Navigation Sensors and INS Mechanization Tuesday 26 Feb 2013 NMT EE 570 Location and Navigation Theory amp Practice Slide 1 of 14 Navigation Sensors and INS Mechanization Navigation ID: 713023
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EE 570: Location and Navigation: Theory & Practice
Navigation Sensors and INS Mechanization
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation
Equations – The Fundamental Problem
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
The Fundamental Inertial Navigation Problem:
Using inertial sensors (
accels
& gyros) and an initial position and orientation, determine the vehicle’s (i.e. body frame) current position, velocity, and attitude (PVA)Assumptions:Know where we started (initial PVA: , , & )Inertial sensors ( and ) are error free (relax later)Have a gravity () and/or gravitational () modelWhere am I ? – Current PVA ?With respect to which frame?
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Navigation Sensors and INS Mechanization
Navigation Equations
– Inertial Navigation
Inertial NavigationThe process of “integrating” angular velocity & acceleration to determine one’s position, velocity, and attitude (PVA)
Effectively “dead reckoning”
To measure the acceleration and angular velocity vectors we need at least 3-gyros and 3-accels
Typically configured in an orthogonal
triad
The “mechanization” can be performed wrt:The ECI frame,The ECEF frame, orThe Nav frame.Tuesday 26 Feb 2013NMT EE 570: Location and Navigation: Theory & PracticeSlide 3 of 14Slide4
Navigation Sensors and INS Mechanization
Navigation Equations
– ISA, IMU, & INS
An Inertial Navigation System (INS)
ISA – Inertial Sensor Assembly
Typically, 3-gyros + 3-accels + basic electronics (power, …)
IMU – Inertial Measurement Unit
ISA + Compensation algorithms (i.e. basic processing)
INS – Inertial Navigation SystemIMU + gravity model + “mechanization” algorithmsIMU- Basic ProcessingISACompAlgsRaw sensor outputs
Mechanization
Equations
INS
Initialization
Position, Velocity, and Attitude (PVA)
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
Gravity
Model
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Mechanization
Equations
Navigation Sensors and INS Mechanization
Navigation Equations
– Mechanization Process
Gravity /
Gravitational
Model
PriorAttitudePriorVelocity
Prior
Position
Updated
Attitude
Updated
Velocity
Updated
Position
Prior PVA
Updated PVA
IMU Measurements
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations
– A Four Step Mechanization
Can be generically performed in four steps:
Attitude Update
Update the prior attitude (rotation matrix) using the current angular velocity measurement (
)
Transform the specific force measurement (
)Typically, using the attitude computed in step 1.Update the velocityEssentially integrate the result from step 2. with the use of a gravity/gravitation model ()
Update the PositionEssentially integrate the result from step 3.
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations – A Four Step Mechanization
2. SF
Transform
Prior
Attitude
3. Position
Update
GravModelPrior
Velocity
Prior
Position
3. Velocity
Update
1. Attitude Update
Updated
Attitude
Updated
Velocity
Updated
Position
Prior PVA
Updated PVA
IMU Measurements
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations – Case 1: ECI Mechanization
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
CASE 1: ECI Frame Mechanization
Determine the Position, Velocity, and Attitude of the
Body
frame with respect to the
Inertial FrameDetermine our PVA wrt the ECI framePosition: Vector from the origin of the inertial frame to the origin of the body frame resolved in the inertial frame: Velocity: Velocity of the body frame wrt the inertial frame resolved in the inertial frame: Attitude: Orientation of the body frame wrt the inertial frame Slide 8 of 14Slide9
Navigation Sensors and INS Mechanization
Navigation Equations –
Case 1: ECI Mechanization
1. Attitude Update: Method ABody orientation frame at time “
k
”
wrt
time “
k-1”t = Timek – Timek-1
Body Frame
at time “k-1”
Body Frame
at time “k”
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations –
Case 1: ECI Mechanization
1. Attitude Update: Method B
Body orientation frame at time “k”
wrt
time “k-1”
t = Timek – Timek-1
Body Frame
at time “k-1”
Body Frame
at time “k”
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations –
Case 1: ECI Mechanization
1. Attitude Update:High Fidelity
Lower Fidelity
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations – Case 1: ECI Mechanization
2. Specific Force Transformation
Simply coordinatize
the specific force
3. Velocity Update
Assuming that we are in space (
i.e
. no centrifugal component)Thus, by simple numerical integration4. Position UpdateBy simple numerical integration
Tuesday 26 Feb 2013NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations – Case 1: ECI Mechanization
1. Attitude Update
Grav
Model
3. Velocity
Update
3. Position
Update
2. SF
Transform
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
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Navigation Sensors and INS Mechanization
Navigation Equations – Case 1: ECI Mechanization
Tuesday 26 Feb 2013
NMT EE 570: Location and Navigation: Theory & Practice
In continuous time notation:
Attitude:
Velocity:
Position:
Combining into a state-space equation:
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