Flight Dynamics System • Manfred Bester
Flight Dynamics System • Overview • Coordinate Systems • Flight Dynamics Software • Software User Training • Product Generation • Orbit Determination • Attitude Determination • Issues, Concerns and Risks
Inertial Coordinate Systems • Earth Centered Inertial Coordinate Systems • Defined by Intersection of Equator and Ecliptic • Motions of Defining Planes • Equator (Celestial Pole) • Gravitation Attraction of Sun and Moon on Equatorial Bulge • Two Components: Lunisolar Precession and Nutation • Ecliptic • Gravitational Attraction of Other Planets • Planetary Precession: Includes Eastward Movement of Equinox and Decrease of Obliquity • Related Coordinate Transformations • General Precession • Includes Both Lunisolar and Planetary Precession • Nutation • Includes Nutation in Longitude and in Obliquity
Inertial Coordinate Systems • Mean Equator and Mean Equinox • AKA Mean-of-date • Includes Precession Only and Neglects Nutation • B1950.0 • AKA B1950.0 Inertial • AKA Mean-of-date B1950.0 • J2000.0 • AKA J2000.0 Inertial • AKA Mean-of-date J2000.0 • True Equator and True Equinox • AKA True-of-date • Includes Precession and Nutation • True Equator and Mean Equinox • AKA TEME • Includes Precession and Nutation, Ignores Equation of Equinoxes • Used with Two-line Elements
Coordinate Transformations • Transformations Between Inertial Coordinate Systems • Mean-of-date to Mean-of-date (Different Dates) • Involves Rotation Around Three Axes • Described by Time Dependent Precession Parameters • Rotation Angles ζ, θ and ξ • Mean-of-date to True-of-date (Same Date) • Correct for Nutation • Described by Time Dependent Nutation Parameters • True Obliquity ε • Nutation in Longitude δψ • Mean-of-date to True-of-date (Different Dates) • Apply Combined Precession and Nutation Transformation • TEME to True-of-date • Disregard Equation of the Equinoxes, i.e. Use Mean Sidereal Time • B1950.0 and J2000.0 • Use Different Sets of Precession and Nutation Parameters
Software User Training • GTDS • Upgrade to Latest Version • Orbit Determination • GMAN • Configuration of Spacecraft Definition Files • Maneuver Planning • Generation of Thruster Command Sheets • FreeFlyer • Alternate Commercial Solution for Maneuver Planning • Determine if FreeFlyer Meets Mission Requirements • Consulting Agreement with AI Solutions Under Development • MSASS / MTASS • Configuration of Resource Files • Real-time Attitude Determination • Post-pass Attitude Determination for Science Data Analysis
Ephemeris Products • Ephemeris Products • Ephemeris, Special Vectors and Two-line Elements • Attitude and Beta Angle Predicts • Ground Station and TDRSS View and Link Access Periods • Earth and Lunar Shadows • Region Crossings • Orbit Events • Antenna Track Files • Solar Interference • Mutual RF Interference Analysis • Approach Analysis • Maneuver Timelines • Coordinate Systems and Units • True-of-date Used Consistently for All Ephemeris Products • Metric Units Only
Ground System Automation • Berkeley Flight Dynamics System • Hardware Configuration • Multiple Redundant Systems (2.8 GHz Pentium IV, Linux) • Software Tools • SatTrack Suite V4.5 • Automated Product Generation • Generates All Required Products Every Night for All Missions Via Autoproducts Scripts • SatTrack Gateway Server (SatTrack/GS) • Central Scheduling and Event Distribution System • Control of Various Ground System Elements • Network Monitoring • Event Messaging • Anomaly Notification • Interfaced Via TCP/IP Network Socket Connections • BGS Automation Accomplished by Integration of SatTrack/GS and SatTrack/MCS
Product Utilization Berkeley Ground Data System
Orbit Determination • Orbit Determination Based on Two-way Doppler Tracking • Ground Stations Provide Two-way Doppler Tracking Data in Universal Tracking Data Format (UTDF) • One Station Sufficient to Provide Required Accuracy (10 km at Perigee, 100 km at Apogee) Over Multiple Passes (GNCD Analysis) • Data from Multiple Stations Plus Angle Tracking Yield Better Solution • UTDF Files • Converted to 60-byte Format by SatTrack • Processed with GTDS to Obtain New Orbit Solutions • New State Vectors Used to Generate Updated Planning Products • Digital Range Measurement System (DRMS) • OD Technology Demonstration During Second Year • DRMS Measures Round-trip Delay of Digital Data Stream
Doppler Accuracy Tests • Rationale for Doppler Accuracy Tests • Prediction of Orbit Determination Accuracy • Two-way Doppler Accuracy Difficult to Predict for THEMIS Ground System Configuration • Use Telemetry Receivers Instead of Dedicated Track Receivers • Microdyne 700−MR (WB) with 758−D (W) Multi-mode Demodulator • Different Modulation Schemes Used, Dependent on Probe Range • Determination of Potential Error Sources • Generate Baseline for Expected Accuracy • Predict Accuracy of Range Rate Measurements as Function of CNR for BPSK and PCM/PSK/PM Modulation • Test Results Will Tell How Many Tracking Arcs Are Required to Perform Orbit Determination for THEMIS • Tests Performed with WFF Equipment on Loan to UCB • Functional Check-out of Equipment (CDMS, TDF and GPS Clock) • Long Loop RF Tests with Modulated Carrier & Telemetry Playback • On-orbit Tests with FAST and RHESSI Spacecraft
Test Equipment Setup • Test Equipment Setup • Wallops Flight Facility Kindly Loaned Equipment to UCB • Apogee Labs Model 7701 Carrier Doppler Measurement System (CDMS) • Apogee Labs Model 2208 Tracking Data Formatter (TDF) • TrueTime Model XL-DC GPS Time and Frequency Receiver • Test Timeline • CDMS and TDF Equipment Arrived at Berkeley on 09-Oct-2003 • GPS Receiver Arrived on 31-Oct-2003 • Purchased 2 Mini-Circuits Amplifiers (ZRL-400) to Match LO Signal Power Levels Between Microdyne 700-MRB Receiver Outputs and CDMS Inputs • Installation in Berkeley Ground Station Completed on 17-Oct-2003 • Preliminary Functional Checks Completed by 17-Oct-2003 • Initial Doppler Tracking Tests Performed on 01-Nov-2003 • Ground Based Loop-back Tests and On-orbit Tests with FAST and RHESSI Completed on 24-Dec-2003
Doppler Test Schematic Schematic Diagram for Loop-back Doppler Accuracy Tests
CDMS & TDF Interface Tests • Interface Tests Performed • Verified CDMS Input Signal Levels • 2nd LO from Receivers: RHCP: -0.1 dBm; LHCP: +0.9 dBm • 5 MHz Reference from TrueTime Clock: +2.6 dBm • Sync Pulses from TrueTime Clock: 10 ppm, 0 - 3.3 V, TTL • Verified TDF Input Signal Levels • IRIG-B Time Code from TrueTime Clock: 4.8/1.4 Vpp • Configured TDF • Network Configuration • Two-way Doppler Mode • Transmit Frequency • Sample Rate • Support ID • Tracker ID
CDMS & TDF Functional Tests • Functional Tests Performed • Verified 2nd Local Oscillator Signal Frequency • Used Agilent Frequency Counter to Verify 180 MHz Frequency • Verified CDMS Lock • Green LEDs on CDMS Front Panel Lit Continually • Verified TDF Operation • Displayed Doppler Shift and Range Rate • Compared Reference Signals from GPS Receivers • Compared 10 MHz Reference Signals from Trak Systems and TrueTime GPS Receivers • GPS Antennas Installed on Roof of Building • Observed Lissajous Figures on Oscilloscope • Phase Drift Between 10 MHz Signals of Order 10° / min • TrueTime XL-DC Receiver Provides Much Cleaner Reference • Trak Systems Model 9000B: 3.10 ± 0.10 Vpp • TrueTime Model XL-DC: 2.89 ± 0.01 Vpp
Sources for Doppler Errors • Determined Potential Sources for Doppler Errors • Synchronization of Timing Signals • All Reference Signals Need to Be Generated by the Same Source • 5 MHz RF Reference for Phase-lock Loops • 10 pps Clock for Triggering Measurements • IRIG-B Time Code for Time Tagging Measurements • Lack of Time Synchronization Causes Doppler Bias and Large Fluctuations in Doppler Signal • Lack of Accuracy in IRIG-B Time Code Causes Doppler Bias • Tuning of Receivers and Transmitters • Receiver Loop Stress Due to Finite Tuning Resolution Causes Bias • Mismatch Between Transmit Frequency and TDF Configuration • Imperfect Receiver Lock • Receiver Firmware Can Cause False or Imperfect Lock Under Certain Conditions Leading to Large Doppler Bias • Loop Bandwidth in Demodulator Critical to Avoid Spikes
Loop-back Doppler Tests • Doppler Accuracy Test Procedure for Loop-back Tests • Prepare Ground Station Configuration Files for Loop-back Tests • Transmit Frequency: S-Band • Antenna Feed: RHCP and LHCP • Receive Modulation: BPSK and PCM/PSK/PM • Loop Bandwidth: 3 kHz, 1 kHz and 0.3 kHz • IF Bandwidth: 3.3 MHz • Set Up Ground Station for Facility Self-test in Loop-back Mode • Configure and Calibrate Receivers • Configure Exciter, PTP, Matrix Switch, CDMS and TDF • Record UTDF Data Files with CDMS and TDF • Sample Rate: 10 Hz, 1 Hz and 0.1 Hz • Analyze Recorded Data with SatTrack UTDF Processing Tool • Assess Data Quality • Determine Average Range Rate (Bias) • Determine 1-σ Range Rate Error
Doppler Analysis Software • SatTrack UTDF Processing Tool • Reads and Decodes UTDF Files in 75-Byte Format • Performs Data Quality Checking • Allows Filtering of Spikes • Allows Elimination of Bad Data (e.g. Acquisition Sweeps) • Allows Merging with Calculated Data from Track File, Including Application of Time Bias • Performs Post-pass Averaging • Performs Statistical Analysis • Generates Output File Compatible with SatTrack Graphics Visualization Tool • Generates Output File in 60-Byte Format for Input to GTDS (Not Yet Implemented)
Loop-back Doppler Test Results • Loop-back Test Objective #1 • Determine Standard Deviation of Range Rate as Function of Demodulator Loop Bandwidth for Various CDMS Sample Rates for BPSK Modulation at a Fixed Signal Strength * Discovered that Spikes Appear with BPSK Modulation when Demodulator Loop Bandwidth Is 3 kHz. Calculated Standard Deviation Includes Spikes. Root Cause for Spikes Needs to Be Investigated.
Loop-back Doppler Test Results • Loop-back Test Objective #2 • Check for Spikes in Range Rate as Function of Demodulator Loop Bandwidth for BPSK Modulation in Both Receive Channels (RHCP, LHCP) at a Fixed Sample Rate • Spikes Do Typically Occur in Either Channel with Demodulator Loop Bandwidth of 3 kHz, But Do Not Occur with 1 kHz • Finding Suggests This Is Not a Receiver Malfunction • Need to Limit Demodulator Bandwidth to 1 kHz with BPSK * Spikes Appear with BPSK Modulation Only when Demodulator Loop Bandwidth Is Larger than 1 kHz. Calculated Standard Deviation Includes Spikes. Root Cause for Spikes Needs to Be Investigated.
Loop-back Doppler Tests Tests #22: Downward Spikes Appear with 3 kHz Demodulator Loop Bandwidth for BPSK Modulation. CDMS Sample Rate Is 10 Hz.
Loop-back Doppler Tests Tests #22: Downward Spikes Do Not Appear with 1 kHz Demodulator Loop Bandwidth for BPSK. CDMS Sample Rate Is 10 Hz.
Loop-back Doppler Test Results • Loop-back Test Objective #3 • Determine Standard Deviation of Range Rate as Function of Signal Strength for BPSK Modulation at a Fixed Demod Loop Bandwidth of 1 kHz and a Fixed Sample Rate of 10 Hz
Loop-back Doppler Test Results • Loop-back Test Objective #4 • Determine Standard Deviation of Range Rate as Function of Signal Strength for PCM/PSK/PM Modulation at a Fixed Demod Loop Bandwidth of 0.3 kHz and a Fixed Sample Rate of 10 Hz * Subcarrier Frequency: 1.024 MHz; Modulation Index: 1.35 rad ** Test #39 Performed on 04-Dec-2003, All Others on 14-Dec-2003.
Loop-back Doppler Tests Test #39: PCM/PSK/PM; Subcarrier Frequency: 1.024 MHz; Modulation Index: 1.35 rad; Data Rate: 64 kbps; AGC Level: 17.6 dB; RHCP Channel; Video Averaging: 2 s; Spectrum Represents THEMIS RF Signature.
Loop-back Doppler Test Results • Loop-back Test Objective #5 • Determine if Longer Integration Times in CDMS Are Equivalent to Post-pass Averaging • Recorded Data with 3 Different CDMS Sample Rates and Averaged Samples Post-pass over 10 s • Investigated Behavior for PCM/PSK/PM and BPSK Modulation * PCM/PSK/PM: Subcarrier Frequency: 1.024 MHz; Modulation Index: 1.35 rad
Loop-back Doppler Test Results • Results of Loop-back Doppler Tests • Range Rate Accuracy as Function of Demod Loop Bandwidth • Demodulator Loop Bandwidth in Receivers Is Critical • Range Rate Error Scales With Loop Bandwidth as Expected • Spikes Occur When Loop Bandwidth Is Too Large • BPSK Modulation • Downward Spikes in Range Rate Occur with 3 kHz LBW • Clean Measurements without Spikes at 1 kHz LBW • PCM/PSK/PM Modulation • Downward Spikes in Range Rate Occur with 3 and 1 kHz LBW • Clean Measurements without Spikes at 0.3 kHz LBW • Range Rate Accuracy as Function of Signal Power • Measured Range Rate Accuracy (1−σ) • Ground Based Loop-back Tests Typically Provide < 1.5 mm/s with a Sample Rate of 10 Hz and a Post-processing Integration Time of 10 s • Range Rate Accuracy Appears to Be Independent of Signal Power • Applies to Both BPSK and PCM/PSK/PM Modulation • System Performance at Low Signal Levels • Quality of Telemetry Data Is Degraded at Low Signal Levels, But Range Rate Accuracy Is Not, as Long as Receivers Remain Locked
FAST On-orbit Doppler Tests First BGS On-orbit Doppler Test Performed with FAST on 06-Nov-2003 Transmit Frequency: 2039.645830 MHz; Polarization: RHCP; Modulation: PCM/PSK/PM; Loop Bandwidth: 3 kHz; CDMS Sample Rate: 10 Hz; Spikes Filtered Out ± 0.02 km/s Calculated Range Rate Based on 2-Day Old TLE Set − No Time Bias Applied.
FAST On-orbit Doppler Tests • Doppler Accuracy Test Procedure for FAST On-orbit Tests • Prepare Ground Station Mission Configuration File for FAST • Transmit Frequency: 2039.645830 MHz • Transmit Power: 25 W • Antenna Feed: RHCP • Receive Modulation: PCM/PSK/PM • Loop Bandwidth: 3 kHz, 1 kHz and 0.3 kHz • IF Bandwidth: 12 MHz • Set Up Ground Station in Automated Mission Support Mode • Configure and Calibrate Receivers • Configure Exciter, PTP, Matrix Switch, CDMS and TDF • Record UTDF Data Files with CDMS and TDF • Link Mode: Coherent Two-way • Sample Rate: 10 Hz • Analyze Recorded Data with SatTrack UTDF Processing Tool • Apply Time Bias to Calculated Range Rate to Minimize Residuals • Determine Doppler Bias and 1-σ Range Rate Error
On-orbit Doppler Test Results • On-orbit Two-way Doppler Test Objective #1 • Determine Two-way Doppler Accuracy with Orbiting Spacecraft for PCM/PSK/PM Modulation • Record Range Rate Data During 5 FAST Passes at BGS • FAST Has a Coherent Transponder * Spikes > 0.1 m/s Were Removed and Were Not Included in Range Rate Error. ** FAST Spacecraft Spin Rate of 12 rpm Clearly Visible in Plot of Residual Range Rate after Removing Largest Part of Residual Range Rate by Applying Time Bias to Calculated Data. Calculated Range Rate Is Based on 1.5-d Old TLE Set with Time Bias of -0.272 s.
FAST Doppler Track Analysis • Analysis of On-orbit Doppler Tests with FAST Spacecraft Spacecraft Geometry: Spinning Platform: 12 rpm 4 Spin Plane Wire Booms, 2 Axial Stacer Booms, 2 Magnetometer Booms Spin Axis Pointed Perpendicular to Orbital Plane Cylindrical Antenna, Mounted on Body Axis Coherent Transponder Allows Two-way Ranging Post-launch Analysis of Mass Properties: (Provided by D. Pankow) One of the Spin-plane Wire Booms Did Not Deploy Completely Spin Axis Offset from Center of Mass: 49 mm Tilt Angle Between Body Axis and Spin Axis: 0.37° Resulting Antenna Offset from Spin Axis: 43 mm
FAST Doppler Track Analysis Test #104: Observed Range Rate of FAST at BGS.
FAST Doppler Track Analysis Test #104: Observed − Calculated Range Rate; No Time Bias Applied to Calculated Range Rate.
FAST Doppler Track Analysis Test #104: Time Bias of -0.272 s Applied to Calculated Range Rate, Reduces Residuals by Factor of 60. CDMS Sample Rate 10 Hz; 10 Samples Averaged During Post-pass Analysis. Spacecraft Spin Rate of 12 rpm Clearly Visible.
FAST Doppler Track Analysis Test #104: Time Bias of -0.272 s Applied to Calculated Range Rate, Reduces Residuals by Factor of 60. CDMS Sample Rate 10 Hz; Only 4 Samples Averaged During Post-pass Analysis, Revealing More Complex Spin Doppler Modulation.
FAST Doppler Track Analysis • FAST Doppler Track Analysis • Radius r of Circle on Which Antenna Moves Given by: • r = v / (ω× cos β) • v: Measured Doppler Velocity Associated with Antenna Motion [mm s-1] • ω: Spin Rate [s-1] • β: Elevation Angle of Line-of-sight Above Spin Plane [deg] • Measurement with BGS at 2003/347 02:19:00 UTC: • v = 60.2 ± 10.8 mm s-1 (Range Rate Data − See Red Lines in Above Plot) • ω = 2 π × 12.0 / 60 s-1 (Attitude Sensor Data) • β = 14.3 deg (Orbit Analysis) • r = 49.4 ± 8.9 mm • Measurement Agrees within Error Bars with Mass Properties Obtained from Post-launch Analysis: • r = 43 mm
FAST Doppler Track Analysis • FAST Spacecraft Geometry Top View Antenna Rolls Around Spin Axis Antenna Shown Every 90° of Rotation Spin Axis Displacement of Spin Axis Is Almost Identical to Radius of Cylindrical Antenna, i.e. Antenna Rolls Around Spin Axis (See Above Drawing) Inner and Outer Parts of Antenna Move at Different Linear Velocities, Giving Rise to Differential Doppler Shift (Red and Blue Circles) Associated Phase Shifts May Cause Observed Complex Doppler Signature!
RHESSI Doppler Track Analysis • Analysis of On-orbit Doppler Tests with RHESSI Spacecraft Relevant Spacecraft Features: Sun-pointed Spinning Platform: 15 rpm 4 Patch Antennas – 2 Forward, 2 Aft Non-coherent Transceiver with BPSK Modulation at 4 Mbps
RHESSI Doppler Track Analysis Test #110: RHESSI One-way Doppler Track on Aft Antenna. CDMS Sample Rate 10 Hz; 5 Samples Averaged During Post-pass Analysis. Red Lines Indicate where Spin Doppler Modulation Was Measured. Spin Rate Is 15.0 rpm.
RHESSI Doppler Track Analysis • RHESSI Doppler Track Analysis • Measurements with BGS at 2003/358 04:47:00 − 04:49:00 UTC: • Forward Antenna: Aft Antenna: • v = 372 ± 53 mm s-1 v = 566 ± 53 mm s-1 • ω = 2 π × 15.0 / 60 s-1 ω = 2 π × 15.0 / 60 s-1 • β = 38.4 deg β = 10.7 deg • r = 302 ± 43 mmr = 367 ± 34 mm • Known Spacecraft Geometry: • Forward Antenna: Aft Antenna: • r = 285.8 mmr = 368.3 mm • Measurements and Spacecraft Geometry Agree Well within Error Bars • Interesting Comment: If RHESSI had a coherent transponder the spin Doppler modulation would be canceled out because the transmit and receive antennas are mounted 180° out of phase with respect to the spin axis!
Doppler Test Summary • Summary of Ground Based and On-orbit Doppler Tests • Ground Station Configuration • Doppler Tests Demonstrated that BGS Microdyne 700-MR (WB) Telemetry Receivers Can Be Used to Provide Accurate Range Rate Measurements with BPSK and PCM/PSK/PM Modulation • BGS Equipped with WFF Equipment Provides Doppler Tracking Data with Accuracy Comparable to NASA Ground Stations • Ground Based Loop-back Test Results • Range Rate Accuracy (1−σ) Obtained in Ground Based Loop-back Tests Is Typically < 1.5 mm/s with a Sample Rate of 10 Hz and a Post-processing Integration Time of 10 s • Accuracy Essentially Independent of Signal-to-noise Ratio Down to the Receiver Lock Limit for BPSK and PCM/PSK/PM Modulation • On-orbit Test Results • On-orbit Tests with FAST Verified Range Rate Accuracy • On-orbit Tests with FAST and RHESSI Provided Information on Mass Properties and Spacecraft Geometry Based on Spin Doppler Modulation from the Relative Motion of the Spacecraft Antennas
Implications for THEMIS • Implications for THEMIS • Operational Aspects • Record All Doppler Tracking Data at Rate of 10 Samples per Second to Allow for Detailed Post-pass Analysis • Orbit Determination • Above Results Used as Input to OD Covariance Analysis • Average Over Spin Doppler Modulation for Orbit Determination • Determination of Probe Mass Properties • Short Integration Times of 0.1 s Allow for Analysis of Probe Spin Modulation • Determination of Displacement of Center of Mass from Body Z-Axis as Well as Precession Cone Angle • Observation of Coning and Nutation Damping After Probe Release and After Orbit and Attitude Maneuvers Appears Feasible • Verification of Symmetrical Wire Boom Deployment
OD Covariance Analysis • Tracking Arc Analysis for Orbit Determination • OD Covariance Analysis Performed by Code 595 (M. Beckman) • Provides Details on How Many Tracking Arcs per Orbit Are Needed to Determine Probe State Vectors with Required Accuracy • Accounted for Variety of Errors Sources • Solar Radiation: 30% • Earth, Sun and Moon Gravity Model • Station Location: 3 m in Each Axis • Ionospheric and Tropospheric Refraction • 3.5 mm/s Accuracy (3-σ) for Doppler Measurements in 10-s Integration Time after Post-pass Processing • No Change in Doppler Noise as Function of Range • Various Station Scenarios • One Station (BGS) – One 30-min Pass Per Day • Two Stations (BGS, WGS) – One 30-min Pass Per Day, R < 10 RE • Three Stations (BGS, WGS, AGO) – 35 Passes Over 12 Days