORELATOR
CARRIER
DISCRIMINATOR
90°
I & D
IE
...
H-764G Embedded GPS/INS
H-764G Features
• Small size: 7.0”H x 7.0”W x 9.8”L
• Light weight: 18 lbs*
• Low power: < 40 watt...
Some Inertial Navigation Systems
vendor units
model HG1900 HG1920 comments
volume 16 7.4 in³
Length/Diameter in
Width in
Depth in
mass 0.45 kg
power 3 w
te...
vendor units
model LN-200 comments
volume 32.2 in³
Length/Diameter 3.5 in
Width in
Depth 3.35 in
mass 0.7 kg
power 10 w
te...
vendor units
model SiLMU01 comments
volume 6.1 in³
Length/Diameter 2.36 in
Width in
Depth 1.79 in
mass 0.26 kg
power 5 w
t...
• The AN/WSN-7 was designed
as a form, fit, and function
replacement for the AN/WSN-
1, and -5 for installation on
DDG 51,...
CN-1695/WSN-7(V)
CN-1696/WSN-7(V)
CN-1697/WSN-7(V)
Ring Laser Gyro Navigator
MX-11681/WSN
Inertial Measuring Unit
(Inside ...
Install Schedule
SHIP
CLASS
FY02 FY03 FY04 FY05 FY06 FY07 TO
COMPLETE
CG 47 CG 48
CG 49
DDG 51 DDG 51 DDG 61
DDG 53 DDG 65...
CD-132/WSN-7A(V)
CD-133/WSN-7A(V)
Control Unit, Electronic
IP-1747/WSN
Display Unit, Control
CY-8827/WSN-7A(A)
Enclosure A...
Install Schedule (Cont.)
SHIP
CLASS
FY02 FY03 FY04 FY05 FY06 FY07 TO
COMPLETE
SSN 688 SSN 690 SSN 763
SSN 719 SSN 767
SSN ...
Evolution of Inertial Navigation
3-Axis Gyro Chip
3-Axis Accelerometer Chip
Evolution of Inertial Navigation
Technology
• Size ,cost,power of Inertial Systems greatly reduced by technology developme...
Low Cost Guidance and
Navigation
• Low Cost Guidance Package enables cost effective precise positioning to be
embedded in ...
2000 200320022001
LN 205G
ATK SAASM
GPS
•Leveraging LN 200 series development reduces MEMS time-to-market
LN 205
LN 200
IM...
The Future
• Over the next 3 to 5 years, the applicability
of MEMS for high-g tactical applications will
be conclusively d...
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
Introduction to Navigation Systems
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Introduction to Navigation Systems

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Introduction to Navigation Systems

  1. 1. Introduction to Navigation Systems Joseph Hennawy Computer Engineer
  2. 2. Table of Contents  History of Navigation Systems.  Accelerometer Sensors Technologies (Body Speed & Acceleration).  Gyroscope Sensors Technologies (Body Attitude).  Navigation Coordinate Systems.  GEODESY & DATUMS.  INS Systems Error Analysis.  GPS/INS Systems.  Current Navigation Systems  The Future of Navigation Technologies.
  3. 3. Inertial Navigation History Inertial Guidance System of SAGEM used in the Air-Surface Medium- range missile
  4. 4. Dead Reckoning
  5. 5. Early Compasses
  6. 6. Surveyor’s Compass--1820
  7. 7. Jean Bernard Léon Foucault Originator of the Foucault pendulum 1819-68
  8. 8. Foucault's gyroscope (1851)
  9. 9. Mechanical Dead Reckoning Computer: Early 20th century
  10. 10. SG-66 Guidance System for the V-2 (1944)
  11. 11. Charles Stark Draper Gyroscopic Apparatus - Spinning Gyroscope Born 2 October 1901 Died 25 July 1987
  12. 12. First Successful All-Inertial Navigator (1954)
  13. 13. Professor Arnold Nordiseck Holding Early Electrostatically Suspended Gyroscope (1959)
  14. 14. Honeywell Advertisement for Electrostatically Suspended Gyroscope, 1962
  15. 15. Warren Macek of Sperry Circa 1963 Demonstrating the Ring Laser Gyro Concept
  16. 16. Laser Gyro
  17. 17. Tactical Grade Closed-Loop FOG • Tactical FOG IMU funded by USAF • HG1800 FOG IMU is pin-for-pin compatible with HG1700 RLG IMU • Goals: 1 deg/hour Gyro Error 1 milli-G Accel Error • Housing identical to HG1700 IMU <35 cubic inches
  18. 18. INERTIAL NAVIGATION HISTORICAL EVENTS • Newton’s second law: circa 1688 • Leon Foucalt: demonstration of earth rotation using a gyroscope 1852 Greek: “gyro”--rotation; “skopein”--to see • G. Trouve: Mechanical gyroscope with electric motor 1865 • Anschutz: First gyrocompass 1904 • Schuler: Pendulum/gyroscope unaffected by ship/course/speed 1908 • Boykow(Austria): Mathematics of inertial navigation 1938 • Peenemunde Group(Germany): First operating inertial guidance on V2 1942 • Autonetics: Under the ice Nautilus crossing of North Pole 1958 • Autonetics: Transcontinental purely inertial flight 1958 • AC-Delco, Litton, Honeywell, Sperry, Singer-Kearfott, Sagerm(French): 1960’s Military bombers, ships, fighter, ballistic missiles • MIT/Delco: Apollo guidance system 1969 • Honeywell: Electrically suspended gyro navigator 1967 • Sperry: First ring laser gyro 1963 [ ]IVm dt d F  =
  19. 19. INERTIAL NAVIGATION HISTORICAL EVENTS(2) •Various: First inertial navigation systems in commercial aircraft late 60’s • RLG: based strap down systems on commercial aircraft early 80’s • RLG: based strapdown systems in military mid 80’s • First Fiber Optic Gyro Based inertial systems early 90’s • First Embedded GPS-INS systems early 90’s • Low cost tactical microelectromechanical sensors(MEMS) NOW
  20. 20. Accelerometers
  21. 21. FORCER VERTICAL PIVOT PICKOFF AMPLIFIER Simple Pendulum Accelerometer
  22. 22. Torque Balance Pendulous Accelerometer Schematic
  23. 23. EMERGING ACCELEROMETER TECHNOLOGY APPLICATIONS
  24. 24. MEMS/MOEMS Mech. Silicon Quartz
  25. 25. WSN-7 Accelerometer
  26. 26. Physical •Weight 1.54 pounds (700 grams) •Size 3.5 inches (8.9 cm) diameter by 3.35 inches (8.5 cm) high •Power 10 watts steady-state (nominal) •Cooling Conduction to mounting plate •Mounting 4 mounting bolts – M4 Activation Time 0.8 sec (5 sec to full accuracy) Performance – Gyro •Bias Repeatability 1°/hr to 10°/hr 1σ •Random Walk 0.04 to 0.1°/√hr power spectral density (PSD) level •Scale Factor Stability 100 ppm 1σ •Bias Variation 0.35°/hr 1σ with 100-second correlation time •Nonorthogonality 20 arcsec 1σ •Bandwidth > 500 Hz Performance – Accelerometer •Bias Repeatability 200 µg to 1 milli-g, 1σ •Scale Factor Stability 300 ppm 1σ •Vibration Sensitivity 17 µg/g2 1σ •Bias Variation 50 µg 1σ with 60-second correlation time •Nonorthogonality 20 arcsec 1σ •White Noise 50 µg /√Hz PSD level •Bandwidth > 500 Hz Operating Range •Angular Rate ±1000°/sec •Angular Acceleration ±100,000°/sec/sec •Acceleration ±40g •Velocity Quantization 0.00169 fps •Angular Attitude Unlimited Reliability (predicted) 23,345 hours MTBF (30°C missile launch environment) Input/Output RS-485 Serial Data Bus (SDLC) Data Latency < 1msec Environmental •Temperature -54°C to +85°C operating •Vibration 11.9g rms – performance 17.9g rms – endurance •Shock 90G, ms terminal sawtooth Summary of Ln-200 IMU Characteristics
  27. 27. Accelerometer Name $2K(1) Part of System Name $2Ksystem(1) Where Found IMU Performance vs. Cost Velocity Random Walk 0.60 (meters/sec)/√(rt-hr) Bias 1000 micro-g Misalignment 412 arcsec Scale Factor 500 ppm Second Order Scale Factor Non-Linearity 60 micro-g/g2 Additional Terms Notes
  28. 28. Accelerometer Name $20K Part of System Name $20K Where Found IMU Performance vs. Cost Velocity Random Walk 0.03 (meters/sec)/√(rt-hr) Bias 100 micro-g Misalignment 10.3 arcsec Scale Factor 10 ppm Second Order Scale Factor Non-Linearity 3 micro-g/g2 Additional Terms Notes
  29. 29. Velocity Random Walk 0.0003 (meters/sec)/√(rt-hr) Bias 100 micro-g Misalignment 3 arcsec Scale Factor 100 ppm Second Order Scale Factor Non-Linearity 0.5 micro-g/g2 Additional Terms Notes Accelerometer Name $100K Part of System Name $100K Where Found IMU Performance vs. Cost
  30. 30. Gyroscopes
  31. 31. INERTIAL ROTATION SENSOR TECHNOLOGY E;CoursesGyros
  32. 32. INERTIAL SENSOR APPLICATION 1 5 25 125 625 3125 1e-005 0.0001 0.001 0.01 0.1 1 10 WEIGHT SENSORPERFORMANCE(deg/hr) TACTICAL MISSILES GBI / ASAT RV MEDIUM ACCURACY AIRCRAFT COMMERCIAL AIRCRAFT HIGH ACCURACY AIRCRAFT ICBMSDI POINTING SURFACE SHIP SUB
  33. 33. Inertial Sensor Technology Comparison Inertial Acronym Definitions ESG Electrostatic Gyro FOG – Fiber Optic Gyro HRG – Hemispherical Resonator Gyro MS – Multisensor MEMS – Micromachined Electromechanical Sensor QRS – Quartz Rate Sensor RLG – Ring Laser Gyro Inertial Acronym Definitions ESG Electrostatic Gyro FOG – Fiber Optic Gyro HRG – Hemispherical Resonator Gyro MS – Multisensor MEMS – Micromachined Electromechanical Sensor QRS – Quartz Rate Sensor RLG – Ring Laser Gyro ESG RLG FOG MS QRS HRG MEMS G yroD rift (deg/hr) Submarines Strategic MX Surface Ships Aircraft Cruise Missles UAVs Precision Guided Munitions (PGM) SCUD-B NO-DONG Unguided GGP FOG EGI SLAM-ER SLAM F-18 TLAM JDAM AGM-L30 EKGM All sensor perf ranges are estimates based on available information All sensor perf ranges are estimates based on available information
  34. 34. Honeywell Gyro Technology Heritage 1920 1960 1970 1980 2000 202020101990 Iron Gyros Optical Gyros MEMS Optical Gyros  Ring Laser Gyro  Fiber Optic Gyro  Digital Output  Moderate Cost Iron Gyros  Spinning Wheel  Analog Output  High Cost MEMS Gyros  Silicon Sensor  Analog or Digital Output  Low Cost World’s first application gyros invented by Elmer Sperry
  35. 35. IMU Product Evolution Overview RLG FOG MEMS • EGI • GGP • Future • MAPS • PSN Growth • Digital Laser Gyro • HG1700 • HG1800 • HG1900 - in production - developmental - in development Tactical Grade IMUs Navigation Grade Systems and Components EGI Embedded GPS Inertial Integrated System - aircraft, et al MAPS Modular Azimuth & Positioning System - surface vehicles GGP GPS Guidance Package - host of DoD platforms PSN Precision Strike Navigator - precision guided munitions
  36. 36. Rate Gyro Principles and Designs Type Principle Rotor 1 and 2 2 1 Constancy of Angular Momentum Sagnac Effect 1 1 Preservation of Plane Vibration 1 Degrees of Freedom Design Vibration Optical Hemispherical Resonant Ring Laser. Fibre Optic. Rigid Rotors. Dry Tuned. Nuclear Resonant. Example Etak Hitachi Andrews Murada Delco Draper Bosch
  37. 37. CURRENT GYRO TECHNOLOGY APPLICATIONS
  38. 38. Sagnac Effect Active Approach Passive Approach RING LASER FOG INTERFEROMETER OPTICAL GYRO TECHNOLOGIES ∆ƒ = (4Α/λΡ)Ω ∆Φ = (8πΝΑ/λ )Ωc
  39. 39. Suitability of RLG for Strapdown •Wide Dynamic Measuring Range •Direct Digital Output •Excellent scale factoring Linearity and Repeatability •Excellent Bias Repeatability •Rapid Reaction •No G Sensitivity
  40. 40. GG 1320 Digital Ring Laser Gyro • Characteristics — < 5.5 cubic inches — < 1 lb — < 2.5 watts — DC power in (+ 15 and +5 Vdc) — Compensated serial digital data output — No external support electronics — All high voltages self-contained — Built on proven RLG technology (> 60,000 RLGs delivered) — Proven mechanical dither • Demonstrated better than 1.0 nmi / hr performance — Low random walk — Excellent scale factor stability — Superb bias stability — No turn-on bias transients — Low magnetic sensitivity Laser Block in full-scale production (900 gyros in 1992, 1300 in 1993, 1400 in 1994)
  41. 41. Honeywell Ring Laser Gyros (RLGs)
  42. 42. Ring Laser Gyro Operation
  43. 43. The Fiber Optic Gyro • Consists of: 1. Semiconductor laser diode as light source. 2. Beam splitter. 3. Coil of optical fiber. 4. Photodetector The Fiber Optic Gyro (FOG) measures rotation by analyzing the phase shift of light caused by the signac effect
  44. 44. Tactical Grade Closed-Loop FOG• Tactical FOG IMU funded by USAF • HG1800 FOG IMU is pin-for-pin compatible with HG1700 RLG IMU • Goals: 1 deg/hour Gyro Error 1 milli-G Accel Error • Housing identical to HG1700 IMU <35 cubic inches
  45. 45. Types/Characteristic Applications Ex. Manufacturer Accuracy (deg/hr) Maturity Cable Length (meters) Commercial Grade Automotive, Camera Andrews 100 Present 100 Tactical Grade Attitude/Hdg references; Short-term inertial (min) Litton 200, Honeywell 1 Present 200 Avionic Grade Aircraft & Cruise missile inertial Eg GGP (GPS Guidance Package) Honeywell & Litton .01 - .1 Within next year or two 1000 Strategic Grade Long-term ship inertial Honeywell .00001 Maybe within 5 – 10 years in fleet 5000 - 10000 Quick-Look FOG Status
  46. 46.  SAGNAC Effect (Phase Shift Measured in Nano Radians)  Computer Maintains Spatial Reference  Uses Large Coil LD Product (5 Km Fiber)  Rugged, High Shock Resistance  No Precision Machining Typical High-performance IFOG GYRO ELECTRONICS PUMP LASER WDM Erbium doped fiber LIGHT SOURCE IOC COUPLER X XX X X DET FIBER COIL ESG Spinner Assembly ROTOR TECHNOLOGY DIFFERENCESTECHNOLOGY DIFFERENCES  Spinning Mass (3600 RPS)  Rotor Maintains Spatial Reference  Small Size of Rotating Element 1 cm Rotor)  Not Rugged, Susceptible to Rotor Crashes  Expensive Technology, Precision Machining Ω=∆Φ c NA λ π8
  47. 47. IMU Product Evolution Summary • RLG IMUs and RLG systems are a growth industry with proven track records in the field • FOG Inertial Systems striving to be lower price than comparable RLG-based systems • MEMS gyros offer the lowest price, smallest size, and lowest power for a tactical IMU • MEMS gyro performance will improve to 1 deg/hr in the next few years; ManTech programs will enable affordable MEMS IMUs in quantities
  48. 48. Coordinate Systems
  49. 49. Coordinate Frames AXIS 1 AXIS 2 AXIS 3 Inertial(I) (vernal equinox (in equatorial plane) (polar) Aries) ECEF(E) (through (in equatorial Greenwich) plane) Local Level (north)(in meridian (East) (down) North(N) plane) [ ]3GHA ↓ Aˆ Bˆ Pˆ [ ]3 22 - LoL      − ↓ π mGˆ mG ′ Pˆ Nˆ Eˆ Dˆ [ ]3α- ↓
  50. 50. AXIS 1 AXIS 2 AXIS 3 Wander(WA) (α counterclockwise (α counterclockwise from north) from east) (α chosen such that ) Body (point to bow in (point to starboard (deck to keel) deck plane) in deck plane) Train gunsight(T) (out through gun barrel) don’t care don’t care Coordinate Frames cont’d owBˆ tbdSˆ kDˆ LD ie WA IE sinˆ ω−=•Ω  DW ˆˆ =VˆUˆ [ ] [ ] [ ]321 HPR ↓ Gˆ [ ] [ ]32 AzElv ↓ NOTE: Names, ordering of axes, ordering of rotations are not universally accepted. They are conventions and definition
  51. 51. Coordinate Systems Use Navigation quantities, eg, Position, Velocity, Acceleration, Jerk…. are three dimensional vectors and must, when quantified, be expressed with respect to a reference frame (aka) coordinate system. Likewise navigation measurements, eg distances and angles are made with respect to origins and axes of a coordinate system. Va = = (for example) 5 10 14 V1 a V2 a V3 a Meters/secExample: Three scalar elements of velocity vector wrt a coordinate frame.
  52. 52. GEODESY, DATUMS
  53. 53. Conceptual Reasons for Studying Geodesy • Three main reasons for studying Geodesy/Astronomy related to inertial navigation: 1.Understanding the meaning of inertial coordinate frame. 2.Knowing gravitational attraction. 3.Knowing the shape of the earth to determine Latitude, Longitude , and Height from ECEF position.
  54. 54. The Ellipsoid of Rotation Z P P’ Equatorial Plane a a F O F’ b X a a 22 ba + 12 2 2 2 =+ b Z a X
  55. 55. Shape of the Earth
  56. 56. WGS-84 & WGS-72 Defining Parameters For WGS-84 Ellipsoid
  57. 57. WGS-84 Derived Geometric Constants CONSTANT NOTATION VALUE Flattening(ellipticity) f 1/298.257223563 Semiminor Axis b 6356752.3142m First Eccentricity e 0.0818191908426 First Eccentrity Squared e 2 0.00669437999013 Polar Radius of Curvature c 6399593.6258m Axis Ratio b/a 0.996647189335m Mean Radius of Semiaxis R1 6371008.7714m Equal Area Sphere Radius R2 6371007.1809m Equal Volume Sphere Radius R3 6371000.7900 First Eccentricity Squared= (a2 -b2 )/a2
  58. 58. Different datums may use different ellipsoids. Datums may also differ by the location of the center and orientation of the ellipsoid.
  59. 59. Simply put, a datum is the mathematical model of the Earth we use to calculate the coordinates on any map, chart, or survey system. All coordinates reference some particular set of numbers for the size and shape of the Earth. The problem for warfighters is that many countries use their own datum when they make their maps and surveys--what we call local datums. Other nations' maps often use coordinates computed assuming the Earth is a completely different size and shape from what the Department of Defense uses, but we have to be ready to fight around the world. US forces now use datum called World Geodetic System 1984, or WGS 84. The National Imagery and Mapping Agency (NIMA) produces all for its new maps with this system. Unfortunately, we reprint many of our maps from products made by allied countries that use local datums. Our old maps were made on several different local datums, or sometimes WGS 72 (maps using this datum were often printed "World Geodetic System" with no year identification). So the old maps we're reproducing, and the foreign ones we reprint, might use those other datums. WHAT’S A DATUM?
  60. 60. Gravity Disturbance Effects On INS
  61. 61. TLV = True Local Vertical Perpendicular to Geoid Actual Gravity Vector Astronomic Vertical REV = Reference-Ellipsoid Vertical Perpendicular to Reference Ellipsoid Theoretical Gravity Vector Geodetic Vertical Geodetic Latitude Surface of the Earth Dynamic Sea Level Surface of Reference Ellipsoid Surface of Geoid Gravity Anomaly Deflection of the Vertical Astronomic Latitude TLV REV N SST N = Surface of Geoid - Surface of Ellipsoid SST = Sea Surface Topography Figure 1. Simplified Depiction of Gravity Quantities E:CoursesGeophysical Navigation
  62. 62. APPROACHES TO GRAVITY COMPENSATION STORED MAP APPROACH PATROL AND PRELAUNCH PHASE USE DEFLECTION/GEOD MAPS TARGET OFFSETS USED FOR INFLIGHT EFFECTS COMPUTED FROM A COMBINATION OF GLOBAL/LONG WAVELENTH GRAVITY MODELS AND HIGH FREQUENCY DATA MAPS REAL-TIME COMPENSATION GRAVITY GRADIOMETER/GRAVIMETER MAY BE USED TO LIMIT GRAVITY-INDUCED NAVIGATION ERRORS LAUNCH POINT MEASUREMENTS MAY BE USED TO REDUCE INFLIGHT EFFECTS 6/10/99
  63. 63. Gravity Compensation Techniques GRAVITY COMPENSATON EMBODIES • MAP UTILIZATION/INTERPOLATION AND/OR • REAL-TIME MEASUREMENTS AND • SYSTEM INTEGRATION FUNDAMENTAL ELEMENTS OPTIMAL ESTIMATES OF NAV QUANTITIES NAVAIDS INS GRAVIMETER/ GRADIOMETER STORED GRAVITY MAP SYSTEM INTEGRATION ESTIMATOR + +
  64. 64. INS Error Analysis
  65. 65. Causes of Inertial Navigation Errors • Initial Conditions – An inertial needs three dimensional position, velocity, and attitude (theoretically wrt the inertial coordinate system, but practically wrt a local coordinate system). – For self initialization, these initial condition errors (particularly initial attitude errors) can be caused by sensor errors. – Initial position and velocity often obtained from GPS • Sensor Errors – Gyro and Accelerometer Errors • Bias, Scale factor, Cross axis sensitivities, input axis misalignments, environmental sensitivities
  66. 66. Causes of Inertial Navigation Errors (cont’d) • Inertial Sensor Assembly Misalignments – Each sensors orientation may be misaligned – In general, only one accelerometer input axis can arbitrarily be taken to be correct • Environmental Effects – Gravity Disturbance Errors • Vertical Deflection for horizontal loops • Gravity anomaly for vertical loop • Aiding Sensor Effects – Errors in altimeter either due to instrument or environment; similarly for EM Log or Doppler aiding • Other – Generally small digital data processing (coning and sculling) and timing errors – Latency, synchro conversion, vibration
  67. 67. GPS/INS Systems
  68. 68. Inertial Navigation System Aiding Sources Optimal Processor Corrected Navigation Output (Includes Models of INS errors, aiding errors, and motion models) Non-Complementary Navigation Integration Methodology * * Branches represent potentially individual accels. or gyro. outputs
  69. 69. Inertial Navigation System Aiding Sources Inertial Error Estimates Corrected Inertial Outputs Kalman Filter+ - Inertial + Aiding errors errors True navigation + aiding errors Standard Complementary Filter Methodology in Feedback Configuration
  70. 70. Loosely Coupled GPS/INS Integration ArchitectureRF / IF / A/D MULTI-CHIP CORELATOR CARRIER DISCRIMINATOR 90° I & D IE IP QE QL IL QP } L1 L2 I Q (1000 Hz) IMU KALMAN FILTER MEASUREMENT PROCESSING KALMAN FILTER Σ NAVIGATION EQUATIONS (CHIP/SEC) (50 Hz) (CYC/SEC) (50 Hz) ρ (1 Hz) ρ (1 Hz) . PVT (1 Hz)∆θ,∆υ PVAtt (1 Hz) LOS VELOCITY AIDING (50 Hz) INERTIAL SYSTEM PROCESSING 1 of N GPS RCVR CHANNELS GPS RCVR PROCESSING + - GPS NAV PROCESSING (256 HZ) MEASUREMENT PROCESSING CODE NCO CARRIER NCO KFILTER FILTER K NAVIGATION EQUATIONS CODE GENERATOR CODE DISCRIMINATOR ΣΣ LOS PROJECTION + - Σ CARR. NCO BIAS (1 Hz) CODE NCO BIAS (1 Hz) E:CoursesGPS[10] GPS-INS
  71. 71. Tightly Coupled GPS/INS Integration ArchitectureRF / IF / A/D MULTI-CHIP CORELATOR CARRIER DISCRIMINATOR 90° I & D IE IP QE QL IL QP } L1 L2 I Q (1000 Hz) IMU (CHIP/SEC) (50 Hz) (CYC/SEC) (50 Hz) ρ (1 Hz) ρ (1 Hz) . PVT (1 Hz) ∆θ,∆υ PVAtt (1 Hz) LOS VELOCITY AIDING (50 Hz) INERTIAL SENSOR PROCESSING 1 of N GPS RCVR CHANNELS GPS RCVR PROCESSING GPS NAV PROCESSING (256 HZ) CODE NCO CARRIER NCO KFILTER FILTER K MEASUREMENT PROCESSING CODE GENERATOR CODE DISCRIMINATOR ΣΣ LOS PROJECTION + - Σ CARR. NCO BIAS (1 Hz) CODE NCO BIAS (1 Hz) NAVIGATION EQUATIONS KALMAN FILTER PVAtt PV E:CoursesGPS[10] GPS-INS
  72. 72. Intimately Coupled GPS/INS Integration Architecture RF / IF / A/D MULTI-CHIP CORELATOR CARRIER DISCRIMINATOR 90° I & D IE IP QE QL IL QP } L1 L2 I Q (1000 Hz) IMU (CHIP/SEC) (50 Hz) (CYC/SEC) (50 Hz) PVT (1 Hz) ∆θ,∆υ PVAtt (1 Hz)INERTIAL SENSOR PROCESSING 1 of N GPS RCVR CHANNELS GPS RCVR/NAV PROCESSING (256 HZ) CODE GENERATOR CODE DISCRIMINATOR LOS PROJECTION + - Σ NAVIGATION EQUATIONS KALMAN FILTER FILTER FILTER CARRIER NCO CODE NCO ∆ρ, ∆ρ (1 Hz) . PV (1 Hz) T (100 Hz) E:CoursesGPS[10] GPS-INS
  73. 73. H-764G Embedded GPS/INS H-764G Features • Small size: 7.0”H x 7.0”W x 9.8”L • Light weight: 18 lbs* • Low power: < 40 watts* • High MTBF: > 6,500 hours* • GPS/INS and two expansion slots in one small package • Single i960 Microprocessor • Mature, High-Performance Inertial Sensors • 15-year Inertial Calibration Interval • Collins GPS receiver Module • Flight-Proven Ada Software • Turn-Key System Missionization * Will vary depending upon how the expansion slots are populated
  74. 74. Some Inertial Navigation Systems
  75. 75. vendor units model HG1900 HG1920 comments volume 16 7.4 in³ Length/Diameter in Width in Depth in mass 0.45 kg power 3 w temperature range -55 to +85 ºC vibration shock 10000 g update rate 100 Hz range 20 g bias 1 .6-6.4 mg scale factor 300 84-2700 ppm nonlinearity 500 200 ppm resolution µg noise mg/√Hz bandwidth Hz random walk .19-.17 m/s/√hr range 1440 º/sec bias 30 09-76 º/hr scale factor 150 91-524 ppm nonlinearity ppm resolution º/hr noise deg/sec bandwidth Hz random walk 0.1 .02-.17 º/√hr data source gyro http://content.honeywell.com/ds Honeywell/Draper imu accelerometer Honeywell/Draper
  76. 76. vendor units model LN-200 comments volume 32.2 in³ Length/Diameter 3.5 in Width in Depth 3.35 in mass 0.7 kg power 10 w temperature range -54 to 85 ºC vibration 18 g rms shock 90 g update rate Hz range 40 g bias 1 mg scale factor 300 ppm nonlinearity ppm resolution µg noise mg/√Hz bandwidth Hz random walk 0.012 m/s/√hr range 1000 º/sec bias 10 º/hr scale factor 100 ppm nonlinearity ppm resolution º/hr noise deg/sec bandwidth 500 Hz random walk 0.1 º/√hr data source gyro imu Northrup-Grumman accelerometer Northrup-Grumman
  77. 77. vendor units model SiLMU01 comments volume 6.1 in³ Length/Diameter 2.36 in Width in Depth 1.79 in mass 0.26 kg power 5 w temperature range -40 to +72 operating ºC vibration shock 100 11 ms, .5 sine g update rate Hz range 50 ± g bias 2 1 σ mg scale factor 2000 1 σ ppm nonlinearity 1500 ppm resolution µg noise 5 mg rms in band mg/√Hz bandwidth 75 Hz random walk 1 m/s/√hr range 1000 ± º/sec bias 100 º/hr scale factor 400 accuracy ppm nonlinearity 100 ppm resolution º/hr noise 0.5 rms inband deg/sec bandwidth 75 Hz random walk 1 º/√hr data source http://www.baesystems- BAE imu accelerometer gyro BAE
  78. 78. • The AN/WSN-7 was designed as a form, fit, and function replacement for the AN/WSN- 1, and -5 for installation on DDG 51, CG 47, CV, CVN, LHA 1 and LHD 1 Class platforms. • The AN/WSN-7A was designed as a form, fit, and function replacement for the AN/WSN-3 on SSN688 Class platforms. • Provides attitude (roll, pitch, and heading), position, and velocity data to ship system users. WSN-7 Information Courtesy Spawar Systems Center, Norfork (Carvil, Galloway)
  79. 79. CN-1695/WSN-7(V) CN-1696/WSN-7(V) CN-1697/WSN-7(V) Ring Laser Gyro Navigator MX-11681/WSN Inertial Measuring Unit (Inside Cabinet) IP-1747/WSN Display Unit, Control Equipment AN/WSN-7(V) 1/2/3 RLGN Courtesy Spawar Systems Center, Norfork (Carvil, Galloway)
  80. 80. Install Schedule SHIP CLASS FY02 FY03 FY04 FY05 FY06 FY07 TO COMPLETE CG 47 CG 48 CG 49 DDG 51 DDG 51 DDG 61 DDG 53 DDG 65 DDG 56 DDG 73 DDG 59 DDG 74 DDG 52 DD 963 LHA LHA 5 LHA 3 LHA 1 LHD LHD 4 LHD 1 LHD 2 LHD 3 LHD 6 AGF/LCC LCC 19 LCC 20 CV/CVN CVN 65 DDG DDG 93 DDG 94 DDG 95 DDG 97 DDG 102 DDG 103 DDG 104 CVN CVN 67 LHD LHD 8 TOTAL SHIPS 18 7 2 4 OPNSCN
  81. 81. CD-132/WSN-7A(V) CD-133/WSN-7A(V) Control Unit, Electronic IP-1747/WSN Display Unit, Control CY-8827/WSN-7A(A) Enclosure Assembly, Inertial Measuring Unit MX-11681/WSN Inertial Measuring Unit MX-11682/WSN-7A(V) Support, Electronics Unit MX-11682/WSN-7A(V) Support, Electronics Unit IP-1746/WSN Display Unit, Secondary Control IP-1747/WSN Display Unit, Control Equipment (Cont.) AN/WSN-7A(V) Red/Green RLGN Courtesy Spawar Systems Center, Norfork (Carvil, Galloway)
  82. 82. Install Schedule (Cont.) SHIP CLASS FY02 FY03 FY04 FY05 FY06 FY07 TO COMPLETE SSN 688 SSN 690 SSN 763 SSN 719 SSN 767 SSN 721 SSN 768 SSN 722 SSN 771 SSN 754 SSN 772 SSN 756 SSN 701 SSN 757 SSN 760 SSN 713 SSN 715 SSN 709 SSN 715 SSN 752 SSN 756 SSN 761 SSN 764 SSN 698 SNN 699 SSN 720 SSN 769 SSN 21 SSN 21 SSN 22 SSN 21 SSN 774 SSN 778 SSN 779 SSN 780 SSN 784 SSN 782 SSN 783 SSN 784 SSN 785 SSN 786 thru SSN 803 SSGN SSGN 726 SSGN 728 SSGN 727 SSGN 729 TOTAL SHIPS 11 3 7 11 5 3 18 OPNSCN
  83. 83. Evolution of Inertial Navigation 3-Axis Gyro Chip 3-Axis Accelerometer Chip
  84. 84. Evolution of Inertial Navigation Technology • Size ,cost,power of Inertial Systems greatly reduced by technology developments • MEMS Technology promises the next major step in Inertial System evolution Litton SiGyTM S/N#0004 FPGA Gimbaled Technology Strapdown Technology Ring Laser Technology Fiber Optic Technology MEMS Technology
  85. 85. Low Cost Guidance and Navigation • Low Cost Guidance Package enables cost effective precise positioning to be embedded in low value, high volume quantity systems GPS Low Cost Guidance and Navigation Package MEMS Inertial Sensors DSP’s Processors Electronics Applications • Air/Ground Manned /Unmanned Platforms • Guided Rockets • Guided Munitions • Soldier Man Pack • Re-supply Vehicles • ……. • …. • ..
  86. 86. 2000 200320022001 LN 205G ATK SAASM GPS •Leveraging LN 200 series development reduces MEMS time-to-market LN 205 LN 200 IMU LN 300 LN 300GLitton SiAcTM S/N#0001 Litton SiAcTM S/N #0001 Litton SiAcTM S/N#0001 Litton SiGyTM S/N #0001 Litton SiGyTM S/N#0004 ANALOG DEVICES ANALOG DEVICES ANALOG DEVICES ANALOG DEVICES Digital Asic Analog Asic LN 200G IMU LN300 /LN 200 MEMS INS/GPS Roadmap
  87. 87. The Future • Over the next 3 to 5 years, the applicability of MEMS for high-g tactical applications will be conclusively demonstrated. • From 5 to 10 years, the insertion of high- volume production MEMS IMUs and INS/GPS into tactical systems will occur at an ever- increasing rate. • The realization of 3 gyros on a chip and 3 accelerometers on a chip, represents the next order-of-magnitude size reduction. • Commercial applications will exploit the development MEMS technology into quantities of billions. 3-Axis Gyro Chip 3-Axis Accelerometer Chip

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