September 2014
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GPS/IRS HYBRIDIZATION
IENAC T12
Anne-Christine Escher
Paul Thevenon
September 2014
September 2014
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GPS NAVIGATION
AND GNSS FOR CIVIL AVIATION
September 2014
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Outline
1. GPS principles
1. Positioning principle
2. GPS segments
2. GPS measurements
1. Measuring the distance
2. Satellite position and time (navigation
message)
3. User position
1. GPS measurement model
2. GPS position computation
4. GPS precision
1. SPS accuracy
2. Error budget
3. Constellation geometry
5. GNSS for Civil Aviation
1. Reminder of GNSS definition
2. Development of GNSS in Civil
Aviation
3. SiS & ICAO requirements
4. GNSS Autonomous integrity
monitoring
5. Onboard autonomous integrity
monitoring
6. Signal characteristics
6. Annex
GNSS receivers
Definitions
Reference documents
September 2014
1. GPS Principles
Positioning Principle
– GPS position estimation is based on “triangulation“ from satellites.
– Basic principle
• To measure the distances and relative velocities between satellites with known
orbits and a receiver with unknown position to find the location and the velocity of
the receiver.
• Satellites only broadcasts to the user (no return link).
– Measurements:
• The measured distances are propagation delays between the satellite and the
receiver.
• The measured velocities are the Doppler offset of the received signals.
– Result:
• Thanks to these measurements, any user can determine the position and velocity of
its antenna and synchronize its receiver oscillator with the GPS time reference. It is
thus possible to estimate the PVT parameters: Position, Velocity and Time.
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September 2014
1. GPS Principles
GPS space segment: constellation
–
–
–
–
Minimum of 24 satellites on 6 circular orbital planes with 55° inclination
Orbit radius of ~26600 km (altitude ~20200 km)
Orbit repetition: 12 siderial hours
Ground tracks repeat every 24 siderial hours (= 23h 56m 04.0905s )
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September 2014
1. GPS Principles
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GPS space segment: signals
– Each satellite has 3 or 4 atomic clocks (Cesium and Rubidium, the last ones with Rb).
– The satellite uses 2 or 3 carrier frequencies in the L band
• L1: 1575.42 MHz in an ARNS band
• L2: 1227.60 MHz not in an ARNS band
• L5: 1176.45 MHz in an ARNS band for new satellites (Block IIF, 2009-?)
– An ARNS (Aeronautical Radio Navigation Services) band is allocated by the ITU to
aeronautical radionavigation systems.
Providing a safety service, such allocations permit to claim protection from other systems.
September 2014
1. GPS Principles
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GPS space segment : signals and services
– The signals are transmitted using spread spectrum techniques: a binary signal is the
product of the
Nav message
• navigation message with a low data rate
GPS
signal
• a pseudo-random noise sequence (PRN)
PRN sequence
with a very high rate.
f
c
L1 C/A
L1 P(Y)
L5
Carrier freq
1575.42 MHz
1575.42 MHz
1176,.5 MHz
Nav message
50 bps
50 bps
50 bps
PRN sequence
1.023 MHz
10.23 MHz
10.23 MHz
– Example:
• The C/A code means Coarse/Acquisition, and was initially created to acquire more
rapidly the P(Y) code. Actually, it is used by all civil receivers.
• The P(Y) code is a PRN code that can either be the P (Precise) code, or the Y code.
The P code P is public, the Y code is secret. This signal is used for (US + allied)
military applications.
• L5 is a civil signal, opening accuracies to the civil world reserved to military
applications up to now: faster coderate + dual frequency processing.
September 2014
1. GPS Principles
GPS control segment
– Functions :
• Control the characteristics of the transmitted signals from each satellite
• Compute ephemeris data (Keplerian elements) and satellite clock corrections
• Upload the navigation message to each satellite
– Structure :
• It contains
– control stations,
– upload stations,
– a master control station (MCS) in Colorado.
• The MCS receives the measurements from each control station, and estimates the
ephemerides and clock drift model parameters for each satellite.
• There are 4 upload stations (1 to 3 upload per day per satellite).
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September 2014
1. GPS Principles
GPS control segment
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September 2014
2. GPS Measurements
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Measuring the distance (1/4)
– Each satellite (SV) generates its own PRN code.
• They are Gold codes whose correlation functions are very typical and interesting for
SV identification and signals synchronisation.
• The faster the code are transmitted, the more precise synchronisation can be
AUTOCORRELATION OF 1 GPS GOLD CODE
achieved. 1.2
INTERCORRELATION BETWEEN 2 DIFFERENT GPS GOLD CODES
0.08
0.06
1
0.04
0.8
0.02
0.6
0
0.4
-0.02
0.2
-0.04
0
-0.06
-0.20
200
400
600
800
DELAY [chips]
1000
1200 -0.08
0
200
400
600
800
DELAY [chips]
1000
1200
September 2014
2. GPS Measurements
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Measuring the distance (2/4)
– Each signal transmitted by the satellites is modulated using a PRN code.
– The receiver (Rx) measures the delay between :
• the direct signal received by the antenna coming from the satellite, and
• a local replica of that signal generated by the receiver
 Asuming the Rx and the SV are generating the same PRN code at the same time, the
process consists in detecting the correlation peak.
September 2014
2. GPS Measurements
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Measuring the distance (3/4)
– SVs are equipped with atomic clocks, but it is not the case for the Rx: Rx clocks are far
less accurate.
 There is a shift between the SV reference time and the Rx reference time.
– The measured delay is referred to as pseudorange (PR). It is the sum of:
• the propagation delay between the satellite and the receiver antennas,
• plus the shift between the satellite time and the receiver time.
September 2014
2. GPS Measurements
Measuring the distance (4/4)
– A reference time is defined (eg. GPS time).
– The shift between the satellite and the receiver times is then the difference between:
• the offset between the satellite time and the reference time, and
• the offset between the receiver time and the reference time.
Reference time scale
– The shift between the satellite and the reference times can be corrected
 We get the corrected pseudorange
𝑃𝑅𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 = 𝜏 + ∆𝑡𝑅𝑥 . 𝑐 + 𝜀
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September 2014
2. GPS Measurements
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Satellite position and time (1/2)
– The propagation time depends upon the relative position between the receiver
antenna and the satellites antenna.
 Assuming the position of the satellites is known as well as the shift between
satellite and reference times, the user can estimate its own position and its time
shift with respect to the reference time.
– The GPS Control Segment estimates these 2 sets of parameters – satellite positions
and time shift - for each satellite.
– Because of the very stable oscillators onboard satellites, it is possible to have an
accurate model of the satellite time to reference time drift.
– Ths information is transmitted to the user through the navigation message contained
in the signal broadcast by the satellites.
September 2014
2. GPS Measurements
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Satellite position and time (2/2)
– Example: GPS navigation message
• Binary data transmitted at 50 bps on L1 and L2 by each satellite
• It is composed of 25 frames of 1500 bits that repeats. The total duration of the message
is: 25*1500/50 = 750 s = 12,5 min
• Each frame is decomposed into 5 sub-frames of 300 bits.
• Each sub-frame is decomposed into 10 words of 30 bits
Frame
TLM
HOW
Clock Corrections /URA/Satellite Health (transmitting sat)
Sub-frame 1
TLM
HOW
Ephemeris data (transmitting sat)
Sub-frame 2
TLM
HOW
Ephemeris data (transmitting sat)
Sub-frame 3
TLM
HOW
Almanach/Iono/UTC over 25 frames (all sats)
Sub-frame 4
TLM
HOW
Almanach/Health over 25 frames (all sats)
Sub-frame 5
Total duration of a sub-frame: 6 secondes
September 2014
3. User Position
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GPS measurements model
The GPS corrected measurements general model is the following:
𝑃𝑅𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑 = 𝑋𝑆𝑉 − 𝑋𝑢𝑠𝑒𝑟 + 𝑏𝑢𝑠𝑒𝑟 + 𝜀
with
𝑋𝑆𝑉 , the satellite location
𝑋𝑢𝑠𝑒𝑟 , the unknown receiver location
𝑏𝑢𝑠𝑒𝑟 , the unknown receiver clock bias
Corrected
pseudorange
User
clock bias
Line of constant
pseudorange
September 2014
3. User Position
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GPS position computation
– From a set of pseudo-ranges, we can define a set of non-linear equations linking the
observations and the user position:
1
1
𝑃𝑅𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑
= 𝑋𝑆𝑉
− 𝑋𝑢𝑠𝑒𝑟 + 𝑏𝑢𝑠𝑒𝑟 + 𝜀 1
2
2
𝑃𝑅𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑
= 𝑋𝑆𝑉
− 𝑋𝑢𝑠𝑒𝑟 + 𝑏𝑢𝑠𝑒𝑟 + 𝜀 2
⋮
𝑁
𝑁
𝑃𝑅𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑒𝑑
= 𝑋𝑆𝑉
− 𝑋𝑢𝑠𝑒𝑟 + 𝑏𝑢𝑠𝑒𝑟 + 𝜀 𝑁
– At least 4 equations are required to solve the 4 unknowns : (x,y,z)user and buser
– The solving of this system can be done
• at each epoch by using a Non-Linear Least Square estimation technique, usually, taking
into account a weighting matrix  Weighted Least Square estimation.
• using all previous epochs with a Kalman filter
September 2014
4. GPS Precision
Performance with GPS L1 C/A
– [GPS SPS PS, 2008] specifies the following time/position performance:
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September 2014
4. GPS Precision
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Error budget - Atmospheric errors
– Ionosphere:
• Ionized layer of the upper atmosphere
• Dispersive (error depends upon the frequency)  can be corrected by dual frequency receiver
• Spatial and temporal correlation of the error
– Troposphere:
• lower atmosphere,
• Spatial and temporal correlation of the error
Satellite at horizon  goes
through a thick layer
– Corrections are broadcast in the navigation message
Satellite at zenith  goes
through a thin layer
Ionosphere
50-1000 km
Troposphere
0-50 km
September 2014
4. GPS Precision
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Error budget - Multipath errors
– Satellite signal reflections from the local environment interfere with the direct signal.
– The result is a barrage of signals arriving at the antenna: the direct one and delayed
replicas known as multipaths.
– If the bounced signals are strong enough, they can confuse the receiver and cause
erroneous measurements.
Diffraction
September 2014
4. GPS Precision
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Error budget – Measurements Model
– L1 C/A code pseudorange raw measurement at the output of the receiver DLL, for satellite 𝑖
Satellite to receiver
distance
≈ 20,000km
Orbit
uncertainty
Satellite
clock bias
≈ 1km
Tropo.
delay
≈ 2-30m
Iono.
delay
≈ 0,15-30m
Receiver
thermal noise
≈ 1m
L1 C/A code
multipath error
≈ 0-150m for 1 ray
𝐶1𝑖 = 𝑑 𝑖 + 𝑐 ∙ 𝑡𝑢 + 𝑈𝑅𝐸 𝑖 − 𝑐 ∙ 𝑡𝑆𝑉 𝑖 + 𝑑𝑡𝑟𝑜𝑝𝑜 𝑖 + 𝑑𝑖𝑜𝑛𝑜𝐿1 𝑖 + 𝑛𝑛𝑜𝑖𝑠𝑒𝐶1 + 𝑀𝑃𝐶1 𝑖
Code meas.
[m]
User clock bias
≈ 300m
Estimated by the user, as part
of the navigation solution
Partially compensated using
error correction
mathematical models
May be mitigated using code-carrier
smoothing
– After corrections application, we get the corrected L1 C/A code pseudorange measurement
for satellite 𝑖
𝑃𝑖 = 𝑑 𝑖 + 𝑐 ∙ 𝑡𝑢 + 𝜀𝑈𝑅𝐴 𝑖 + 𝜀𝑡𝑟𝑜𝑝𝑜 𝑖 + 𝜀𝑖𝑜𝑛𝑜𝐿1 𝑖 + 𝜀𝑛𝑜𝑖𝑠𝑒𝐶1 + 𝜀𝑀𝑃𝐶1 𝑖
𝑈𝑠𝑒𝑟 𝐸𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑅𝑎𝑛𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 𝑈𝐸𝑅𝐸 : 𝜀𝑖
September 2014
4. GPS Precision
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Error budget - User Equivalent Range Error (UERE)
– UERE represents the impact of errors affecting the propagation of the signal or the
signal processing on the pseudorange measurements after application of the errors
correction or mitigation techniques
– For instance for GPS, the following error budget is proposed by [GPS SPS PS, 2008]:
(AOD = Age of data)
September 2014
4. GPS Precision
Constellation geometry – DOP
– The DOP (Dilution Of Precision) value translates the quality of the constellation
geometry of the visible satellites to estimate a position or time
– It is a unitless parameter which only depends on satellites positions relative to user
location.
– 𝜎𝑃𝑉𝑇 = 𝜎𝑈𝐸𝑅𝐸 ∗ 𝐷𝑂𝑃
Good DOP
Poor DOP
 The lower the DOP, the more accurate the estimate
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September 2014
5. GNSS for Civil Aviation
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Reminder of GNSS definition
– GNSS (Global Navigation Satellite System):
• It is a theoretical concept elaborated by the FANS (Future Air Navigation Systems) committee
from ICAO (International Civil Aviation Organization).
• It is a part of the global concept of CNS/ATM (Communication Navigation Surveillance/Air
Traffic Management). C, N and S support air traffic, while ATM supports its management.
– ICAO definition of GNSS: GNSS is defined as a system able to estimate the position
and time of the user, and that includes one or several satellite constellations,
onboard receivers, and an integrity monitoring system, augmented if necessary, in
order to reach required navigation performances for the desired aircraft operation.
– The GNSS concept was widely inspired from the GPS and GLONASS systems that were
just starting at that time.
– Usual definition of GNSS: it is very common to refer to any global satellite-based
navigation system as GNSS.
September 2014
5. GNSS for Civil Aviation
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GNSS development in Civil Aviation (1/2)
– Feb. 94: ICAO Council recommended the use of satellite navigation technology while
using as soon as possible existing constellations (GPS, GLONASS, augmentations).
– 1994/1996 GPS GLONASS offers:
• Oct. 1994: Letter from the US government to ICAO offering, without any direct user charges, an
open worldwide positioning service to civil aviation with GPS. At least 6 years notice prior to
termination.
• June 1996: Similar letter from the Russian federation to ICAO proposing a GLONASS open service
for a period of at least 15 years.
• Offers were reiterated at various occasions, e.g. February 2007 (180th Session of the ICAO
Council) [J. Nagle, ‘ICAO policy on GNSS, GNSS SARPs and global GNSS developments’]
– 1998: Assembly resolutions A32-19 and A32-20
• A32-19: “Charter on the Rights and Obligations of States Relating to GNSS Services”
• A32-20: “Development and elaboration of an appropriate long-term legal framework to govern
the implementation of GNSS”
September 2014
5. GNSS for Civil Aviation
GNSS development in Civil Aviation (2/2)
– GNSS Panel work has led ICAO to approve and publish in November 2002 in the Annex
10 to Chicago convention, GNSS Standards And Recommended Practices (SARPS) to
support all phases of flight up to Cat I (Precision Approach).
– In 2003, the 11th Air Navigation Conference recommends a worldwide transition to
GNSS-based air navigation.
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September 2014
5. GNSS for Civil Aviation
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Signal In Space & ICAO requirements
–
Signal in Space (SiS) is the signal transmitted by satellites
•
It is part of the Navigation System Error (NSE)
― ICAO SiS requirements are set assuming the combination of GNSS elements and a faultfree GNSS user receiver.
― GNSS comprises
•
•
•
Core constellations.
Augmentations: ABAS, SBAS and/or GBAS
Onboard receivers
― Requirements are defined
per operation as:
•
•
•
•
Accuracy (-95%),
integrity,
continuity,
and availability
Operation
Accuracy- 95%
Integrity
Continuity
Availability
En-route
En-route, Terminal
Initial Approach,
Intermediate, NPA,
Departure
APV1
APV2
CAT1
ICAO GNSS standards were first published in November 2002 in
Annex 10 of the Chicago Convention.
September 2014
5. GNSS for Civil Aviation
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Signal In Space & ICAO requirements
–
Accuracy: characterize typical behavior of the system in presence of nominal errors.
–
Integrity: Limit risk of abnormal behavior of the system due to errors resulting from
system faults. It is composed of several parameters:
– Maximum Tolerable Error / Alert Limit
– Time to Alert
– Integrity risk: probability that error > MTE
MTE Pos error
being detecting after TTA
Actual position
True position
–
Continuity: Limit risk of losing the service unexpectedly
–
Availability: fraction of time that one has Accuracy + Integrity + Continuity
September 2014
5. GNSS for Civil Aviation
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ICAO Signal In Space requirements (1/2)
Table 3.7.2.4-1 in Annex 10, Chapter 3 of the Chicago Convention
Operation
Accuracy- 95%
Integrity
Continuity
Availability
Horizontal
Vertical
Time to
Alert
Integrity Risk
En-route
3.7km
N/A
5min
1-1x10-7/h
1-1x10-4/h to
1-1x10-8/h
0.99 to
0.99999
En-route, Terminal
0.74km
N/A
15s
1-1x10-7/h
1-1x10-4/h to
1-1x10-8/h
0.99 to
0.99999
Initial Approach,
Intermediate, NPA,
Departure
220m
N/A
10s
1-1x10-7/h
1-1x10-4/h to
1-1x10-8/h
0.99 to
0.99999
APV1
16m
20m
10s
1-2x10-7 in any
approach
1-8x10-6 per 15s
0.99 to
0.99999
APV2
16m
8m
6s
1-2x10-7 in any
approach
1-8x10-6 per 15s
0.99 to
0.99999
CAT1
16m
6m to 4m
6s
1-2x10-7 in any
approach
1-8x10-6 per
15s
0.99 to
0.99999
September 2014
5. GNSS for Civil Aviation
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ICAO Signal In Space requirements (2/2)
Table 3.7.2.4-1 in Annex 10, Chapter 3 of the Chicago Convention
Operation
Alert Limit
Horizontal
Vertical
En-route (oceanic/continental low density)
7.4km
N/A
En-route (continental)
3.7km
N/A
En-route, Terminal
1.85km
N/A
NPA
556m
N/A
APV1
40m
50m
APV2
40m
20m
CAT1
40m
35m to 10m
September 2014
5. GNSS for Civil Aviation
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GNSS autonomous integrity monitoring
– Civil aviation requirements can be very stringent and up to now, the bare satellite
navigation systems alone cannot be used as a means of navigation.
– To ensure the levels required in terms of accuracy, integrity, continuity of service and
availability, ICAO standards define different architectures to augment the basic
constellations:
• Some of them use control stations to monitor satellite signals and provide corrections:
– GBAS (Ground-Based Augmentation System)
– SBAS (Satellite-Based Augmentation System)
• Others only use GNSS measurements redundancy or combine them with on-board navigation
sensors:
– ABAS (Aircraft-Based Augmentation System)
– These solutions are based onto a Fault Detection (FD) or a Fault Detection and Exclusion
(FDE) function
• FD allows to perform the detection of signals anomalies that is to say to make sure of the
integrity of the used signals
• Upon detection, FDE allows to make sure of the continuity of the navigation after detection
occurs.
September 2014
5. GNSS for Civil Aviation
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GNSS autonomous integrity monitoring
– FD performances are measured by computing protection level - H/VPL - values.
– The xPL is a bound of the positioning error which translates the quality of the
positioning from an integrity point of view.
 The lower the xPL, the more confident the positioning.
The xPL computed value depends on the constellation
geometry and the UERE.
HPL
HAL
Pos error
Actual position
– Example:
True position
In horizontal plane using RAIM for Fault Detection:
 HPL is a bound of the positioning error computed such as any error causing the horizontal
positioning error to exceed HPL is guaranteed to be detected with a given probability (eg. 10-3 for
NPA) that itself guarantees the Integrity Risk is satisfied.
 The GNSS means of navigation is claimed to be available, that is usable for navigation in the
intended operation, whenever HPL<HAL provided it also fulfills the ICAO accuracy and continuity
requirements.
September 2014
5. GNSS for Civil Aviation
Onboard autonomous integrity monitoring
Receiver Autonomous Integrity Monitoring (RAIM)
– Uses redundant GPS measurements only
– RAIM availability allows ICAO aviation operations from en route down to NPA.
– Widely implemented from general aviation to commercial aviation.
Aircraft Autonomous Integrity Monitoring (AAIM)
– Based on GPS measurements redundancy and onboard inertial information
– AAIM availability allows ICAO aviation operations from en route down to NPA
•
For instance, Northrop Grumman AIME is certified as a primary means of navigation on
Airbus aircrafts family
•
Supports Fault Detection and Exclusion (FDE) with an increased availability wrt RAIM and
better anomalies detection performances.
– Implemented on higher end commercial aviation only
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September 2014
5. GNSS for Civil Aviation
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Signal characteristics (1/2)
– Core constellation satellites are to be observed at an
elevation angle of at least 5° (mask angle)
• To guarantee the power of the received signal
in an unobstructed location (-160 dBW to -153 dBW)
• To limit multipath effects
• In ICAO Annexe 10, core constellation is defined as GPS+GLONASS
[www.spacegeodesy.re.kr/sgd/sgd02.aspx]
– WGS-84 is the position reference frame
– Signal processing thresholds are set to
• 𝐶 𝑁0 = 29.93 𝑑𝐵𝐻𝑧, for signal acquisition
• and 𝐶 𝑁0 = 32.4 𝑑𝐵𝐻𝑧, for signal tracking and demodulation. This guarantees a WER of 10−3
– Today, only mono-frequency code pseudorange measurements are used for
positioning on board C/A aircraft
• GPS L1 C/A signals are used worldwide.
September 2014
5. GNSS for Civil Aviation
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Signal characteristics (2/2)
– To be used for approach operations, a code-carrier smoothing must be
implemented to mitigate multipath and noise impact on the used measurements
• Indeed, carrier measurement are less affected by noise and multipath (typically,
cm-level accuracy)
• This filter has a 100s-constant time: the receiver must wait 3.6 times this time
before using the smoothed code measurements for positioning
• Using code-carrier smoothing implies to be able to detect cycle slip occurrences
that would affect the carrier measurements
Residual Multipath Error Std Model (including noise receiver)
• Yet, non-smoothed measurements are used
when implementing inertial hybridization
0.145
0.14
𝜎𝑎𝑖𝑟_𝑚𝑝 = 0.11 + 0.13𝑒𝑥𝑝 −𝐸𝑙/4
0.135
0.13
[m]
– A multipath residual error model for GPS
L1 C/A provides information on the residual
accuracy after smoothing.
• For protection level determination
• For position computation (Weighted LS)
0.125
0.12
0.115
0.11
0.105
0.1
0
10
20
30
40
50
Elevation [deg]
60
70
80
90
September 2014
6. Annexes
Onboard GNSS receivers
– To operate Area Navigation (RNAV) procedures, onboard equipment is not only
composed of the GNSS receiver, but also,
• an RNAV computer to elaborate the guidance,
• an aircraft navigation display
• a Man-Machine Interface for crew interface,
• and an updated navigation data base.
– For general aviation aircraft, this equipment is gathered in 1 or 2 systems.
– For air transport aircraft,
• the core GNSS receiver may be replaced by a Multi-Mode System (MMR) which
gathers many sensors and functionalities (GNSS and ILS receivers; FLS, GLS and MLS
modes) for multiple phases of flight.
• the RNAV computer is in the FMS (Flight Management System) which also includes
the navigation data base and is connected to different navigation sensors as inertia.
• the Man-Machine Interface is achieved through the MCDU (Multi Control Display
Unit)
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6. Annexes
September 2014
Definitions
–
ABAS - Aircraft-Based Augmentation System – is an augmentation system which
augments and/or integrates the information obtained from the other GNSS
elements with information on board the aircraft in order to ensure the SIS
performance.
–
SBAS - Satellite-Based Augmentation System – is a wide coverage augmentation
system in which the user receives augmentation information from a satellitebased transmitter. It is made up of the ground infrastructure, the SBAS satellites,
and the SBAS airborne receiver.
–
GBAS - Ground-Based Augmentation System – consists of ground and aircraft
elements. One ground station can support all the aircraft within its coverage
providing them with approach data, corrections and integrity information for
GNSS satellites in view via a VHF data broadcast (VDB).
–
The Signal In Space (SIS) is the aggregate of guidance signals arriving at the
antenna of an aircraft assuming a fault-free receiver.
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6. Annexes
September 2014
- 38 -
Reference Documents
ICAO document (SARPS)
• International Standards and Recommended Practices, Annex 10 to the Convention on International
Civil Aviation, Volume 1, Sixth Edition, 2006. Amendment 85.
RTCA, Inc. Documents (RTCA DO) documents
• MOPS for airborne supplemental navigation equipment using Global positioning System (GPS), DO
208, 1991
• MOPS for GPS Wide Area augmentation System Airborne Equipment, DO 229C, 2001
• MOPS for GPS Wide Area augmentation System Airborne Equipment, DO 229D, 2007
FAA Standard Technical Orders
• TSO C129a, airborne supplemental navigation equipment using the global positioning system (GPS)
• TSO C145a, airborne navigation sensors using the global positioning system (GPS) augmented by the
Wide Area Augmentation System (WAAS)
• TSO C146a, standalone airborne navigation sensors using the global positioning system (GPS)
augmented by the Satellite Based Augmentation System (WAAS)
• TSO C145c, airborne navigation sensors using the global positioning system augmented by the
Satellite -Based Augmentation System
Other documents
• Global Positioning System Standard Positioning Service - Performance Standard, 4th edition, DoD,
September 2008
September 2014
- 39 -
INERTIAL NAVIGATION
AND GPS/IRS HYBRIDIZATION
September 2014
- 40 -
Outline
1. Inertial navigation
1. INS/IMU components
2. Inertial navigation principle
3. Sensors
4. Navigation problem
presentation
5. Commonly used frames
6. Inertial navigation solution
7. Inertial navigation properties
8. Platform implementation
2. Illustration of IRS classical
implementation for aircraft
1. Simulation assumptions
2. Sensors measurements modeling
3. IRS mechanisation in the NED
navigation frame
4. Simulation results
3. GPS/IRS hybridization
1. Principle and schemes
2. Hybridation architectures
3. Overview of Kalman filtering
4. Example of GPS/IRS tight coupling
using KF
5. Integrity Monitoring
6. Conclusion
September 2014
1. Inertial Navigation
INS/IMU components
Inertial Measurement Unit
IMU
𝑓𝑚/𝐼
𝑝
𝜔𝑚/𝐼
𝑝
computer
[Systron dqi-sd]
–
An Inertial Navigation System (INS) or Inertial Measurement Unit (IMU) is composed
of accelerometers, gyrometers and a computer.
•
•
It aims at estimating the mobile position, velocity and attitude in an appropriate navigation
frame, (N).
Besides the computer may also estimate a series of parameter that are useful for aircraft
piloting and guidance:
• Ground speed
• Track angle (angle between North and the route)
• Flight Path Angle (angle between horizontal plane and the route)
- 41 -
September 2014
1. Inertial Navigation
Inertial navigation principle
– It is based on dead-reckoning navigation
•
•
After the alignment of (p) w.r.t. (N) has been achieved, ie attitude determination, the
accelerometric measurements are integrated to get the mobile velocity in the navigation
frame.
Depending on the platform implementation, this alignment may be performed in either a
mechanical or an analytical manner.
– Strong points:
•
•
•
autonomous – does not depend on external aid in comparison to GPS
non-radiating – in comparison to conventional NAVAIDS
insensitive to external perturbations – meteorological perturbations, jamming, RF
interference, multipath
– Drawbacks:
•
•
Time drift of the position estimate
Cost due to the used technologies to get sensors of great accuracy and great reliability
- 42 -
September 2014
1. Inertial Navigation
Sensors
Accelerometers: principle
– Obtain the vehicle acceleration
– An accelerometer senses the vehicle specific force along its sensitive axis. Its
output has to be corrected to take into account the gravity acceleration.
– Ex: what would be the specific force measured by a free-falling object?
– Two major designs:
• open-loop or vibratory accelerometers
• closed-loop or force-rebalance accelerometer (illustration): standard and
most accurate design
- 43 -
September 2014
1. Inertial Navigation
- 44 -
Sensors
Accelerometers: examples of technologies
Pendulous Integrated Gyro (PIG) Accelerometer - 25 PIGA
Titan II
Pendulous accelerometer
Axe
sensible
Axe
pendule

f
http://www.nasm.si.edu/images/collections/media/full/T20090008003.JPG
Micro-Electronical Mechanical System (MEMS) accelerometer
Analog Device ADXL202
http://www.machinegrid.com/2008/12/accelerometers-for-your-robot-
September 2014
1. Inertial Navigation
- 45 -
Sensors
Accelerometers: error model
𝑓1 = 𝑓1 + 𝑛 + 𝑘0 +
𝑛𝑜𝑖𝑠𝑒
𝑏𝑖𝑎𝑠
𝑘1 𝑓1
+ 𝑘12 𝑓2 + 𝑘13 𝑓3 +
𝑘𝑇 𝑇
𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟
𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑏𝑖𝑎𝑠
f1
f component along the sensitive axis
f2,f3
f "cross-axis" components
k12, k13 are the sensitivity factors
n
Noise – sensor sentitivity threshold
k0
bias
k1
Scale factor - linear
kTT
Temperature difference in comparison to calibration - bias
These parameters characterize the accelerometer accuracy
+⋯
September 2014
1. Inertial Navigation
- 46 -
Sensors
Accelerometers: technologies and applications
Technologies
VBA
Pendulous accelerometer
MEMS
PIGA
Bias (mg)
10
munitions
1
Flight
controls
0.01
0.1
Tactical
missiles
aircraft
navigation
Launchers
AHRS
Applications
0.001
Marine
navigation
Strategic
missiles
[source Thales]
September 2014
1. Inertial Navigation
Sensors
Gyrometers: principle
– Sense the vehicle inertial rotation rate:
•
•
In the stable platform case, they measure the platform rotation which is free from the
mobile.
 The platform frame is kept in a known direction by mechanical means, typically a
system of gimbals and a gyroscopically controlled feedback loop.
In the strap-down case, the platform is linked to the mobile and follows its angular
movements.
– Main designs
•
•
Vibratory gyro, based on mechanical effects
Optical gyro (illustrated), based on the Sagnac effect
- 47 -
September 2014
1. Inertial Navigation
- 48 -
Sensors
Gyrometers: examples of technologies
Mechanical and Fiber-optic gyros
http://www.aerospaceweb.org/question/weapons/
guidance/gyroscope.jpg
Rotor-gyro and housing
Ring laser gyroscopes
Aerospace Topflight ADIRU sheet, Thales
Avionics, 2008.
http://www.laserfest.org/lasers/images/inngyroscope.gif
MEMS gyroscope – GS 12 Robotis
September 2014
1. Inertial Navigation
- 49 -
Sensors
Gyrometers: error model
𝜔1 = 𝜔1 + 𝑛 + 𝑘0 +
𝑛𝑜𝑖𝑠𝑒
𝑏𝑖𝑎𝑠
𝑘1 𝜔1
+ 𝑘12 𝜔2 + 𝑘13 𝜔3 +
𝑘𝑇 𝑇
𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑎𝑙𝑖𝑔𝑛𝑚𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟
𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑏𝑖𝑎𝑠
ω1
f component along the sensitive axis
ω2, ω3
f "cross-axis" components
k12, k13 are the sensitivity factors
n
Noise – sensor sentitivity threshold
k0
bias
k1
Scale factor - linear
kTT
Temperature difference in comparison to calibration - bias
kg
G-dependant bias
+ 𝑘𝑔 𝑓1 …
September 2014
1. Inertial Navigation
Sensors
Gyrometers/accelero: error model
– A mathematical model can be defined, it will involve:
•
•
•
•
noise: random additive error on the measurement,
bias: slow-varying error in the measurement,
scale factor: error depending on the amplitude of the measurement,
mis-alignment error: error in the alignment of the sensor measurement axes from the
orthogonal platform axes.
 But, its exact expression depends on the technology.
– The total effect of the sensor bias and the scale factor error shows up the sensor drift.
– All these errors characterize the sensor accuracy.
- 50 -
September 2014
1. Inertial Navigation
- 51 -
Sensors
Gyrometers: technologies and applications
Technologies
Ring Laser gyros
Vibrating
FOG
ESG
Floated
MEMS
100
munitions
DTG
10
Flight
controls
1
0.1
Tactical
missiles
Drift
(degree/hr)
0.001
0.01
aircraft
navigation
Marine
navigation
Launchers
AHRS
Applications
Strategic
missiles
[source Thales]
September 2014
1. Inertial Navigation
Sensors
Sensor grades
Sensor grades are used to describe the application range targeted by a sensor. They
indicate their performances.
Grade
Position drift
Cost
Application
Marine
1.8 km/day
1 M$
Military ships, submarines,
intercontinental missiles, spacecrafts
Aviation /
Navigation
1.5 km/hour
100 k$
Military and commercial aviation
Intermediate
15 km/hour
20-50 k$
Small aircraft, helicopter
Tactical
Ok for a few minutes
2-30 k$
Guided weapon, UAV
Consumer /
Automotive
Not integrated in
IMU, but rather sold
as individual sensors
1-10$
Pedometer, ABS, active suspension,
airbags
Groves 2013 – Principles of GNSS, Inertial and Multisensor Integrated Navigation Systems, Artech House
- 52 -
September 2014
1. Inertial Navigation
- 53 -
Sensors
Navigation-grade sensors typical figures
Typical strapdown sensor performance requirements for a navigation-grade IRS
[Palmqvist, 1997]:
Performance Parameter
Gyro Bias Uncertainty deg hr 
Requirements
0.01
Gyro Random noise deg
0.003

hr

Gyro Scale Factor Uncertainty  ppm
Acceleration Bias Uncertainty g 
Acceleration Scale Factor Uncertainty  ppm
Sensor Alignement Uncertainty sec 
10
50
100
10
September 2014
1. Inertial Navigation
- 54 -
Navigation problem presentation
– The sensors are implemented onto the gyro-accelerometric platform.
• Accelerometers sense the vehicle rectilinear acceleration. Each one measures, along its sensitive
axis, the inertial specific force of the mobile in the platform coordinate frame.
• Gyrometers sense the vehicle rotational motion which is the mobile angular velocity with
respect to the inertial frame. It is also expressed in the platform coordinate frame
– The measurements corresponds to the specific force or angular velocity of the mobile
(m) with regard to an inertial reference frame (I), expressed in the platform frame (p).
– What we want to obtain is the mobile (m) characteristics with regard to the terrestrial
frame (e), and possibly expressed in the navigation frame (N).
The navigation problem consists in
𝒇𝒎/𝑰
𝒑
?
𝒑𝒎/𝑬
𝒗𝒎/𝑬 𝑵
𝝎𝒎/𝑰 𝒑
𝝆𝒎/𝑵
September 2014
1. Inertial Navigation
- 55 -
Commonly-used frames (1/3)
Z
ZT n
R
O
X

e
M
– Terrestrial frame (ECEF) – (E): (O,XT,YT,ZT)
YT
– Navigation frame – (N): eg. the NED coordinate
frame (M,n,e,v)
Y
L
ωIE.t
n
v
λ
– Space-fixed or inertial frame (ECI) - (I): (O,X,Y,Z)
XT
– Body or mobile frame - (m): (M,x,y,z)
orientation with respect to the NED is defined by the
attitude angles (Euler angles):
• roll (Φ) – rotation around (n),
• pitch (θ) – rotation around (e),
• heading (ψ) – rotation around (v).
Greenwich
meridian
x
X
Y
Z

z 
v
e
y
Xsens Mti IMU
– Gyro-accelerometric platform frame - (p):
• The gyrometers’s position defines the
platform trihedron.
• Accelerometers are placed along the axes of
that trihedron.
– (p) and (m) are assumed to be aligned in this
𝒑
𝒑
𝒎
lecture: 𝒇𝒎/𝑰 = 𝒇𝒎
𝒎/𝑰 , 𝝎𝒎/𝑰 = 𝝎𝒎/𝑰
September 2014
1. Inertial Navigation
Commonly-used frames (2/3)
• Inertial navigation equations can be solved in any frame (I), (E) or (N).
– (I) has the most simple equations.
– (E) or (N) being non-inertial frames, they introduce Coriolis force.
– (N) origin also adds a transport term, since the origin of (N) moves wrt (I).
– However, (N) is often the desired solving frame for users.
• Solving the inertial navigation equations needs to change the coordinates
frame, notably, to express the specific force measurement 𝒇𝒎
𝒎/𝑰 in the desired
solving coordinate frame (N) 𝒇𝑵
𝒎/𝑰 .
𝒎
• This is done thanks to a coordinate transformation matrix 𝒇𝑵
𝒎/𝑰 = 𝑹𝒎𝟐𝑵 . 𝒇𝒎/𝑰
- 56 -
September 2014
2. Illustration of IRS Implementation for
Aircraft
Commonly-used frames (3/3)
Expression of the change of coordinates matrix Rm2N
The components of a vector expressed in the mobile frame may be expressed in the
navigation frame by the series of the three rotations:
 x   cos sin  0  x 
 y   sin  cos 0   y 
  
  
 z    0
0
1  z 
   N
rotation / z 
Rm 2 N
cos  cos 
         sin  cos 
  sin 
– Attitude angles estimates:
 x  cos  0  sin    x 
 y   0
1
0    y
  
 z    sin  0 cos    z  


rotation / y ' 
 sin  cos   cos  sin   sin 
cos  cos   sin  sin   sin 
cos   sin 
   arcsin Rm 2 N 3,1
 Rm 2 N 3,2  



R
3
,
3
 m2 N

R
2,1 
  arctan  m 2 N

 Rm 2 N 1,1 
  arctan 
0
0   x 
u 
1
 v   0 cos  sin     y
 

  
 w m 0  sin  cos    z  


rotation / x '' 
sin  sin   cos  sin   cos  
 cos  sin   sin  sin   cos  

cos   cos 
- 57 -
September 2014
1. Inertial Navigation
- 58 -
Inertial navigation solution in (I) frame
Z
• Let 𝑀 be the mobile location: 𝑅𝐼 = 𝑂𝑀 with 𝑂 the Earth’s center
R
• In the inertial frame, the accelerometric measurement provides:
𝑑2 𝐼
𝐼
𝐼
𝑓 =
𝑅
−
𝑔
𝑅
+
𝜀𝑎
𝑑𝑡 2
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑓𝑜𝑟𝑐𝑒 𝑡ℎ𝑎𝑡
𝑤𝑜𝑢𝑙𝑑 𝑏𝑒 𝑚𝑒𝑠𝑢𝑟𝑒𝑑 𝑏𝑦
𝑎𝑛𝑑 𝑖𝑑𝑒𝑎𝑙 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑜𝑚𝑒𝑡𝑒𝑟
M
O
X
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟
• The first Newton’s law is applied to estimate the vehicle inertial acceleration:
𝑑2 𝐼
𝑅 = 𝑓 𝐼 + 𝑔𝐼 𝑅
2
𝑑𝑡
• The inertial velocity and position are deduced through double integrations
• There are 2 issues in the case of INS measurements:
- The measurement are expressed in the (m) frame  coordinate transformation
- The gravity is absent from the measurement
 gravity model
Y
September 2014
1. Inertial Navigation
- 59 -
Inertial navigation solution in (I) frame
𝑅𝑚2𝐼 (-)
𝑚
𝜔𝑚/𝐼
𝑚
𝑓𝑚/𝐼
1. Update
attitude
2. Transform
specific force
frame
Groves 2013 – Principles of GNSS,
Inertial and Multisensor Integrated
Navigation Systems, Artech House
𝐼
𝑓𝑚/𝐼
3. Update
velocity
𝐼
𝑣𝑚/𝐸
(−)
𝑔𝐼 𝑟
4. Update
position
𝐼
𝑟𝑚/𝐼
(-)
𝑅𝑚2𝐼 (+)
𝐼
𝑣𝑚/𝐼
(+)
𝐼
𝑟𝑚/𝐼
(+)
September 2014
1. Inertial Navigation
- 60 -
Inertial navigation solution in (N) frame
𝑅𝑚2𝑁 (-)
𝑚
𝜔𝑚/𝐼
𝑚
𝑓𝑚/𝐼
1. Update
attitude
2. Transform
specific force
frame
Groves 2013 – Principles of GNSS,
Inertial and Multisensor Integrated
Navigation Systems, Artech House
𝑁
𝑓𝑚/𝐼
3. Update
velocity
𝑁
𝑣𝑚/𝐸
(−)
𝜆𝑚 (−),
𝐿𝑚 (−),
ℎ𝑚 (−)
𝑔𝑁 𝑟
4. Update
position
𝑅𝑚2𝑁 (+)
𝑁
𝑣𝑚/𝐸
(+)
𝜆𝑚 (+), 𝐿𝑚 (+), ℎ𝑚 (+)
September 2014
1. Inertial Navigation
- 61 -
Inertial navigation solution
– Inertial navigation requires computer initialization (position, velocity, attitude)
– Gravity model: Gravity acceleration compensation depends on the current location
(latitude & height over the ellipsoid)
•
•
A gravity loop is implemented to improve the acceleration estimate
The gravity acceleration correction uses the estimated point provided at the end of the
computation chain

g I Rˆ
2
d ˆI
R
dt 2
~I
f
d ˆI
R
dt

t 0
ˆ
d ˆI R
R
dt

I
t 0
R̂ I
September 2014
1. Inertial Navigation
Inertial navigation properties
Position performance
– The accuracy of the computed instantaneous position at the IRS output is due to
• initialisation errors,
• accelerometric and gyrometric measurements errors,
• errors in the (m)-to-(N) frames change of coordinates definition,
• Gravity model uncertainty
• and approximations due to numerical integrations.
– For long-range air-transport aircraft performance must be lower than 2 NM/hr (95%)
- 62 -
September 2014
1. Inertial Navigation
- 63 -
Inertial navigation properties
Position performance example
We assume a strapdown inertial
system mounted in a vehicle
travelling at a constant speed and
at constant height above the Earth:
East velocity: 500 kt (~926km/hr)
•
Latitude: 45°
Illustration of the middle-term
contribution error models.
Initial azimuth error (1 mrad)
Initial speed error (0.3 m/s)
East gyro bias (0.01 °/hr)
Vertical gyro bias (0.01 °/hr)
Accelerometer bias (50 g)
Total RSS error
6
Position Error [km]
•
North Position Error vs Time
4
2
[Titterton, Weston, 2004]
0
0
1
2
Time [h]
3
4
September 2014
1. Inertial Navigation
- 64 -
Platform implementation
Stable platform
– The sensor platform is free from the vehicle.
•
•
Gyroscopes data are used to mechanically stabilized the sensor platform w.r.t. the
navigation frame trihedral (N) (use of actuators).
Sensor measurements are directly in the navigation frame.
𝑓
Inertial
sensors
computer
𝜔
𝜔𝑝
Command laws
for platform
stabilization
Roll, pitch, heading
Gravity
Compensation
Integration
R̂
d ˆ
R
dt
September 2014
1. Inertial Navigation
- 65 -
Platform implementation
Stable platform illustration
Schematic of a three-gimbal platform
www.accessscience.com, Encyclopedia article: Inertial navigation system
Photo of Internals of a Gimballed Inertial Platform
INS Mechanism. © GEC Marconi
http://www.al-nasir.com/www/Jamie/Articles/Technology/...
GimballedINSPhoto.gif
September 2014
1. Inertial Navigation
- 66 -
Platform implementation
Strapdown platform (IRS)
– IRS is for Inertial Reference Sensor.
– The sensor platform is fixed with respect to the vehicle.
•
•
The sensor platform (p/m) is analytically (ie. virtually) aligned with the navigation frame
trihedron (N)
Accelerometric measurements are in the platform coordinate frame.
computer
(p/m) to (N)
alignment
Accelero.
Gravity
Compensation
Integration
Gyro.

Attitude
angles
R̂
d ˆ
R
dt
Roll, pitch,
heading
September 2014
1. Inertial Navigation
- 67 -
Platform implementation
Strapdown platform illustration
Strap-down inertial navigation system.
Litton LTN-92 laser gyro INS
Inertial Navigation Unit,
INU
www.accessscience.com, Encyclopedia article: Inertial navigation system
(After A. Lawrence, Modern Inertial Technology, 2d ed., Springer, 1998)
Command and
http://www.es.northropgrumman.com/solutions/ltn92/assets/LTNDisplay Unit , CDU
92_Ring_Laser_Gyro_Inertia.pdf
Mode Selector
Unit, MSU
September 2014
1. Inertial Navigation
- 68 -
Platform implementation
On board aircraft implementations (1/2)
– On board high end commercial aviation aircraft, the Inertial
Reference Unit is implemented in ADIRU – Air Data Inertial
Reference Unit.
ADIRU is divided in 2 parts, each one can work separately in
case of failure in the other
•
•
the Air Data Reference (ADR) part which supplies barometric
altitude, airspeed, mach, angle of attack, temperature and
overspeed warnings.
the Inertial Reference (IR) part which supplies attitude, flight
path vector, track, heading, accelerations, angular rates,
ground speed and aircraft position.
– Localisation may be output either as pure IRS position with
baro-hybridized vertical axis or GPS/IRS/baro position.
– Hybridization processes are implemented inside the ADIRU.
Aerospace Topflight ADIRU sheet, Thales Avionics,
2008.
September 2014
1. Inertial Navigation
- 69 -
Platform implementation
On board aircraft implementations (2/2)
– On board business, regional and smaller air-transport aircraft, the Inertial Reference
Unit is implemented as AHRS – Attitude & Heading Reference System.
AHRS system may consist of:
• Gyrometers, accelerometers - with lower
performance than for ADIRU (intermediate
grade) - and/or inclinometers, and a
Magnetic Sensing Unit, to provide user with
attitude and heading (magnetic and true).
• It may also provide GPS/AHRS/altitude/AirData velocity and position.
• Hybridization processes are implemented
inside the AHRS.
AHRS diagram example
Extract of DO 334 - RTCA, 2012
September 2014
- 70 -
Part 2
Illustration of IRS implementation for aircraft
1.
2.
3.
4.
Simulation assumptions
Sensors measurements modeling
IRS mechanisation in the NED navigation frame
Simulation results
September 2014
2. Illustration of IRS Implementation for Aircraft
Simulation assumptions
– Computation of a baro-IRS trajectory with Commercial Aviation grade performance
assumptions for the sensors, based on a simulated flight path.
•
IRS provides the pilot with IRS horizontal position and velocity, as well as roll, pitch and
heading angles
Baro-altimeter data provide the pilot with vertical position, and are used to aid the IRS in
the vertical velocity and accelaration computations
Gravity loop is not implemented
•
•
Roulis
0.9
0.2
[rad]
0.4
0
0.85
-0.2
0.8
0
1000
2000
3000
4000
5000
6000
4000
5000
6000
4000
5000
6000
Tangage
0.5
0
0.005
0.015
0.02 0.025
0.03
Longitude [rad]
Trajectoire de reference sur l'axe vertical
4
6
x 10
0.01
0.035
0.04
[rad]
0.75
-0.005
0
-0.5
0
1000
2000
4
3000
Cap
5
[rad]
Altitude [m]
Latitude [rad]
Trajectoire de reference dans le plan horizontal
0.95
2
0
0
1000
2000
3000
Temps [s]
4000
5000
6000
0
-5
0
1000
2000
3000
Temps
- 71 -
September 2014
2. Illustration of IRS Implementation for
Aircraft
- 72 -
Sensors measurements modeling
The IMU and baro-altimeter sensors mesurements are deduced from the reference path
using time difference. The sensors performance are modelled as additionnal errors on
𝑚
𝑚
the ideal measurements 𝜔𝑚/𝐼
, 𝑓𝑚/𝐼
, ℎ𝑏𝑎𝑟𝑜
•
1st order Gauss-Markov process (bias 𝑏𝑎 )
Time constant
300s
Standard deviation (1σ)
25μg
ba
~m
f mI
f mIm
Gyrometers
•
~m

mI
m
 mI
Accelerometers
1st order Gauss-Markov process (bias 𝑏𝑔 )
Time constant
3600s
Standard deviation (1σ)
0.01°/hr
bg
hbaro
~
hbaro
Baro-altimeter
•
Additive white-centered Gaussian noise (𝑛𝑏𝑎𝑟𝑜 )
nbaro   15m
September 2014
2. Illustration of IRS Implementation for
Aircraft
- 73 -
IRS mechanisation in the NED navigation frame
General scheme (w/o gravity loop)
The sensor trihedron, (𝑝), is assumed to be exactly aligned with the mobile trihedron, (𝑚)
outputs
Attitude
Acceleration
Velocity
Position
Specific force wrt to the
Inertial referential frame
+
Acceleration
Integration
Velocity
Integration
+
Accelerometer
Triad
+
Attitude
Computation
Inertial Corrections
+
Gyrometer
Triad
IRU
Gravity Compensation
+
-
computer
September 2014
2. Illustration of IRS Implementation for
Aircraft
- 74 -
IRS mechanisation in the NED navigation frame
Local gravity acceleration modeling
– The local gravity force vector is the vector to which
a ‘plump bob’ would align itself when held above the
Earth. Ignoring any gravity anomaly, it will be assumed
aligned with the vertical:
𝑔𝑙 𝑁 𝑅 = 0,0, 𝑔𝑙 𝜆, ℎ
ωIE
Earth surface
( WGS-84 )
n
Fe
g
𝑇
gl
R
λ
– It is sum of the mass attraction force and the centripetal acceleration:
𝑔𝑙 𝑁 𝑅 ≜ 𝑔𝑁 𝑅 + 𝐹𝑒𝑁 𝑅 with 𝐹𝑒𝑁 𝑅 = −𝜔𝐼𝐸 × 𝜔𝐼𝐸 × 𝑅
𝑁
– Gravity model example:
𝑔𝑙 𝜆, ℎ = 𝑔𝑙
∗
𝑎
𝜆, 0 .
𝑎+ℎ
2
∗
where 𝑔𝑙 𝜆, 0 =
e
𝐺0 1 + 𝑘sin2 𝜆
1 − 𝑒 2 sin2 𝜆
September 2014
2. Illustration of IRS Implementation for
Aircraft
- 75 -
IRS mechanisation in the NED navigation frame
Mobile velocity estimate
The component form of the inertial navigation dynamic equation in the N-frame is






v


e
 R h 
~


 fx 
N
0 

cos

vn 



 vn 


E


~ 
vn
 v   R
   v 
  2
fy  
0    
0
e
m
2
N

 



  e 

RE  h 

~
 fz 
 vv 
 g l  , h 
   E sin     vv 

  ve
 m





tan  
N
N
N


local gravity force
vmE
vmE
 IE
R

h


N
 





N
Errors due to IMU
NI

 


mesurement errors
Errors due to the gravity
Coriolis acceleration in  N 
model uncertainties
In the E-frame, the aircraft location is characterized by its latitude λ, its East longitude ϕ,
and its height h above the reference ellipsoid.
Those time differentiate
 1

equations are nonThey verify:
0
0

   R N  h
  
    0
 h  

0

 mE
p

1
RE  h   cos 
0

 v n 
0    v e 

 v v 
 1 
 vmE
N

linear: they are solved
thanks to numerical
means that introduce
additional errors onto
the velocity estimate.
September 2014
2. Illustration of IRS Implementation for
Aircraft
- 76 -
Simulation results
-3
2
Horizontal path
  [rad]
0.9
0
-2
-4
0.85
reference
IRS
0
4
6
x 10
0.01
Longitude [rad]
Vertical path
0.02
0.03
0.04
  [rad]
-0.01
2000
3000
4000
5000
6000
5000
6000
4000
5000
6000
4000
5000
6000
4000
5000
6000
5000
6000
0.01
0
-0.01
0
1000
2000
3000
4000
Altitude error estimate
20
reference
IRS
[m]
4
0
-20
2
0
1000
2000
-3
1000
2000
3000
Time [s]
4000
5000
6000
2
 [rad]
0
0
1000
0.02
0.8
0.75
-0.02
0
Longitude error estimate
 h [m]
Latitude [rad]
0.95
Latitude error estimate
x 10
Roll error estimate
x 10
0
-2
-4
0
1000
2000
-3
2
 [rad]
– We observe an important drift in the horizontal
position error estimate
0
1000
2000
3000
Heading error estimate
0.02
 [rad]
 As expected, the vertical error remains bounded
3000
Pitch error estimate
x 10
0
-2
 Several kilometers
3000
Time [s]
0.01
0
-0.01
0
1000
2000
3000
temps(s)
4000
September 2014
- 77 -
Part 3
GPS/IRS Hybridization
1.
2.
3.
4.
5.
6.
Principle and schemes
Hybridation architectures
Overview of Kalman filtering
Example of GPS/IRS tight coupling using KF
Integrity Monitoring
Conclusion
September 2014
3. GPS/IRS Hybridization
- 78 -
Principle and schemes
Why coupling?
 Complementary performance of the two systems.
System or means
Strong points
Weak points
type of information
GPS, GLONASS
Long-term accuracy,
worldwide absolute
positioning
Integrity,
continuity,
RF interference
3D position and velocity
Time
INS
Short term accuracy,
immunity from perturbations
Error drift,
cost,
relative positioning
3D position and velocity
Attitude
calibration
(re) alignment
GNSS
INS
(re) acquisition
resistance from RF interference, jamming
integrity monitoring availability
continuity aiding
September 2014
3. GPS/IRS Hybridization
Principle and schemes
Fix point at Toulouse location during 30 min with
σGPS=12.5m and navigation-grade IRS
- 79 -
September 2014
3. GPS/IRS Hybridization
- 80 -
Hybridation architectures
GPS/IRS loose coupling = Position-domain hybridization
Signal preprocessing and
sampling
PRN
Correlators and
tracking loops
Navigation
computer
GPS navigation
solution
PR1
GPS receiver
We assume GPS stands for the true
location.
GPS position is used to help estimating
inertial errors and correct IRS
navigation solution.
There is redundancy of output
navigation solutions.
But, need for at least 4 GPS
measurements and the distribution of
GPS navigation solution needs to be
well known.
Inertial Sensor
measurement
pre-processing
Navigation and
integration
algorithm
Hybridized
navigation
solution
Integration process
IRS navigation
solution
Accelerometers
IRS computer
Gyrometers
IRS platform
Figure extracted from GEBRE-EGZIABHER (D.) – What is the difference between ‘loose’, ‘tight’, ‘ultra-tight’ and ‘deep’ integration strategies for
INS and GNSS ?, InsideGNSS, Jan-Feb 2007, pages 28-33
September 2014
3. GPS/IRS Hybridization
- 81 -
Hybridation architectures
Forward configuration
Inertial
Reference
System
IRS
External aiding
source
GPS
𝑥𝐺𝑃𝐼𝑅𝑆 = 𝑥𝐼𝑅𝑆 − 𝛿 𝑥𝐼𝑅𝑆
+
+
-
IRS errors estimate
+
-
Kalman Filter
Forward configuration
Only a correction is applied to the IRS estimates.
No risk of propagating error modes from one sensor to the other.
But, the KF state propagation model tends to become less and less accurate with time, due to IRS drift.
 Inertial error estimate is getting less and less accurate, whatever the GPS measurements.
September 2014
3. GPS/IRS Hybridization
- 82 -
Hybridation architectures
Backward configuration
Inertial
Reference
System
IRS
IRS errors estimate
External aiding
source
GPS
+
-
Kalman Filter
Backward configuration
IRS calibration is done using the KF state estimates.
The KF state model is far less sensitive to IRS drift: this improves the inertial error estimate.
But, risk of propagating error modes from one sensor to the other.
But, the KF state propagation model tends to become less and less accurate with time, due to IRS drift.
 Need to detect failures, especially GPS ones, as soon as they occur.
September 2014
3. GPS/IRS Hybridization
- 83 -
Hybridation architectures
GPS/IRS tight coupling = range-domain hybridization
Signal preprocessing
and sampling
PRN
Correlators and
tracking loops
PR1
GPS receiver
Inertial Sensor
measurement
pre-processing
Navigation and
integration
algorithm
Hybridized
navigation
solution
Integration process
Accelerometers
Gyrometers
IRS platform
We assume GPS stands for the true location.
GPS measurements are used to help estimating
inertial errors and correct IRS navigation
solution.
Even with less than 4 satellites, GPS will
improve the hybridized solution.
 Inertia provides the state propagation
model; GPS the observation one.
Figure extracted from GEBRE-EGZIABHER (D.) – What is the difference between ‘loose’, ‘tight’, ‘ultra-tight’ and ‘deep’ integration strategies for
INS and GNSS ?, InsideGNSS, Jan-Feb 2007, pages 28-33
September 2014
3. GPS/IRS Hybridization
- 84 -
Hybridation architectures
Architecture
Loose
Advantages
• Provides stand-alone GPS
and INS solutions
• Simpler implementation
Drawbacks
Comment
• Requires 4 satellites
• Requires GPS position
error distribution
• Integrity monitoring = RAIM
(GPS only)
• Works with <4 satellites
Tight
• Requires access to GPS
• KF filter better tuned thanks
pseudoranges
to better error modelisation
measurements
of pseudoranges
• More complex
• Monitoring functions uses
implementation
INS measurements
• Widely used in current
systems
• Integrity monitoring = AAIM
(hybridized)
Forward
• INS drift accumulates
• Requires higher grade of
INS sensors
Backward
• Possible propagation of
error modes between INS
and GPS
• Requires GNSS fault
detection functions
September 2014
3. GPS/IRS Hybridization
Overview on Kalman Filtering (1/3)
Underlying dynamic system model (w/o control-input)
𝑥 𝑘 =𝐹 𝑘 𝑥 𝑘−1 +𝑣 𝑘
𝑦 𝑘 =𝐻 𝑘 𝑥 𝑘 +𝑤 𝑘
•
•
𝑥 is the state to estimate, 𝑥 𝑘 ∈ ℝ𝑛
𝑦 is the measurement, 𝑦 𝑘 ∈ ℝ𝑚
•
𝑣 is the process noise which is assumed to be drawn from a centered multivariate
normal distribution, 𝑣 𝑘 ~𝑁 0, 𝑄 𝑘
𝑤 is the observation noise which is also assumed to be drawn from a centered
multivariate normal distribution, 𝑤 𝑘 ~𝑁 0, 𝑅 𝑘
•
•
•
𝐹 is the 𝑛 × 𝑛 state transition matrix
𝐻 is the 𝑚 × 𝑛 observation matrix
- 85 -
September 2014
3. GPS/IRS Hybridization
Overview on Kalman Filtering (2/3)
Assumptions
•
•
Discrete-time, linear and Gaussian problem
The initial state, and the noise vectors at each step {𝑥 0 , 𝑤 1 , … , 𝑤 𝑘 , 𝑣 1 … 𝑣 𝑘 }
are all assumed to be mutually independent
Solution
•
KF is a recursive estimator that provides the Minimum Mean Squared Error estimator
from the past noisy measurements
 At each instant 𝑘, 𝑥 𝑘 is defined as 𝑥 𝑘|𝑘 = 𝐸 𝑥 𝑘 |𝑦 0 … 𝑦 𝑘
•
The state variance is defined as 𝑃 𝑘 = 𝑃 𝑘|𝑘 = 𝑐𝑜𝑣 𝑥 𝑘 |𝑦 0 … 𝑦 𝑘
 Its stands for the estimation error variance: 𝑐𝑜𝑣 𝑥 𝑘 − 𝑥 𝑘 |𝑦 0 … 𝑦 𝑘
- 86 -
September 2014
3. GPS/IRS Hybridization
- 87 -
Overview on Kalman Filtering (3/3)
Implementation
1. Use of the state transition
model
3. Compute optimal KF gain
(trade-off between the trust
in the state propagation
model and the trust in the
measurements)
4. Correct the
predicted state
2. Compute the innovation
(measurement residual)
September 2014
3. GPS/IRS Hybridization
Example of GPS/IRS tight coupling using KF (1/7)
Definition of the inertial errors
The error terms are defined as the difference between the true value and the
measured or estimated one:
Parameter
State
Model
Position error
p
Dynamics navigation equation
Velocity error
v
Dynamics navigation equation
A priori knowledge of the accelerometric noises
Gravity model uncertainty
Attitude error

Attitude evolution equation
A priori knowledge of the gyrorometric noises
Accelerometer error
f
Assumed stochastics processes to model biases
Gyrometer error

Assumed stochastics processes to model drifts
- 88 -
September 2014
3. GPS/IRS Hybridization
- 89 -
Example of GPS/IRS tight coupling using KF (2/7)
Propagation model of the IRS navigation errors
The general inertial error equations in the N-frame are the following
Position
• The position differential equation is in form of 𝑝 = 𝑓1 𝑝, 𝑣
• The position error propagation equation is thus
𝛿 𝑝 = 𝑓1 𝑝, 𝑣 − 𝑓1 𝑝𝐼𝑅𝑆 , 𝑣𝐼𝑅𝑆 = 𝛻𝑓1 𝑝, 𝑣 . 𝛿𝑝, 𝛿𝑣
or
𝛿 𝑝 = 𝛿𝑣 + 𝜔𝐸𝑁 𝑁 × 𝛿𝑝
𝑇
Velocity
• The velocity differential equation is in form of 𝑣 = 𝑓2 𝑝, 𝑣, 𝜌, 𝑎
• The velocity error propagation equation is thus
𝛿 𝑣 = 𝑓2 𝑝, 𝑣, 𝜌, 𝑎 − 𝑓2 𝑝𝐼𝑅𝑆 , 𝑣𝐼𝑅𝑆 , 𝜌𝐼𝑅𝑆 , 𝑎𝐼𝑀𝑈 = 𝛻𝑓2 𝑝, 𝑣, 𝜌, 𝑎 . 𝛿𝑝, 𝛿𝑣, 𝛿𝜌, 𝛿𝑎
or (with simplifications)
𝑁
𝛿 𝑣 = 𝑅𝑚2𝑁 𝛿𝑓 + 𝜔𝐼𝑁 𝑁 + 𝜔𝐼𝐸 𝑁 × 𝛿𝑣 + 𝛿𝜌 × 𝑓𝑚𝐼 + 𝜀𝑔𝑟𝑎𝑣𝑖𝑡𝑦
Attitude
• The attitude error propagation equation is (with simplifications)
𝛿 𝜌 = 𝑅𝑚2𝑁 𝛿𝜔 + 𝜔 × 𝛿𝜌
𝑇
September 2014
3. GPS/IRS Hybridization
- 90 -
Example of GPS/IRS tight coupling using KF (3/7)
Corrected code measurement general model
– Corrected code pseudorange measurement general model (satellite 𝑖, time 𝑘) is
𝑃𝑖 𝑘 = 𝑋𝑆𝑉 𝑖 𝑘 − 𝑋𝑢 𝑘
𝑃𝑖 𝑘 =
where,
𝑥𝑖 𝑘 − 𝑥 𝑘
2
𝑋𝑢 𝑘 = 𝑥 𝑘 , 𝑦 𝑘 , 𝑧 𝑘
+ 𝑏𝑢 𝑘 + 𝜀 𝑖 𝑘
+ 𝑦𝑖 𝑘 − 𝑦 𝑘
2
+ 𝑧𝑖 𝑘 − 𝑧 𝑘
2
+ 𝑏𝑢 𝑘 + 𝜀 𝑖 𝑘
is the 3D user location to estimate
𝑏𝑢 𝑘 is the receiver clock bias to estimate, as well
𝑋𝑆𝑉 𝑖 𝑘 = 𝑥 𝑖 𝑘 , 𝑦 𝑖 𝑘 , 𝑧 𝑖 𝑘 is the 3D SV 𝑖 location
𝜀 𝑖 𝑘 stands for the pseudorange residual error
– Let 𝑋 𝑘 = 𝑋𝑢 𝑘 , 𝑏𝑢 𝑘 𝑇 be the 4D user location
 The true pseudorange mathematical model is
ℎ𝑖 𝑋 𝑘
=
𝑥𝑖 𝑘 − 𝑥 𝑘
2
+ 𝑦𝑖 𝑘 − 𝑦 𝑘
2
+ 𝑧𝑖 𝑘 − 𝑧 𝑘
2
+ 𝑏𝑢 𝑘
𝑑 𝑖 𝑋𝑢 𝑘
– Let 𝑋 𝑘 be the user location estimate
 The SV 𝑖 predicted pseudorange measurement around 𝑋 𝑘 is 𝑃𝑖 𝑘 = ℎ𝑖 𝑋 𝑘
September 2014
3. GPS/IRS Hybridization
- 91 -
Example of GPS/IRS tight coupling using KF (4/7)
General principle
𝑥 𝑡 = 𝑓 𝑥, 𝑡 + 𝑢 𝑡
𝑥 𝑘 =𝐹 𝑘 𝑥 𝑘−1 +𝑢 𝑘
⟹
𝑦 𝑘 =𝐻 𝑘 𝑥 𝑘 +𝑣 𝑘
𝑦 𝑡 = ℎ 𝑥, 𝑡 + 𝑣 𝑡
Solved with linearized Kalman Filtering (eg., see [Farrell, Barth, 1999] for details)
– The state vector 𝑥𝑘 components are the errors - inertial errors (+ GPS Rx clock bias).
•
The propagation model is defined from the inertial errors propagation models.
– The measurement vector 𝑦𝑘 consists of the difference between the measured
pseudoranges at the output of the GPS receiver and, the range between the satellites
location and the user location as estimated by the IRS.
•
The measurement must be an observation of the quantitities to estimate: here, the inertial
errors.
•
The observation model is defined from the GPS measurements model.
 Using this measurement vector, the integration process calculates corrections to the inertial
solutions, makes sure of the integrity of the corrected solution and computes the integrity
level.
September 2014
3. GPS/IRS Hybridization
- 92 -
Example of GPS/IRS tight coupling using KF (5/7)
Implementation
𝑷𝒊 𝒌
Observation
model
𝒊
𝒚 𝒌 =
𝑷 𝒌 − 𝑷𝒊 𝒌
𝒊
GPS
Receiver
𝒚 𝒌
𝑯 𝒌
𝑹 𝒌
Kalman filter implementation
Prediction
𝒙 𝒌|𝒌 − 𝟏 = 𝑭 𝒌 − 𝟏 𝒙 𝒌 − 𝟏|𝒌 − 𝟏
𝑿𝑺𝑽 𝒊 𝒌
Compute
𝚺 𝒌|𝒌 − 𝟏 = 𝑭 𝒌 − 𝟏 𝚺 𝒌 − 𝟏|𝒌 − 𝟏 𝑭𝑻 𝒌 − 𝟏 + 𝑸 𝒌
𝑷𝒊 𝒌 = 𝒅𝒊 𝒑𝑰𝑹𝑺 𝒌
Innovation
𝒑𝑰𝑹𝑺 𝒌
𝒙𝑮𝑷𝑰𝑹𝑺 𝒌 =
𝑰 𝒌 = 𝒚 𝒌 − 𝑯 𝒌 𝒙 𝒌|𝒌 − 𝟏
𝒙𝑰𝑹𝑺 𝒌 + 𝒙 𝒌|𝒌
Update IRS
output
Inertial
Reference
System
State model
Error
propagation model
𝒙 𝒌|𝒌
𝚺 𝒌|𝒌
𝑽 𝒌 = 𝑯 𝒌 𝚺 𝒌|𝒌 − 𝟏 𝑯𝑻 𝒌 − 𝟏 + 𝑹 𝒌
𝒙 𝒌 − 𝟏|𝒌 − 𝟏
𝚺 𝒌 − 𝟏|𝒌 − 𝟏
𝑭 𝒌−𝟏
𝑸 𝒌
Estimation
𝑲 𝒌 = 𝚺 𝒌|𝒌 − 𝟏 𝑯𝑻 𝒌 − 𝟏 ∙ 𝑽 𝒌
−𝟏
𝒙 𝒌|𝒌 = 𝒙 𝒌|𝒌 − 𝟏 + 𝑲 𝒌 𝑰 𝒌
𝚺 𝒌|𝒌 = 𝟏 − 𝑲 𝒌 𝑯 𝒌 ∙ 𝚺 𝒌|𝒌 − 𝟏
September 2014
3. GPS/IRS Hybridization
- 93 -
Example of GPS/IRS tight coupling using KF (6/7)
Simulation hypotheses
Baro-IRS/GPS hybridization with C/A performance assumptions for the inertial sensors,
based on the following simulated flight path.
Roulis
0.4
0.9
0.2
[rad]
Latitude [rad]
Trajectoire de reference dans le plan horizontal
0.95
0
0.85
-0.2
0.8
0
1000
2000
3000
4000
5000
6000
4000
5000
6000
4000
5000
6000
Tangage
0.5
0
0.005
0.015
0.02 0.025
0.03
Longitude [rad]
Trajectoire de reference sur l'axe vertical
4
6
x 10
0.01
0.035
0.04
[rad]
0.75
-0.005
0
0
1000
2000
3000
Cap
5
[rad]
Altitude [m]
-0.5
4
2
0
0
1000
2000
3000
Temps [s]
4000
5000
6000
0
-5
0
1000
2000
3000
Temps
GPS measurements assumptions
•
Time-correlated L1 C/A code pseudorange measurements (Appendix R to D0 229D)
•
All GPS observations are independent each one from the other
September 2014
3. GPS/IRS Hybridization
- 94 -
Example of GPS/IRS tight coupling using KF (7/7)
Simulation results
-3
  [rad]
2
Horizontal path
0.95
-2
-4
0
1000
2000
3000
4000
5000
6000
5000
6000
5000
6000
5000
6000
5000
6000
Longitude estimate error
reference
baro-IRS
GPIRS
0.85
0.8
0.02
  [rad]
Latitude [rad]
baro-IRS
GPIRS
0
0.9
0.01
0
-0.01
-0.01
0
4
x 10
0.01
Longitude [rad]
Vertical path
0.02
0.03
0.04
[m]
1000
2000
3000
4000
20
0
-20
reference
baro-IRS
GPIRS
4
0
Altitude error estimate
 h [m]
0.75
-0.02
6
Latitude estimate error
x 10
0
1000
-7
5
2
2000
3000
Time [s]
4000
GPIRS latitude estimate error
x 10
0
0
1000
2000
3000
Time [s]
4000
5000
6000
  [rad]
0
-5
-10
-15
The important drift formerly observed in the horizontal
plane has been corrected.
 On the vertical axis, the position error uncertainty is
reduced as well as its frequency
1000
-7
5
2000
3000
4000
GPIRS longitude estimate error
x 10
0
  [rad]
 At the end of the path the error is only of few meters
0
-5
-10
-15
0
1000
2000
3000
Time [s]
4000
September 2014
3. GPS/IRS Hybridization
Integrity Monitoring
• Integrity monitoring consists of 2 functions:
– Detection and mitigation of faults
• Fault Detection
• Fault Detection and Isolation
• Fault Detection and Exclusion
: alert to the user
: … + uncontaminated nav solution
: … + the recovered nav solution is fault-free
– Solution protection: determination of whether a navigation solution is safe
to use (xPL)
• Hybridation brings advantages to both functions.
- 95 -
September 2014
3. GPS/IRS Hybridization
Integrity Monitoring
– INS
Faults
• Equipment failure: not more data, wrong biases, etc…
• Threat model less known
– GNSS
• Satellite faults:
– wrong orbit, onboard clock anomaly, wrong emitted power, etc.
– In principle, the GPS Control Segment provides monitoring function, but with performances incompatible
with ICAO requirements (eg time to alert = 8s, Alert Limit may be several km)
• Unusual atmospheric propagation
– High Ionosphere gradient, Ionospheric scintillation, etc.
• Local tracking channel failure
– NLOS reception, strong multipath, low C/No, cycle slip, etc.
• General equipment failure
– Antenna problem, local oscillator problem, jamming
– In hybridized systems, we try to detect the GNSS failures assuming
the INS is not affected by any.
- 96 -
September 2014
3. GPS/IRS Hybridization
Integrity Monitoring
Fault Detection Examples
• 2 examples of FD
– Kalman Filter Innovation monitoring
• Innovation = difference between predicted observations and actual observations
• Allow to check the consistency between the KF states and the measurements
– Direct Consistency Checks (Solution Separation)
• Use of redundancy of measurements to identify a faulty measurement
– M measurements required  M+1 for FD  M+2 for FDE
– M=4 for GNSS, M=3+3 for INS (accelero + gyro)
• Comparison of consistency between solutions computed with different of sets of
measurements.
– Principle: A fault can be detected by hypothesis testing (detection theory)
• A chosen test statistic is supposed to have a known distribution in fault-free mode
• Using a threshold on the test statistic, a fault can be detected
- 97 -
September 2014
3. GPS/IRS Hybridization
- 98 -
Integrity Monitoring
Fault Detection and Isolation example
– Direct Consistency Checks for GPS only
• N positions are computed using N-1 measurements
• For each position, the pseudo-ranges between the estimated position and the satellite are
computed.
• Then, the pseudo-range residual is computed to compare the computed pseudo-ranges to the
observed pseudo-ranges
• A hypothesis test is applied to the residual to detect the presence of a faulty measurement.
• FDI is directly implemented by choosing the fault-free combination for the position solution
1,2,4,5
1,3,4,5
1,2,4,5
True
1,2,3,5
1,3,4,5
2,3,4,5
2,3,4,5
True
1,2,3,5
1,2,3,4
1,2,3,4
No fault
Fault on sat 1
September 2014
3. GPS/IRS Hybridization
Integrity Monitoring
Fault Detection and Isolation example
– Parallel-filter INS/GNSS integrity monitoring
• Does not monitor INS integrity (no redundant inertial sensor)
• N Kalman Filter are run in parallel, each excluding one GNSS measurement.
• A fault detection algorithm is applied to each position solution (range check, KF innovation
monitoring, residual method) (tight architecture)
OR
• An hypothesis test is done in the position-domain (solution-separation method) (loose or
tight architecture)
• FDI is directly implemented by choosing the fault-free combination for the position solution
- 99 -
September 2014
3. GPS/IRS Hybridization
- 100 -
INTEGRITY MONITORING
PARALLEL-FILTER INS/GNSS INTEGRITY MONITORING EXAMPLE
IMU
Inertial
navigation
equations
Hybridation
(tight)
Main
integration
algorithm
- Ch 1
Antenna
and frontend
Ch 1
- Ch 2
Ch 2
- Ch 3
Ch 3
- Ch 4
Ch 4
Integrity
Monitoring
max separation solution
Sensor & measurements
solution-separation
method:
– Each sub-filter solution
is compared to the
main integration
solution.
– A position residual is
computed and used as
test statistic for
hypothesis testing
output
September 2014
3. GPS/IRS Hybridization
Conclusion
– Civil Aviation has its specifities
• ICAO Requirements: accuracy, integrity monitoring
• Equipment:
– GNSS: GPS L1 C/A, in the future: multi-constellation, multi-frequency?
– Inertial sensor: navigation grade
– Inertial Navigation can provide position
• with an error drift < 2 NM/h
• To obtain this, navigation-grade sensors are required (~100 k$)
– Hybridization algorithms are based on Kalman filtering
• with different possible architecture: loose, tight, (deep)
– Hybridization between GNSS and INS allows:
•
•
•
•
Increased accuracy
Increased continuity
Increased integrity performances
Increased availability
- 101 -
September 2014
Additional slides
- 102 -
Reference documents
[Farrell, Barth, 1999] J. A. Farrell, M. Barth, The global positioning system and inertial navigation, Mc
Graw Hill, 1999
[Kayton and Fried, 1996] M. Kayton, W.R. Fried, Avionics navigation Systems
[Kubrak, 2007] D. Kubrak, Etude de l’hybridation d’un récepteur GPS avec des capteurs bas coûts pour la
navigation personnelle en milieu urbain, Ph.D. Thesis report, ENST, 2007
[Palmqvist, 1997] J. Palmqvist, On integrity monitoring of integrated navigation systems, Thesis No. 600,
Linköping Studies in Science and Technology, 1997
[Titterton, Weston, 2004] D. Titterton, J. Weston, Strapdown Inertial navigation Technology, 2nd edition
IEE Radar, Sonar and navigation series 17
September 2014
Additional slides
- 103 -
GPS
IRS
Kalman Filter
Fix point at Toulouse location with
navigation-grade IRS and σGPS=12.5m
GPS/IRS
September 2014
Additional slides
- 104 -
How to get Rm2N from the gyro. measurements?
m
m
 Nm
  NI

– In the direct method, we solve 𝑅𝑚2𝑁 = 𝑅𝑚2𝑁 . 𝑊𝑁𝑚
•
𝑚
m
𝑊𝑁𝑚 𝑚 is the skew-symetric matrix associated to 𝜔𝑁𝑚 𝑚 , WNm
We have to solve 9 equations with 9 unknows
– Using a quaternion vector, we solve
 0

m
WNm
  z
  y

 z
0
  is the quaternion vector associated to 
• 
N
Nm
x
y 

 x 
0 
m
Nm
  
m

mI

from gyrometer
 0  z  y 


  z
0  x 
  y  x
0 

m
,  Nm  0  x
 y  z T
• qis the unknown quaternion vector associated to the single rotation describing the rotation
of (m) in (N)
a  



 
 b   cos  real part
 
2 




, E rotation axis guiding unit vector,  rotation angle
q

c       

  sin    E imaginary part 


d    2 
•
Rm 2 N
2bc  ad 
2bd  ac  
a ²  b ²  c ²  d ²
  2bc  ad 
a ²  b²  c²  d ²
2cd  ab  
 2bd  ac 
2cd  ab 
a ²  b ²  c ²  d ² 
We have to solve 4 equations with 4 unknows; more stable.
September 2014
Additional slides
- 105 -
Further on frames definition
Frame
Inertial
Terrestrial
Appellation
s
Spacestable
or Spacefixed frame
ECEF
Conventiona
l Terrestrial
System
Frame origin
Earth
center
of
mass
Ox
Oy
Pointed along the
vernal equinox
Oz
Mean position
90° East / Ox
of the spinning axis
on the equatorial plane
of the Earth
Intersection of the
Mean position
equatorial plane
90° East / Ox
of the spinning axis
and the Greenwich on the equatorial plane
of the Earth
reference plane
Local-level
Geographic
Navigation
frame
Body
Body frame
Platform
Platform
axes
platform
Axes of
Computer
Computing
frame
Center
of gravity
Supposed
axes
of
the
platform
True
True axes
True
axes
of
the
platform
vehicle
center
of mass
Geographic North
direction
Roll axis,
pointed to forward
East direction
Pitch axis,
pointed to the right
wing
the
accelerometers
Normal to the
reference ellipsoid
Yaw axis,
pointed to down
1, 2 and 3
Observations
- Newton laws
- Computing
burden
- Stabilized INS
- Earth -fixed
- Computing
burden
- horizontal
navigation
- Stabilized
on the north
- Vehicle fixed
- Strapdown INS
/
- Frame
providing the
solution
/
September 2014
Additional slides
- 106 -
Inertial sensors error sources and classical models
Error source
Error type
Gyroscope
Gravity
Observations
due to the accelerometers
mounting on the platform
Bias
Specific force error
supposed as linear in the range of
Scale factor
measured specific forces
Other (nonlinearities...)
/
due to the gyroscope mounting on
Alignment error
the platform
One of the most
g-insensitive drift
Random walk
significant errors
Random
proportional to the specific force
g-sensitive drift
constant
(unbalance-type error)
Random
induced by
g²- sensitive drift
constant
anisoelastic torques
Random
supposed as linear in the range of
Scale factor
constant
accelero measured velocities
The gravitation potential depends
Deflections
1st order
on tides
and gravity anomaly
Markov process
(moon and sun effects ...)
Alignment error
Accelerometer
Adopted
model
Random
constant
Random walk
Random
constant
?
Random
constant