Real‐Time Thermospheric Density Estimation via Two‐Line Element Data Assimilation

Inaccurate estimates of the thermospheric density are a major source of error in low Earth orbit prediction. To improve orbit prediction, real-time density estimation is required. In this work, we develop a reduced-order dynamic model for the thermospheric density by computing the main spatial modes of the atmosphere and deriving a linear model for the dynamics. The model is then used to estimate the density using two-line element (TLE) data by simultaneously estimating the reduced-order modes and the orbits and ballistic coefficients of several objects using an unscented Kalman filter. Accurate density estimation using the TLEs of 17 objects is demonstrated and validated against CHAMP and GRACE accelerometer-derived densities. Finally, the use of the model for density forecasting is shown.

[1]  R. A. DeCarlo.  Linear Systems: A State Variable Approach With Numerical Implementation , 1989 .

[2]  E. Sutton,et al.  New density estimates derived using accelerometers on board the CHAMP and GRACE satellites , 2016 .

[3]  G. March,et al.  High-fidelity geometry models for improving the consistency of CHAMP, GRACE, GOCE and Swarm thermospheric density data sets , 2019, Advances in Space Research.

[4]  T. S. Kelso,et al.  Revisiting Spacetrack Report #3 , 2006 .

[5]  J. Lean,et al.  Thermospheric density 2002-2004: TIMED/GUVI dayside limb observations and satellite drag , 2006 .

[6]  Sean L. Bruinsma,et al.  The DTM-2013 thermosphere model , 2015 .

[7]  A. Hedin.  MSIS‐86 Thermospheric Model , 1987 .

[8]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[9]  L. Jacchia.  Revised static models of the thermosphere and exosphere with empirical temperature profiles , 1971 .

[10]  Richard Linares,et al.  Data-driven framework for real-time thermospheric density estimation , 2018, ArXiv.

[11]  William J. Burke,et al.  A New Empirical Thermospheric Density Model JB2008 Using New Solar and Geomagnetic Indices , 2008 .

[12]  R. Murray,et al.  Model reduction for compressible flows using POD and Galerkin projection , 2004 .

[13]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[14]  J. Forbes,et al.  Principal modes of thermospheric density variability: Empirical orthogonal function analysis of CHAMP 2001–2008 data , 2010 .

[15]  S. Solomon,et al.  The NCAR TIE‐GCM , 2014 .

[16]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[17]  M. Hejduk,et al.  A CATALOGUE-WIDE IMPLEMENTATION OF GENERAL PERTURBATIONS ORBIT DETERMINATION EXTRAPOLATED FROM HIGHER ORDER ORBITAL THEORY SOLUTIONS , 2013 .

[18]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[19]  M. Loève,et al.  Elementary Probability Theory , 1977 .

[20]  Richard Linares,et al.  A methodology for reduced order modeling and calibration of the upper atmosphere , 2017 .

[21]  Eric K. Sutton,et al.  A New Method of Physics‐Based Data Assimilation for the Quiet and Disturbed Thermosphere , 2018, Space Weather.

[22]  Kefei Zhang,et al.  Review and comparison of empirical thermospheric mass density models , 2018, Progress in Aerospace Sciences.

[23]  Eric K. Sutton,et al.  Thermospheric basis functions for improved dynamic calibration of semi‐empirical models , 2012 .

[24]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[25]  B. Bowman.  True Satellite Ballistic Coefficient Determination for HASDM , 2002 .

[26]  D. Drob,et al.  Nrlmsise-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues , 2002 .

[27]  Richard Linares,et al.  A Quasi‐Physical Dynamic Reduced Order Model for Thermospheric Mass Density via Hermitian Space‐Dynamic Mode Decomposition , 2018, 1802.08901.

[28]  J. M. Picone,et al.  Thermospheric densities derived from spacecraft orbits: Accurate processing of two‐line element sets , 2005 .

[29]  Zhejun Lu,et al.  Estimation of ballistic coefficients of space debris using the ratios between different objects , 2017 .

[30]  Felix R. Hoots,et al.  Models for Propagation of NORAD Element Sets , 1980 .

[31]  Qile Zhao,et al.  Calibrating the scale of the NRLMSISE00 model during solar maximum using the two line elements dataset , 2015 .

[32]  Steven L. Brunton,et al.  Dynamic Mode Decomposition with Control , 2014, SIAM J. Appl. Dyn. Syst..

[33]  Richard Linares,et al.  A New Transformative Framework for Data Assimilation and Calibration of Physical Ionosphere‐Thermosphere Models , 2018, Space Weather.

[35]  Bruce R. Bowman,et al.  High Accuracy Satellite Drag Model (HASDM) , 2002 .

[36]  R. Roble,et al.  Migrating thermospheric tides , 2001 .

[37]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[38]  E. Sutton.  Effects of solar disturbances on the thermosphere densities and winds from CHAMP and GRACE satellite accelerometer data , 2008 .

[39]  James Mason,et al.  Orbit Determination and Differential-drag Control of Planet Labs Cubesat Constellations , 2015, 1509.03270.

[40]  S. Solomon,et al.  Seasonal variation of thermospheric density and composition , 2009 .

[41]  M. J. Walker.  A set of modified equinoctial orbit elements , 1985 .

[42]  Gábor Tóth,et al.  The Global Ionosphere-Thermosphere Model , 2006 .

[43]  T. S. Cssi Kelso,et al.  Validation of SGP4 and IS-GPS-200D Against GPS Precision Ephemerides , 2007 .

[44]  Eelco Doornbos,et al.  Use of two-line element data for thermosphere neutral density model calibration , 2008 .