Attitude Determination of Small Satellite: The GNSS Paradigm Dr. Najam Abbas Naqvi Assistant Professor Department of Aeronautics and Astronautics Institute of Space Technology Islamabad, Pakistan
Personal Profile Academics PhD. Aerospace (GNC-GNSS), China Specialized MS-GNSS, Italy MS Electrical Engineering, NUST, PK BS Electrical Engineering, UET, PK Professional Experience Assistant Professor, IST, PK Satellite Control Engineer, SUPARCO Publications Attitude Determination and Control Global Navigation Satellite System
Scope Motivation and Objective Attitude Determination (AD) Global Navigation Satellite System Research Design and Methodology Results and Analysis Conclusion
Motivation and Objective To design and implement a short baseline, multiantenna, stand-alone, commercial-off-the-shelf (COTS), GPS based attitude determination system for a Spacecraft using the Code measurements of GPS signals.
Attitude Determination and Control System Spacecraft Computer Desired Attitude None (Passive) Linear Limit Cycle Non-Linear Control Law Real Time Attitude Estimation Control Commands Attitude Actuators Thrusters Magnetic Torque Rod Momentum and Reaction wheel Movable Components Deterministic Filters Real Time Attitude Determination Internal Disturbance Torques Spacecraft Dynamics External Disturbance Torques Definitive Attitude Determination Solar Arrays Flexible Components Rotating Mechanisms Fuel Slosh People Aerodynamics Magnetic Gravity Gradient Solar Radiation Filter Bias Determination Attitude Measurement Earth, Sun, Stars Magnetometer Gyroscopes Payload Sensors Attitude Sensors
ADS Flow diagram Mission Requirements Attitude Representation Selection Attitude Coordinate System Selection Attitude Sensors Selection Modeling of Orbit Propagator Satellite Kinematics Dynamics Modeling Modeling of Disturbance s & Sensors AD Algorithm Selection and Implementation
Attitude Sensors Sensor Pros Cons Sun Sensor Horizon Scanner Reliable, Simple, Cheap Expensive No measurement in eclipse Orbit dependent, Poor in yaw Magnetometer Cheap Continuous Coverage Low Altitude only Star Tracker Gyroscope Very Accurate High Band Width Expensive-Heavy- Complex Expensive-Drifts with time GPS Receiver Single Sensor Several Errors
Accuracy Comparison of Sensors Sensor Mass (Kg) Power (Watt) Accuracy (3σ) Measured Angles Cost (K$ U.S) Gyroscope 3-25 10-200 Drift Rate: 0.003 o to 1 o /hour Roll, Pitch, Yaw 10-100 Sun Sensor 0.5-2 0-3 0.005 o -3 o Roll Coarse, Precise Yaw 10-50 Star Sensor 3-7 5-20 0.0003 o -0.01 o Roll, Pitch, Yaw 100-200 Horizon Sensor 2-5 5-10 0.1 o -1 o Roll Coarse, Precise Pitch 15-20 Magneto-meter 0.6-1.2 <1 0.5 o -3 o Roll, Pitch, Yaw 15-50 GPS (for Space) 2.2-3.5 3.5-10 0.4 o -1 o Roll, Pitch, Yaw >100
Attitude Representation Comparison Method Euler Angles Direction Cosines Quaternions Pros If given φ, ψ, θ, then a unique orientation is required Orientation defines a unique DCM Computationally Robust Cons Singularity 6 constraints Non Intuitive Not Intuitive Need Transforms Application Best for Analytical and Design work Best for Design and analysis Ideal for digital control Implementation
Attitude Determination Algorithms
AD : Recursive Estimation Algorithms REQUEST OPTIMAL REQUEST MME Euler-q Adaptive Optimal REQUEST Kalman Filter Unscented Filters Particle Filter The Orthogonal filter The Predictive filter Nonlinear observers Adaptive approaches
GNSS: Global Navigation Satellite System GNSS is a generic name for Global Navigation Satellite System, consisting of a Space Segment having a constellation of satellites in Medium Earth orbit at the height of 20,000 Km and above, Control Segment having Monitoring and Control stations to monitor / control/update the constellation of satellites and the User Segment; consisting of Receivers to give POSTION, VELOCITY and TIME of the static and mobile user all over the globe at all time using at least four satellites of the constellation in view.
Architecture of GNSS Space Segment Ground Control Segment User Segment
The Evolution Of GNSS Four Major GNSS GPS (US Fully Operational Since 1994) GLONASS (USSR - Fully Operational Since 1995 suspended and partially operated after collapse- since 2011 Soviet GLONASS is fully operational) Galileo (Europe expected fully operational in 2020) Beidou (CHINA expected fully operational in 2020)
Regional Navigation Satellite System Satellite Based Augmentation System Quasi-Zenith Satellite System (QZSS) Indian Regional Navigation System IRNSS Wide Area Augmentation System (WAAS) European Geostationary Navigation Overlay Service (EGNOS) Multi-functional Satellite Augmentation System (MSAS) GPS Aided Geo Augmented Navigation (GAGAN) The GLONASS System for Differential Correction and Monitoring (SDCM), proposed by Russia. The Satellite Navigation Augmentation System (SNAS) proposed by China.
Comparison of Major GNSS
17 The GNSS (Triliteration) Principle ),, ( o o o z y x x y z ),, ( k k k z y x b r ρ k known measured unknown r k k k k b z z y y x x + + = 2 0 2 0 2 0 ) ( ) ( ) ( ρ
GNSS in 2020 Source: cited from Asia Oceania is the 'Showcase of the New GNSS Era',presented at 5th QZSS user meeting (KOGURE, Satoshi Mr., 10th March 2010)
GNSS Market 7 bln GNSS devices by 2022 almost one for every person on the planet (billions) 300 250 200 150 100 CAGR: 9% Global GNSS market size CAGR: 5% 50 0 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Core revenue (Global) Enabled revenue (Global) The projected long-term growth gives significant business opportunities for GNSS market. Along with the rapid development of new services and applications, the business environment of GNSS market is demanding and requires constant innovation on the supply side. Source: http://ec.europa.eu/programmes/horizon2020/ The European GNSS Programmes 19
Basic Principle of AD using GNSS
AD Using GNSS: Performance Factors Antenna Baseline Line Bias GPS Geometry Geometric Dilution of Precision; GDOP Attitude Dilution of Precision; ADOP Multipath Measurement Errors Signal To Noise Ratio; SNR Cycle Slip Antenna Positioning Receiver Noise Ambiguity Resolution
Error Sources in GNSS Observables
GADACS SPARTAN RADCAL REX II Gravity Probe B UNISAT Gyrostat UOSAT-12 ALSAT-1 GPS Based AD: Flying Experiments
GNSS based AD Georgi-ION-GNSS-2010 / Dec 2011 (PhD thesis)
X-Sat Antenna Platform Lin et.al. IEEE 2004
GNSS Range and Phase Model P ( t) = ρ ( t, t τ ) + I + T + dm + c[ dt ( t) dt ( T τ )] + s s s s s s s s r, f P, r, f r r, f r r, f r r c[ d ( t) + d ( t τ )] + ε s s s r, f f r P, r, f Φ ( t) = ρ ( t, t τ ) I + T + δ m + c[ dt ( t) dt ( t τ )] s s s s s s s s r, f Φ, r, f r r, f r r, f r r + c[ δ ( t) + δ ( t τ )] + λ [ φ ( t ) φ ( t )] + λ z + ε s s s s s s r, f f r f r, f 0 f 0 f r, f Φ, r, f ρ ( t, t τ ) = r ( t τ ) + dr ( t τ ) r ( t) dr ( t) s s s s s s P, r, f r r f r r r, f
Single Difference Code and Phase Observables
Double Difference Code and Phase Observables
Antenna Placements
Time Calculations GPS Master Observation File Time 06 10 29, 01 44 23 Julian Day 2.4540e+006 GPS Week 1399 Second of Week (SOW) 6.1104e+005
Ephemeris Parameters of Visible Satellites SV-PRN 1 6 10 16 17 af 2 0 0 0 0 0 M 0 1.611359 0.773601-1.32079-0.90191 0.145283 Root a 5099.02 5099.02 5099.02 5099.02 5099.02 Delta n -9.57E-11-9.57E-11-9.57E-11-9.57E-11-9.57E-11 E 0.009 0.009 0.009 0.009 0.009 omega 0 1.047198 1.884956-3.14159-2.93215 Cuc -3.73E-09-3.73E-09-3.73E-09-3.73E-09-3.73E-09 Cus -3.73E-09-3.73E-09-3.73E-09-3.73E-09-3.73E-09 Crc -0.5-0.5-0.5-0.5-0.5 Crs 0.5 0.5 0.5 0.5 0.5 i 0 0.959931 0.959931 0.959931 0.959931 0.959931 I dot 0 0 0 0 0 Cic 1.86E-09 1.86E-09 1.86E-09 1.86E-09 1.86E-09 Cis -1.86E-09-1.86E-09-1.86E-09-1.86E-09-1.86E-09 Omega0-9.03E-05 1.047107 1.047107 3.141502 3.141502 Omega dot -8.44E-09-8.44E-09-8.44E-09-8.44E-09-8.44E-09 Toe 10800 10800 10800 10800 10800 af 0 0 0 0 0 0 af 1 0 0 0 0 0 Toc 10800 10800 10800 10800 10800
SV-PRN 21 22 26 30 af 2 0 0 0 0 M 0-1.73967-0.69248-2.57743 1.611359 Root a 5099.02 5099.02 5099.02 5099.02 Delta n -9.57E-11-9.57E-11-9.57E-11-9.57E-11 E 0.009 0.009 0.009 0.009 Omega -2.0944-1.88496-1.0472-0.20944 Cuc -3.73E-09-3.73E-09-3.73E-09-3.73E-09 Cus -3.73E-09-3.73E-09-3.73E-09-3.73E-09 Crc -0.5-0.5-0.5-0.5 Crs 0.5 0.5 0.5 0.5 i 0 0.959931 0.959931 0.959931 0.959931 I dot 0 0 0 0 Cic 1.86E-09 1.86E-09 1.86E-09 1.86E-09 Cis -1.86E-09-1.86E-09-1.86E-09-1.86E-09 Omega0-2.09449-2.09449-1.04729-1.04729 Omega dot -8.44E-09-8.44E-09-8.44E-09-8.44E-09 Toe 10800 10800 10800 10800 af 0 0 0 0 0 af 1 0 0 0 0 Toc 10800 10800 10800 10800
Visible Satellites in Inertial Frame Visible Satellite in ECEF Frame Sub-Satellite Points
Visible Satellites by Master Antenna (PRN) 10 26 21 22 6 30 1 17 16 Pseudorange from Master Observation File (E+07 meters) 10 26 21 22 6 30 1 17 16 2.34 2.05 2.07 2.23 2.20 2.23 1.96 2.24 2.40 Position of Visible Satellites in ECEF Frame (meters) 10 26 21 22 6 30 1 17 16 2.2605E+07 1.3102E+07 1.2132E+07 2.2489E+07 1.5324E+06 1.1185E+07 1.8978E+07 1.9660E+07 7.3887E+06 1.2709E+07 1.1217E+07-9.6433E+06 1.2618E+07 1.7183E+07-1.8554E+07 4.0405E+06-1.5135E+07-1.2980E+07-2.9577E+06 1.9765E+07 2.1097E+07 2.9725E+06 1.9140E+07 1.4122E+07 1.7096E+07 7.0749E+06 2.1289E+07
Elevation of Visible Satellites (Degrees) 10 26 21 22 6 30 1 17 16 17.75 61.12 55.02 28.27 29.47 27.88 78.16 25.59 11.37 Elevation of Visible Satellites`
Visibility Window during Mission Sky Plot of Visible Satellites
Number of Visible Satellites during Mission
Clock Errors (sec) Satellite Clock Offset Error 10 26 21 22 6 30 1 17 16-5.73061 6.055018 6.03479 2.430854-1.5411 0.630551-2.62313 3.76358 4.23142 Satellite Clock Relativistic Error 10 26 21 22 6 30 1 17 16-1.91E-08 2.02E-08 2.01E-08 8.11E-09-5.14E-09 2.10E-09 2.01E-08 8.11E-09-5.14E-09 Ionospheric Errors (meters) 10 26 21 22 6 30 1 17 16 14.19272 13.1952 13.57591 14.09869 14.10058 14.13489 13.57591 14.09869 14.10058 Tropospheric Errors (meters) 10 26 21 22 6 30 1 17 16 7.8599 2.7640 2.9531 5.0931 4.9036 5.1574 2.4734 5.5784 11.9709
Corrected Pseudorange (meters) 10 26 21 22 6 30 1 17 16 2.34+E07 2.05+E07 2.07+E07 2.23+E07 2.20+E07 2.23+E07 1.96+E07 2.24+E07 2.4+E07 Corrected Satellite Positions (meters) 10 26 21 22 6 30 1 17 16 2.2622E+07 1.3040E+07 1.2629E+07 2.2503E+07 0.1027E+07 1.1222E+07 1.8541E+07 1.9874 E+07-0.6826E+06 1.2809E+07 1.1778E+07-0.9294E+07 1.2723E+07 1.6891E+07-1.8125E+07 0.4315 E+07-1.5152 E+07-1.3258 E+07-0.2253E+07 1.9478E+07 2.0955E+07 0.2264E+06 1.9432E+07 1.4650E+07 1.7513E+07 0.6394E+07 2.1297E+07 Dilution of Precisions GDOP TDOP PDOP HDOP VDOP 1.8082 0.8299 1.6065 1.1672 1.0174
DOPs Variation
Mean Position of Master Antenna from 200 Epoch (meters) X Y Z 3991093.637 563015.311 4927059.123 Master Antenna Position Variations
Flow diagram of differential Positioning using code observation
Mean Position of Slave-1 Antenna from 400 Epochs (meters) X Y Z 4043173.94257238 607358.280965177 4945463.54148828 Slave-1Antenna Position
Mean Baseline Components between Master and Slave-1 (meters) X Y Z -58241.241-44221.107-26114.976 Variations of Baseline Components
Mean Position of Slave-2 Antenna from 200 Epoch (meters) X Y Z 4041342.4665337 605836.035363518 4944858.77077987 Slave-2 Antenna Position
Baseline Components between Master and Slave-2 (meters) X Y Z -56196.501-42703.504-25242.770 Variation of Baseline Components
Attitude Determination Using Code Observations Direct Method (Degrees) Attitude Mean Std Yaw 51.5514 0.4221 Pitch -38.9321 0.4972 Roll 26.0295 1.0161
Attitude Determination Using Code Observations LS Method Orientation Mean/Degree Std/Degree Yaw 51.5533 0.4115 Pitch -38.9311 0.4832 Roll 26.0309 1.0314
Difference between Direct and Least Square Method (Degrees) Orientation Direct Method Least Square Method Difference Yaw 51.5514 51.5533-0.0019 Pitch -38.9321-38.9311 0.0010 Roll 26.0295 26.0309-0.0014
Precise AD Using GNSS: Future AD Using GNSS AD Using GNSS AD Using GNSS AD Using GNSS LAMBDA Modified LAMBDA Constrained LAMBDA Multi Constrained LAMBDA EKF/UKF EKF/UKF EKF/UKF
GNSS at Institute of Space Technology Islamabad, Pakistan Maters of Science in Global Navigation Satellite System MS-GNSS
MS GNSS Curriculum According to the GNSS curriculum designed by the United Nations Office for Outer Space Affairs (UNOOSA)
Thank You Q & A Dr.Najam Naqvi najm_naqvi@yahoo.com 0093-321-5041155