https://ntrs.nasa.gov/search.jsp?R=20170005601 2018-04-29T17:09:18+00:00Z Mission Operations Working Group June 13-15, 2017 International Earth Science Constellation Mission Operations Working Group June 13-15, 2017 Earth Observing System Covariance Realism Updates Juan Ojeda Romero, a.i. solutions, Inc. / Code 595 Fred Miguel, a.i. solutions, Inc. / Code 595 EOS FDS, esmo-eos-fds@lists.nasa.gov, +1.301.614.5050 1
Mission Operations Working Group June 13-15, 2017 Agenda • Overview of Aqua/Aura Covariance Operations – Earth Observing System (EOS) Flight Dynamics System (FDS) Covariance Realism QA (Quality Assurance) and Tuning Flowchart – Covariance QA Automation – Aqua and Aura Covariance Tuning – Automation Results to Date – Covariance Propagation through Maneuvers • Future Analysis/Work – Covariance Propagation Implementation through Maneuvers – Covariance Propagation using Polynomial Chaos Expansion • Conclusion 2
Mission Operations Working Group June 13-15, 2017 Overview of Aqua/Aura Covariance Operations • Aqua and Aura Owner/Operator (O/O) covariances are being used in operations to compute the probability of collision (P C ). • This only includes daily operations and Drag Make-Up (DMU) maneuver planning. • Software has been delivering tuned covariance since June 14, 2016. • Software ensures covariances are tuned for periods devoid of persistently high and extreme solar activity as well as post maneuver propagation errors. • Aqua’s last tuning date was on November 7, 2016. • Aura’s last tuning date was on November 9, 2016. 3
Mission Operations Working Group June 13-15, 2017 EOS Covariance Realism QA and Tuning Flowchart • The acceleration variances in Step 1 Step 1: Input can only be changed after the Radial, In-Track, Step 2: Propagate Daily Definitive tuning process. Updated variances Cross-Track (RIC) Ephemeris + Covariance using Component RIC Component Acceleration are configuration managed and Acceleration Variances require approval before they are Variances deployed to operations. • Step 2 is performed as part of the Step 4: Compute the Chi- nominal daily product delivery. Step 3: Collect Sets of Square Statistic over Propagation Errors and • Steps 3 to 6 represent the QA of the multiple propagation points Predictive Covariances covariance and are performed via automation using FreeFlyer and MATLAB. Step 6: Perform the 3- • QA of Aqua and Aura covariances Step 5: Use the Normalized degree of freedom (DOF) is performed over a rolling 90-day Standard In-Track Errors to Chi-Square Distribution timespan. Determine Outlier Test to Determine Realism Propagations • Testing with a 3-day cadence is Pass Percentage statistically required in order to isolate the affects of the 2 ½ days Step 7: Tune Covariance if worth of rolling Tracking and Data the Pass Percentage falls Relay Satellite (TDRS) under a User Specified observations that go into daily Threshold Flight Dynamics Facility (FDF) 4 orbit determination runs.
Mission Operations Working Group June 13-15, 2017 Covariance QA Automation 01/07/17(01) Visual Aids Presented to Analyst (1 of 2) 01/13/17(02) 01/16/17(03) 01/19/17(04) 9 25 700 01/22/17(05) 01/25/17(06) Cross-Track State Estimate Error (m), Set 1 Identified 8 In-Track State Estimate Error (m), Set 1 01/28/17(07) Radial State Estimate Error (m), Set 1 600 Outlier 20 01/31/17(08) 7 02/03/17(09) 500 02/12/17(10) 6 02/15/17(11) 15 400 5 02/18/17(12) 02/21/17(13) 4 02/24/17(14) 300 10 03/02/17(15) 3 03/11/17(16) 200 03/14/17(17) 2 5 03/17/17(18) 100 03/23/17(19) 1 04/04/17(20) 0 0 0 Mean Error 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 Propagation Time (Days) Mean RIC Variance Propagation Time (Days) Propagtion Time (Days) 04/01/17(Outlier) • Example Aqua Set 1 QA Results for April 11, 2017 are given above. 1 • 0.9 Component Estimate Error plots give an idea of how far each 0.8 component covariance is deviating from its mean root mean squared 0.7 (RMS) component error. 3 DOF 2 CDF, Set 1 0.6 • An empirical 3-DOF Chi-Square distribution for each propagation 0.5 point is assessed against its parent distribution. 0.4 • The Cramer-Von Mises empirical distribution function (EDF) test is 0.3 Ideal Estimated used to determine the likelihood each set of covariances represents a 0.2 realistic distribution of the corresponding set of propagation errors 0.1 tied to it – A “Pass Percentage” is used to determine Covariance 0 0 5 10 15 20 C -1 Realism. 5
Mission Operations Working Group June 13-15, 2017 Covariance QA Automation Visual Aids Presented to Analyst (2 of 2) Normalized In-Track Error Normal CDF, Set 1 1 5 • Standard Component Errors are available for Identified Radial, In-Track, and Cross-Track directions. 4 Outlier 0.8 In-Track Standard Errors are utilized in In-Track Standard , Set 1 3 Outlier Identification Process. 2 0.6 • Any propagations outside of the ± 1 σ Ideal 1 Estimated bounds in the In-Track Component are tested 0.4 0 for outlier identification -1 • 0.2 Normal Gaussian distribution based on -2 Component Errors are also available. 0 -3 -4 -2 0 2 4 6 0 1 2 3 4 Propagation Time (Days) C -1 • The Probability Value (P-Value) vs. Propagation Time chart gives 0.3 information regarding where in the propagation the covariances are 0.25 passing the realism testing. • A “Pass - Percentage” is calculated for all sets based on the P -values 0.2 P-value, Set 1 calculated through the timeframe at every step. Based on seasonal 0.15 covariance tuning from 2014 to 2016, FDS recommended this threshold be set to 60% – a statistically commendable result. 0.1 • Periodicity in the Radial Propagation Error is causing low levels of 0.05 realism between 0.5 to 1.25 days. The Covariance is oversized in this P-Value Threshold timeframe. 0 0 1 2 3 6 Propagation Time (Days)
Mission Operations Working Group June 13-15, 2017 Covariance QA Automation Outlier Identification Confirmation 5 • Automation identifies potential outliers based on the In- Potential Track standard errors. Propagations with an In-Track 4 Outlier standard error outside ± 1 σ bounds after 3.5 days will be Propagations In-Track Standard , Set 1 tested. 3 • Automation uses a Rosner Outlier Test on any deviant 2 normalized In-Track standard errors – the test will detect outliers that are either much smaller or larger than the rest 1 of the data and is designed to avoid the problem of masking, where an outlier close to another outlier goes 0 undetected. -1 • The outliers are entered into the test in order of most to least deviant. -2 • Naturally, the solar activity in the timeframe of the propagation start date is used to determine if there was a -3 0 1 2 3 4 peak or persistently high solar activity. See figure to the Propagation Time (Days) left. Estimated Solar Flux Geomagnetic Index Identified Outlier Geomagnetic Index Solar Flux F10.7 100 100 Note: Only the four most deviant April 1 st , 2017 propagations are tested using the Rosner 50 50 Outlier Test. 7 02/06/17 Date 03/08/17 04/04/17
Mission Operations Working Group June 13-15, 2017 Covariance QA Automation Tune the Covariance (Aqua) Radial Covariance vs. Mean Error from QA Sets • Aqua’s P -value Pass Percentage decreased below the FDS 5 Mean RMS Set 1 imposed threshold (60%) on November 7, 2016. Aqua was Mean RMS Set 2 After Tuning Mean RMS Set 3 4 tuned to improve covariance realism. • Uncertainty, (m) The component acceleration variances are changed until Before Tuning 3 the Pass Percentages for all three sets of covariances exceed the user specified threshold. 2 • The current strategy is to tune the covariance to the largest 1 Mean RMS Component Error in the Radial and In- Track directions at the final propagation point and to 0 0 0.5 1 1.5 2 2.5 3 3.5 Time,Days the mid propagation point in the Cross-Track direction (to achieve the highest level of realism). Decrease in In-Track Acceleration Variance Cross-Track Covariance vs. Mean Error from QA Sets In-Track Covariance vs. Mean Error from QA Sets 15 350 Mean RMS Set 1 Mean RMS Set 1 The Cross-Track covariance is tuned Mean RMS Set 2 Mean RMS Set 2 to the mid propagation point 300 Mean RMS Set 3 Mean RMS Set 3 After Tuning 250 10 Uncertainty, (m) Uncertainty, (m) 200 Before Tuning Before Tuning 150 5 100 After Tuning 50 0 0 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 Time,Days Time,Days 8
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