1. METHOD OF PERTURBED OBSERVATIONS FOR BUILDING REGIONS OF POSSIBLE PARAMETERS IN ORBITAL DYNAMICS INVERSE PROBLEM Avdyushev V.

2. Planet ERRORS OF OBSERVATIONS Satellite Real We See Satellite Error Orbit Parametric Error Probabilistic Region True

3. LEAST-SQUARES (LS) PROBLEM System of Equations Solution of System Linear Case Nonlinear Case

4. CONFIDENCE REGION RMS Error Normal Distribution Covariance Matrix Vector Length:

5. TWO TECHNIQUES FOR BUILDING REGIONS OF POSSIBLE PARAMETERS Technique 2 (LS-scattering) Technique 1Cholesky Matrix

6. LS-SCATTERING Nonlinear Problem Linear Problem REPARAMETRIZATION

7. LS-Estimations True Positions Observations GEOMETRIC INTERPRETATION Linear Case

8. GEOMETRIC INTERPRETATION Planar Case Non-planar Case MODIFICATION

9. NUMERICAL EXAMPLE PROBLEM ObjectS/2003 J04 (Jupiter’s Satellite) POPO (Емельянов и др, 2006) PCPC (Авдюшев, Баньщикова, 2007) Parameters

10. PROBABILISTIC REGIONS Small Scale

11. PROBABILISTIC REGIONS Vast Scale

12. Astronomy & Space Geodezy Department Tomsk State University Avdyushev V. Thanks!

13. DISTRIBUTION OF SUMS OF SQUARES F-distribution

14. CURVATURE OF ESTIMATE SPACE