GPS Vorlesung 2015 File

Transcrição

GPS Navigation
Part 1: Principles (Day1)
Part 2: Spaceborn Navigation (Day2)
Part 3: Onboard Navigation Systems (Day2)
Part 4: Receiver Technology (opt.)
Markus Markgraf (DLR/GSOC)
Slide 1
Universität Würzburg > Informatik für Luft- und Raumfahrt > SS2015
GPS Navigation
Part I: Principles
Slide 2
GPS Navigation – Principles
Radio Navigation
GPS System Elements
Signal Structure
Positioning
Slide 3
Radionavigation (I)
Development started ~ 1940
Use of radio waves, for example.
Long waves: 30-300 kHz, 1-10 km
Very High Frequencies (VHF): 30-300 MHz, 1-10 m
UHF: 300 MHz - 3 GHz, 10 cm-1m
Application dependent use of different frequencies
Long waves provides extended range (surface waves, marine)
High frequencies provide more accurate measurements
(short wavelength, reduced propagation effects)
λ = c /f
λ
wavelengths =
speed of light
frequency
c
Slide 4
Radionavigation (II)
One-Way Ranging
Distance ≙ Propagation time
Propagation time =
Reception time - Transmission time
↔
Two-Way Ranging
Distance ≙ 1/2 x Propagation time
( + transponder delay)
Slide 5
Radionavigation (III)
Distance dependent signal propagation time
Speed of light 300000 km/s
300 km per millisecond
300 m per microsecond
Example:
Time signal Braunschweig: signal takes 2 ms to reach Munich
Geostationary satellite: altitude 36000 km corresponds to 0.12 s
Earth-Moon: distance 400000 km corresponds to 1.3 s
Frequency depends on relative velocity
Doppler effect: df/f=-v/c
Compare signal horn (ambulance/police)
Slide 6
GPS System Elements
Space segment
2051.1/2227.5 MHz (S)
• Telemetry
• Telecommand
• Navigation data
Control segment
• Main control station
• 4 ground stations
• 5 monitoring stations
1575.42 MHz (L1)
1227.60 MHz (L2)
• Ranging signals
• Position data
• Atmospheric data
User segment
Slide 7
GPS Space Segment
Altitude 20200 km
Orbital period ~12h (11h58m)
2 revs per Earth rotation
6 orbital planes (A-F)
Inclination 55°
60° offset (ascending node)
Minimum 4 satellites/plane
5-8 satellites simultaneously visible
Presently 31 satellites in orbit
SVN = Space Vehicle Number
(for example #54; identifies satellite)
PRN = Pseudo Random Number
(for example #18 identifies signal)
Slide 8
GPS Satellites
Manufacturer
Block II/IIa
Block IIR/IIRM (L2C)
Block IIF (L5)
Rockwell
International
Lockeed Martin
(AS-4000 Bus)
Boeing
(formerly Rockwell)
1.5 x 1.9 x 1.9 m
2.5 x 2 x 2 m
Size
Launch weight
1660/1816 kg
2032 kg
Life time
7.5 years
10 years
15 years
Payload power
0.7 kW
1.1 kW
2.4 kW
Clocks
Cs, Rb
Rb
Rb
Number
0/8
12/7
4
(Total: 31)
Slide 9
GPS Master Control Station
Falcon/Schriever Airforce Base
(AFB), Colorado Springs
Monitoring and operations of
spacecraft bus and payload
Maneuver planning
Orbit determination using data of
monitoring stations
Generation and upload of
navigation message
Time synchronization
User informations
Slide 10
Ground Stations and Monitoring Stations
Colorado
Springs
Cape
Canaveral
Hawaii
Kwajalein
Diego
Garcia
Ascension
Island
Master Control Station
(+ground/monitoring station)
Ground station
(+monitoring
station)
Monitoring
station
NIMA Monitoring
station
Slide 11
GPS Time Representation and Coordinate System
GPS time representation
Weeks (w) since 6 Jan. 1980 (MJD 44244.0)
Seconds (t) since start of week ([0,604800[)
Sunday = day 0, Monday = day 1, etc.
Example 6 Nov. 2001, 0h: w=1139, t=172800s (Day 2, 0h)
Other Than UTC, not perturbed by leap seconds (GPS is now 16s
ahead of UTC)
World Geodetic System 1984 (WGS-84)
Standard GPS reference system
Earth-Fixed, Earth-Centered (ECEF)
Reference plane: Earth equator
Reference direction: Greenwich Meridian
WGS84 reference ellipsoid (R⊕ = 6378.137km, f=1/298.257...)
Slide 12
GPS Signal Components
Carrier
Sinusoidal radio waves
2 frequencies (L1 & L2)
Third frequency (L5) planned
Ranging code
Unique assignment to GPS satellites
2 codes: C/A (coarse/acquisition) and P(Y) (precise)
Pseudo-random noise (PRN) sequences of „0“s and „1“s
with good cross- and autocorrelation properties
Navigation data
Binary data stream („0“/“1“)
Low data rate (50 bit/s, 1 bit = 20 ms)
Period: 30s (critical data), 12.5min (all data)
Slide 13
GPS Frequency Plan
Component
Frequency
Base freqeuncy
f0
10.23 MHz
L1 carrier
154 f0
1575.42 MHz (~19.0 cm)
L2 carrier
120 f0
1227.60 MHz (~24.4 cm)
L5 carrier (planned)
115 f0
1176.45 MHz (~25.5 cm)
P-code
f0
10.23 MHz (~29.3 m)
C/A-code (L1 only)
f0/10
1.023 MHz (~293 m)
W-code (encryption)
f0/20
0.5115 MHz
Navigation data
f0/204600
50 Hz
All frequencies are derived from a common base frequency
All signals are synchronized
Slide 14
Signal Generation
C/A Code c(t)
AC/A·c(t)·d(t)·cos(f1·t)
c(t)·d(t)
AC/A
Σ
Navigation Data d(t)
Antenna
AP(Y)
p(t)·d(t)
AP(Y)·p(t)·d(t)·sin(f1·t)
P Code p(t)
90°
Carrier sin(f1·t)
L1: C/A & P(Y) Code
L2: only P(Y) Code
Slide 15
PRN Codes
Code Division Multiple Access (CDMA) – Spread Spectrum
All GPS satellites employ the same transmit frequency
Each GPS satellite has a unique signal
Signal spreading over the frequency band
Pseudo ramdom noise (PRN) sequences
Fixed pattern of „0“s and „1“s
Fixed length, typically 2n-1 (31, 1023, etc.)
Continuous repetition
Different PRN codes have almost no correlation
Identical but shifted PRN codes have almost no correlation
Signal < Noise !!
Slide 16
PRN Codes (Example)
GPS C/A code chips (linies = PRN 1-32)
Code correlation
© Peter Dana, Dept. Geography, Univ. Bolder Colorado
http://www.Colorado.EDU/geography/gcraft/notes/gps/gps.html
Slide 17
GPS C/A-Code Generation
G1 Generator (1+x3+x10)
G1=...10101111111111
1
2
3
4
5
6
7
8
9
10
Clock
1.023 MHz
XGi
G2i
Selektor
C/A Code
Reset
S1
1111111111
S2
G2i is a time shifted copy of G2
1
2
3
4
5
6
7
8
9
10
G2=...01001111111111
G2 Generator (1+x2 +x3 +x6 +x8 +x9 +x10)
Slide 18
Structure of GPS
12.5 min
Time
Navigation Data
1.0 min
Frame 25
TL
M
TL
M
HOW
2
HOW
3
Frame 2
0.5 min
Frame 1
TLM HOW Clock correction, Status
6s
12s
18s
TLM HOW Almanac, Ionosphere Model, dUTC
30s
5
3
TLM HOW Ephemeris Parameters
TLM HOW Almanac
1
4
2
TLM HOW Ephemeris Parameters
24s
1
4
5
Time
Slide 19
GPS Observables (I)
Pseudorange measurement
Propagation time from code correlation
C/A-code (L1), P(Y)-code (L1/L2)
Measures distance (+clock offset)
Carrier phase measurement


Beat frequency f-f0
Fractional phase [0,1[ or [0,2π[
Integer cycle count
Measures range change
Doppler shift
Offset from nominal frequency f0
Measures line-of-sight velocity
(+ frequency offset)
Slide 20
(Pseudo-)Range Measurement
t
p = c(t rcv − t tm )
tm
Transmitted signal

Propagation time

Received signal
t
rcv
Slide 21
GPS Observables (2)
Beat frequency f-f0
Integer cycle count
Doppler shift
Slide 22
Carrier Phase Measurement
f-fL1
f
Beat frequency
fL1
Measurement of fractional phase
Zero-transition count
Distance change
t
dr
Slide 23
Comparison of Code and Phase Measurements
distance
Code measurement
absolute pseudorange with
moderate accuracy (~1m)
constant
offset
time
Phase measurement
pseudorange with offset
(„biased pseuodrange“) but
with very high accuracy
(~1mm)
Slide 24
GPS Observables (3)
Beat frequency f-f0
Integer cycle count
Doppler shift
Slide 25
Positioning – Problem Formulation
Given data
Pseudorange measurements pi (i=1,...,n)
GPS satellite positions
Ri (i=1,...,n)
Approximate receiver position r0
Unknown data
Receiver position r
Clock offset
b=c·δt (δt = trcv-tGPS)
Notes:
2-dimensional positioning: minimum 3 observations
3-dimensional positioning: minimum 4 observations
Slide 26
GPS Positioning
Pseudorange Measurement =
Radius of a sphere
Slide 27
Basic Measurement Equation
pi
Satellite i
Ri=(Xi,Yi,Zi)
Distance
= ρ i + cδt
=
( x − X i )2 + ( y − Yi )2 + ( z − Z i )2 + cδt
ρi
Receiver
r=(x,y,z)
Clock offset cδt
Slide 28
Linearisation
Consider small changes relative to an approximate initial point
p = ρ (r ) + cδt
∂ρ
p ≈ ρ (r0 ) +
∆r + cδt
∂x
∂ρ
∂ρ
∂ρ
= ρ (r0 ) +
( x − x0 ) +
(y − y 0 ) +
( z − z0 ) + cδt
∂x
∂y
∂z
Slide 29
Least Squares Method - Solution
Square-sum of residuals
J (x) = ( Ax − z ) ( Ax − z )
T
∂f T g
∂g
∂f
= fT
+ gT
∂x
∂x
∂x
T
∂Ax
=A
∂x
z = Observations
x = Estimated position
Ax = Modelled PRs
 ∂J( x ) 


 ∂x 
= 2 A ( Ax − z ) = 0
Minimum condition
( AT A) ⋅ x
= ( AT z )
Normal equations
T
!
Slide 30
Error Budget and Accuracy Analysis
Accurate pseudorange modeling needs to account for
Light time (correction up to 75m)
Earth rotation correction (when working in ECEF system; up to
35m)
Relativistic clock correction (up to 15m)
Atmosphere
Tropospheric delay
Ionospheric delay
Ephemerides errors (GPS satellite position error)
Clock Offsets
Multipath Effects
Receiver Noise
Slide 31
The Atmosphere
Troposphere
Altitude 0 - 10 km
Neutral (no charged particles)
Exponentially decreasing density
Scale height ~7 km
Ionosphere
Altitude 80 -1000 km
Free electric charges
Density exhibits ~ Chapman profile
Electron density maximum at
300 - 400 km
© Rutherford Appleton Laberatory
Slide 32
Multipath Errors
Pseudorange errors in
case of strong reflections
C/A-code 50-100m
C/A-code with narrow
correlator 5-10m
P-code 5-10m
Direct
Signal
Typical pseudorange
errors
1-5 m
Reflected
Signal
Phase errors
Maximum λ/4 (5-6cm)
Typical 0.5-1 cm
Obvious from signal
strength variations
Slide 33
User Equivalent Range Error (UERE) Examples
Standard Positioning
Service (S/A on)
SPS
(S/A off)
Geodetic
Single Point
Positioning
Satellite clock &
ephemerides
25 m
1m
0.1 m
Atmospheric
delay modeling
5m
5m
0.2 m
Noise and
multipath
1-5 m
1-5 m
0.5-2 m
Total
26 m
5-7 m
0.6-2 m
UERE Contribution
Slide 34
Dilution of Precision (DOP)
Position error in case of unit measurement error
Depends only on geometry and number of measurements
RMS(Pos) = DOP·UERE
Statistical
position error
=
geometry factor
x
Statistical error of
individual range
measurement
UERE = User Equivalent Range Erro
Slide 35
GNSS – A System of Systems
(Image: D.Turner, DOS)
Slide 36
Galileo – The European Alternative
MEO constellation
23200 km altitude
14h 05m (17 revs in 10 d)
56° inclination
3 orbital planes
30 satellites
27 operational
3 spare
9 + 1 per plane
Deployment
Soyuz (2 sats)
Ariane-5 (6 sats)
Slide 37
Working Together
Principles
Compatibility:
don‘t cause interference
Interoperability: benefit from joint use
Measures
Spectral separation vs common bands
Different modulations
Different codes
Intergovernmental coordination
Bright future or Pandora‘s box?
1+1 = ?
Receiver design
Algorithms
Slide 38
GPS Navigation
Part II: Spaceborne GPS
Slide 39
GPS Navigation – Spaceborne GPS
Orbit Determination
Science Applications
Spaceborne GPS Receivers
Slide 40
Ground Station Coverage
Horizon
Station
Orbit
15 revolutions per day
4-6 ground station contacts per day
5-15 min contact time
Poor coverage with tracking data
Need for dynamical orbit modeling
Altitude
Time
Range
300 km
8 min
2000 km
600 km
12 min
2800 km
1000 km
17 min
3700 km
Slide 41
Spaceborne GPS – Why?
Instantaneous 4D measurement
Position
Velocity
Time
Onboard availability
High accuracy
Continuous availability (in LEO)
Acceptable h/w cost and
mass/power budget
Slide 42
GPS Based Orbit Determination Concepts
Kinematic
Single point solution from 4++
pseudoranges
Smoothing with carrier phase
measurements
Arbitrary motion (e.g. maneuvers)
Dynamic
Connect individuals point by dynamical
model
Kalman filter or global adjustment
Estimation of dynamical model parameters
High(er) complexity
Slide 43
GPS Based Orbit Determination Methods
Method
Data
Accuracy
Real-time navigation solution (single-frequency)
C/A
10 m
Real-time navigation solution (dual-frequency)
P1, P2
3-5 m
Kalman-filtered navigation solution (GRAPHIC)
C/A+L1
1m
Kalman-filtered navigation solution (dual-frequency)
P1,P2, L1,L2
0.5 m
Reduced-dynamic POD using navigation solutions
XYZ
1-2 m
C/A+L1
0.1-0.5 m
P1,P2, L1,L2
0.05 m
Reduced-dynamic POD (offline, GRAPHIC)
Reduced-dynamic POD (offline, dual-frequency)
Gill E., Montenbruck O.; „Comparison of GPS-based Orbit Determination Strategies“; 18th International
Symposium on Space Flight Dynamics, 11-15 Oct. 2004, Munich, Germany (2004).
Montenbruck O., Ramos-Bosch P.; „Precision Real-Time Navigation of LEO Satellites using Global Positioning
System Measurements“; GPS Solutions 12(3):187-198 (2008). DOI 10.1007/s10291-007-0080-x
Slide 44
Reduced Dynamic Orbit Determination (GHOST)
High accuracy trajectory model
High order (e.g. 100x100) gravity field model, tides,
Drag, luni-solar gravity, radiation pressure,
Thrust arcs, empirical accelerations
Numerical trajectory integration
Undifferenced code and carrier phase measurements
Least-squares adjustment
Slide 45
Normal equations
Solve-for parameters
Epoch-wise clock offsets
Epoch state, CR, CD, thrusts
Empirical accelerations
Pass-by-pass biases
Typically 4000 parameters for 24h arc
with 30s observation and 10 min
intervals for emp. accelerations
Sparse matrix
Factorization and elimination of clock
offsets leaves problem of dimension
1000 x 1000
Slide 46
Mission Requirements
Mission
TerraSAR-X
(SAR)
Sentinel-1
(SAR)
NRT (1-3h)
STC
NTC
10 m 3D
2 m 3D
10 cm 3D
2m xyz
Sentinel-2
(Optical)
Sentinel-3
(Altimeter)
MetOp
(Occultations)
5 cm xyz
2m xyz
8 cm radial
3 cm radial
2 cm radial
0.1 mm/s along
(~10 cm)
Slide 47
Satellite Laser Ranging (GRACE-B)
Slide 48
Formation Flying
PRISMA
Formation flying and
rendezvous technology
demonstration
Single-frequency GPS for realtime and offline navigation
© SSC
TanDEM-X
Bistatic SAR Interferometry
Dual-frequency GPS for precise
baseline reconstruction
Slide 49
Carrier Phase Differential GPS Navigation (CDGPS)
Receiver-receiver difference (∆)
eliminates/reduces
Atmospheric delays
GPS orbit and clock errors
Satellite-satellite difference (Ñ) eliminates
Receiver clock errors
Linebiases
Double difference (Ñ ∆)
Depends mainly on relative geometry
Yields integer ambiguities
Ambiguity fixing converts carrier phases into
highly accurate pseudoranges
Slide 50
PRISMA GPS Hardware
Phoenix-S GPS Receiver
Commercial-off-the-shelf
hardware platform
DLR software
12 channels L1 C/A code tracking
Power 0.8 W (BOL) at +5V
Latch-up protection (SSC)
Performance
C/A code noise 0.5 m @ 45 dB-Hz
Carrier tracking 1 mm @ 45 dB-Hz
Integer ambiguities
Redundancy & Flexibility
Two receivers and amplifiers
Two passive antennas
Switch branches via TC
Slide 51
PRISMA Relative Real-Time Navigation
6.7 cm
3D rms
Slide 52
Scientific Applications
Gravity Field Determination
Occultations
Sea Surface Reflections
Slide 53
Gravity Field Determination
Satellite motion depends on gravity
GPS measurements provide highly
accurate satellite positions
Representation by spherical harmonics
expansion
Example: Eigen-1S model (GFZ et al.)
Combination of previous model & SLR
data (LAGEOS, etc.) with CHAMP
GPS & accelerometer (88d)
Coefficients up to 100 x 100
(max. 119)
Purely satellite based model
Full information up to 35 x 35
Slide 54
Atmospheric Profiling by GNSS Radio Occultations
While a GNSS satellite ‘sets’ or ‘rises’ behind the horizon:
Bending of the GNSS signal’s ray path due to refraction
in the atmosphere
The GNSS receiver measures the excess Doppler shift
(Dual frequency, high temporal resolution)
GPS Satellite
(Reference)
LEO Satellite
(CHAMP)
GPS Satellite
(Rise/Set)
GPS Network
Slide 55
GPS Occultations – Results (CHAMP)
Slide 56
GRAS Instrument on MetOp
Occultation
Antenna
R/F Conditioning Unit
Electronic Unit
Antenna Diagram
Slide 57
MetOp Occultation Events
• 338 Setting Occultations
• 322 Rising Occultations
(Loiselet et al. 2006)
Slide 58
GNSS Reflectometry (Bistatic Radar)
Utilization of parasitic microwaves
Martin-Neira (1993)
CHAMP, DMS/UK, SURGE
High gain, downlooking LHCP
antenna
Less accurate but wider coverage
than traditional altimeter
Sea surface height from time delay
of direct and reflected signal
Ocean winds and soil humidity from
amplitude and distribution of
reflected signals
Also ice and land applications
GNSS
Transmitter
GNSS
Receiver
Ocean, Ice, Land
1 chip
Slide 59
Spaceborne GPS Technology
Politics
Signal Dynamics
Acquistion and Tracking
Space Environment
Testing
Receivers
Slide 60
Space Environment
Temperature
E.g. –20°C ... +60°C inside a representative
satellite
Compatible with consumer electronics
Vacuum
Outgassing, leakage
Vibration
Only a few minutes at launch
(unlike a car on a bumby road)
But: risk of resonances
Radiation
Total Ionization Dose (aging, current increase,
death)
Single Event Effects (bit errors, hick-up,
desctructive latch-up)
Slide 61
Testing of Space Hardware
Co-60 Source
Signal Simulator
Thermal Vacuum Chamber
€€€€
Shaker
Proton Cyclotron
Slide 62
Spaceborne GPS Receivers
MosaicGNSS (Astrium)
IGOR (Broadreach/JPL)
Lagrange (Alcatel)
Missions
SAR-Lupe, TerraSAR-X
TerraSAR-X
Cosmo-Skymed
Type
L1, 8 channels
L1/L2, 16 x 3 channels
L1/L2, 16 x 3 channels
Navigation
10/20m (un-/filtered)
10m (1-freq., unfiltered)
20m (1-freq., unfiltered)
Raw data
accuracy
C/A 5 m
L1 3 mm
C/A, P(Y) 0.1 m
L1, L2
0.5 mm
C/A, P(Y) 0.2 / 0.1 m
LA, L2
2 mm
Power, Mass
10 W, 1 kg
16 W, 5 kg
30 W, 5 kg
Radiation
35 krad
12 krad
20 krad
Purpose
ADCS support & timing,
OD, Real-time navigation
Offline POD &
Scientific applications
ADCS support & timing
Offline POD
Slide 63
GPS Navigation
Part III: Onboard Navigation Systems
Slide 64
GPS Navigation – Onboard Navigation Systems
Motivation
Algorithms
Examples
Phoenix-XNS
BIRD ONS
Slide 65
Mission Needs ...
Timing (~ 1 µs)
Synchronization of onboard clock
Local Orbital Frame (~ 10 m, ~ 1 cm/s)
Conversion of star camera attitude
Instrument pointing (nadir or other)
Geocoding (1 – 10 m)
Blending of payload data with position information (SAR, optical)
Autonomous Instrument and Mission Operations (1 m – 100 m)
Open-loop altimeter operations
Target and ground station acqusition
Slide 66
... and how to meet them
Adequate maturity and availability of spaceborne GPS technology
Single-frequency (navigation)
Dual-frequency (science, POD)
Conservative, bulky, costly!
Performance in LEO compatible with Standard Positioning Service
No urban canyons, lower ionosphere
Few satellites above the poles
Typical positioning accuracy of 10 (-20) m
Slide 67
Real-Time Navigation Cookbook
Ingredients
Dynamical model
Numerical integration
Measurement model
Filtering
Montenbruck O., Ramos-Bosch P.; „Precision Real-Time
Navigation of LEO Satellites using Global Positioning
System Measurements“; GPS Solutions 12(3):187-198
(2008). DOI 10.1007/s10291-007-0080-x
Slide 68
Gravitational Accelerations
Earth gravity field
Spherical harmonics expansion
GM ⊕
a = ∇
r
∞
n
R⊕n
∑ ∑ rn
Pnm (sin φ )(Cnm cos mλ + Snm sin mλ )
n =0 m =0
Cunningham L. E.; „On the Computation of the Spherical Harmonic
Terms needed during the Numerical Integration of the Orbital Motion
of an Artificial Satellite“; Celestial Mechanics 2, 207–216 (1970).
Degree and order 20 to 50
Optional: solid Earth tide (k2)
Luni-Solar Perturbations
Point mass model
Low-order analytical series of luni-solar coordinates (1‘ to 5‘)
Simplified ICRF-to-ITRF transfomation (precession, Earth rotation)
Slide 69
Non-Gravitational Accelerations
Air Drag
No r/t access to solar flux & geomagnetic indices
Simple desity model (Harris Priester)
1
A
a = − CD ρ ⋅ v ⋅ v
2
m
Adjustable drag coefficient
Solar Radiation Pressure
Cannon-ball model
A s
a = PSun ⋅ CR ⋅ 3 ⋅ AU2
m s
Cyclindrical shadow model
Adjustable rad. pressure coefficient
Maneuvers
Empirical Accelerations
a = ar ⋅ er + at ⋅ et + an ⋅ en
Adjustable parameters
Compensation of force model deficiencies
Slide 70
Numerical Integration
Real-time navigation systems
Frequent measurement updates
Short propagation intervals (0.001 to 0.01 revs)
Limited resources
Use low order Runge-Kutta methods
y
h
h
2h
t0
t1
t2
t
RK4 with Richardson Extrapolation
Combines two RK4 steps of size h
with one step of size H=2h
Gives 5th order at 6 function calls per h
Hermite interpolation
5th order polynomial for y(t)=(r,v)
from y0, y1 , y2 , y´0, y´1 , y´2
Gill E., Montenbruck O., Kayal H.; “The BIRD Satellite Mission as a Milestone Towards GPS-based
Autonomous Navigation”; Navigation - Journal of the Institute of Navigation 48/2, 69-75 (2001).
Montenbruck O., Gill E.; „State Interpolation for On-board Navigation Systems“; Aerospace Science
and Technology 5, 209-220 (2001). DOI 10.1016/S1270-9638(01)01096-3).
Slide 71
Measurement Model
Ionosphere-free measurements
Dual-frequency pseudorange (P12)
Dual-frequency pseudorange and carrier phase (P12 & L12)
GRAPHIC (GRoup and PHase Ionospheric Calibration) (C/A+L1)
Average of code and carrier phase measurement
Biased measurement
Noise reduced by 50%
Requires only C/A code tracking (better signal-to-noise ratio)
Broadcast ephemerides
Signal-In-Space-Range-Error ~ 1-1.5 m
ICD-GPS-200 models for GPS position, velocity, clock
Slide 72
Filtering (I)
„Least-Squares Estimation“ versus „Kalman Filtering“
Least-Squares:
Batch estimation method (not
suited for real-time applications)
Solving entire system in one step
Kalman Filter:
Sequential processing (real-time
filtering)
Requires system model
Minimize sum of residuals
Two-stage process
Requires system model
Requires convergence time
Measurement noise needs to be
known
System(Process) noise and
measurement noise need to be
known
Slide 73
Filtering (II) – Kalman Filter
x = State Vector,
P = State Covariance Matrix,
Φ = State-Transition Matrix,
Q = System/Process Noise,
K = Kalman Gain,
H = Sensitivity Matrix,
R = Measurement Noise,
y = Measurements/Observations
h = Modeled Measurements Vector
Slide 74
Filter State Vector and Process Noise Model
State Vector
Parameter
 r 


 v 


C
 R 
Y =  CD 


 aemp 


 cδt 
 B 


Position
Velocity
3
3
Maneuver-free arcs: none
Radiation pressure coeff.
1
None
Drag coefficient
1
None
Empirical accelerations
3
Expon. Correlated Random Vars.
Clock Offset
1
White noise
Biases
Dim
nCH
Process Noise
Maneuvers: white noise
(White noise)
Slide 75
Phoenix-XNS
Extension of DLR‘s Phoenix GPS receiver
32-bit ARMTDMI microprocessor @30 MHz
12 Channels L1 tracking
Real-time Kalman filtering of GPS raw
measurements
Ionosphere-free C1+L1 combination
Code noise ~ 0.4 m, carrier phase <1 mm
Complements Phoenix standard software for
GPS tracking and navigation
C++ software extension
40x40 gravity model
30s filter update rate
First in-flight demonstration on PROBA-2
Montenbruck O., Markgraf M., Santandrea S., Naudet J., Gantois K., Vuilleumier P.; „Autonomous and Precise Navigation
of the PROBA-2 Spacecraft“; AIAA-2008-7086; AIAA Astrodynamics Specialist Conference, 18-21 Aug. 2008, Honolulu,
Hawaii (2008).
Slide 76
Phoenix-XNS Flight Results (PROBA-2)
Position ~1 m
Velocity ~ 1 mm /s
3D rms
Slide 77
GPS Navigation
Part IV: Receiver Technology
Slide 78
GPS Navigation – Receiver Technology
Receiver building blocks
Signal acquisition
Code and carrier tracking
Measurement noise
Multipath errors
1.5
1.4
Carrier Phase [mm]
Pseudorange [m]
Doppler [m/s]
Measurement Noise
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
C/N0 [dB-Hz]
Slide 79
Receiver Tasks
Amplification and filtering
Despreading (separation of different PRNs)
Doppler compensation
Code- and carrier phase measurement
Navigation solution computation
Slide 80
Traditional Receiver Architecture (Mitel GPS Orion)
Frontend
(GP2015)
Oszillator
(10 MHz)
Correlator
(GP2021)
EPROM
(256 kB)
CPU
(ARMP60)
RAM
(512kB)
Slide 81
Block Diagram
Antenna
Memory
Amplifier
Frontend
Correlator
Processor
Oscillator
Analog
Digital
Slide 82
Frontend
Signal Preprocessing/Conditioning
Amplification
Automatic Gain Control (AGC)
Filtering
Frequency conversion
Mixing(n)
Filtering
Analog-to-Digital Conversion
Slide 83
Mixing
Carrier
f
f − fm
f − fm
Filter
f + fm
Mixing frequency fm
cos( 2πft ) ⋅ cos( 2πfmt ) =
1
1
cos( 2π (f − fm )t ) + cos( 2π (f + fm )t )
2
2
Slide 84
Sampling and Analog/Digital Conversion
Amplitude
Time
Time
Slide 85
Correlator
Digital signal processing
Doppler compensation
Separation of PRN signals (despreading)
Code and phase delay measurement
Parallel Architecture
Typically 12 (-16) C/A-code channels
Simultaneous processing of multiple PRNs
Opt. units for P(Y)-code processing
Opt. units for GLONASS, etc.
Mostly ASICs (Application Specific Integrated Circuits)
Application specific hardware
Optimised for one application, limited flexibility
Alternative: FPGA, DSP
Slide 86
Numerically Controlled Oscillator (NCO)
Increment
Clock
cos(ωt )
COS
Table
Summation
Register
ϑ
+π
sin(ωt )
SIN
Table
Amplitude
0
Increment
Time
Register
−π
0
2n
high/low
Frequency
Slide 87
Doppler Compensation,
In-Phase and Quadrature Channel
„In-Phase“
A(t ) ⋅ cos( 2π (fD − fD̂ )t − θ )
Intermediate frequency
(Doppler-shifted)
„Quadrature“
A(t ) ⋅ sin( 2π (fD − fD̂ )t − θ )
A(t ) ⋅ cos( 2π (fIF + fD )t )
sin( 2π (fIF + fD̂ )t + θ )
cos( 2π (fIF + fD̂ )t + θ )
NCO
fIF + fD̂
Intermediate frequency +
approx. Doppler offset
Slide 88
Correlation
 I  = 1 c (t − τ )c (t − τˆ ) ⋅ cos(2π∆f t + ∆θ )dt
Q 
 sin 
D
  T


∫
c (t − τ ) ⋅ cos(2π∆fDt + ∆θ )
 sin 
1
T
PRN code, partly
Doppler compensated
c (t − τˆ )
C/A-Code
Generator
Code-Delay
1
T
τˆ
I
∫ (•)dt
Q
∫ (•)dt
Integrator 1ms
R( ∆τ , ∆fD ) = I 2 + Q 2
Correlation
Power
Slide 89
Correlation (Example)
Slide 90
Sequential Search
Sequence
53124
500 Hz
1023
chips
1/2 chip
Search time
• 1ms / cell
• 2s / bin
• ~ 40-50s total
0 chips
-5 kHz
0 kHz
+5 kHz
Slide 91
Code Correlation
In
Replica
0 chips
1/2 chip early
1/2 chip late
1 chip early
1chip late
Correlation
R(∆τ)
∆τ = τˆ − τ [chips]
-2
-1
+1
+2
Slide 92
„Early-Prompt-Late“ Correlators
Three separate correlators per channel
„Prompt (P)“: replika of the PRN Codes, which shall be synchronided with the
incoming code
„Early (E)“: replica with a ½ chip advanced code
„Late (L)“: replica with a ½ chip delayed code
Implementation
One PRN-code generator
Shift register for time delay
Standard correlator: 1.0 chip offset between E and L arm
„Narrow correlator“: 0.1 chip offset between E and L arm
Slide 93
Early-Minus-Late Discriminator
E
E-L
P
+1
L
E
P
L
-1
L P
E
-1/2
+1/2
∆τ [chips]
L
P E
Working range
[-1/2 chip,+1/2 chip]
L
P
E
-1
Slide 94
Digital Signal Processing (Single Channel)
Slide 95
Delay-Locked Loop (DLL)
further processing
Signal
In-Phase &
Quadrature
Correlation
Discriminator
I, Q
c (t − τ )
C/A-code
generator
& NCO
∆τ
τ ,τ
Error signal
Loop Filter
Estimated
code phase
Code phase
Slide 96
Phase-Locked Loop (PLL)
Code phase
Data
Demodulation
Signal
(I/F)
Mixing
(In-Phase &
Quadrature)
Code
Correlation
(DLL)
I, Q
Phase
Discriminator
∆θ
Carrier
NCO
Estimated
I/F Phase
θ ,θ
Loop Filter
Carrier Phase
Slide 97
Phase Discriminator
Q
Q 

I
 
(I,Q)
∆θ
∆θ = arctan
I
(-I,-Q)
Sign change in case of
changing data bit
Slide 98
Example IQ-Vectors
Uncorrelated (no signal)
Correlated
Slide 99

GPS Vorlesung 2015 File

Transcrição

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