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Consider Covariance Analysis Example 6.9, Spring-Mass

Consider Covariance Analysis Example 6.9, Spring-Mass. George H. Born ASEN5080 Statistical Orbit Determination II 3/14/07, Lecture 6, . Example 6.9, page 420. Solution Steps. 1. Iterate batch processor to convergence – solving for. with IC (for 20% perturbation).

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Consider Covariance Analysis Example 6.9, Spring-Mass

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  1. Consider Covariance AnalysisExample 6.9, Spring-Mass George H. Born ASEN5080 Statistical Orbit Determination II 3/14/07, Lecture 6,

  2. Example 6.9, page 420 Solution Steps 1. Iterate batch processor to convergence – solving for with IC (for 20% perturbation) *using 1.8kg for mass and 3.0 for , as indicated in the text, reduces ω to the point where the initial conditions are out of the linear range and the Batch Processor fails to converge.

  3. Example 6.9, page 420 , (6.5.23) Iterate to convergence using (4.6.4)

  4. Example 6.9, page 420 2. Compute where (6.9.9) Use true values, those in Eq. 6.9.13, for all parameters to compute is computed using (Eq. A) and Eqns (6.9.9)

  5. Example 6.9, page 420 3. Compute the sensitivity and consider covariance matrix at t0 using initial conditions from Eq. A, and Where is the covariance matrix of the consider parameters and remains constant since we are not estimating the consider parameters

  6. Example 6.9, page 420 The sensitivity matrix is given by: (6.4.4) where (6.5.24) The consider covariance for the estimated parameters is given by: (6.4.6) (6.4.7) note:

  7. Example 6.9, page 420 4. The complete consider covariance is given by (6.6.16) where 5. Map through the observation and prediction span (6.6.15) where

  8. Example 6.9, page 420 For this example we compute where and Note typo in Eq (6.9.11), i.e.,

  9. Example 6.9, page 420 6. Plot results as in Fig 6.9.1 and are computed from where Plot the bounds on and from the data noise covariance, , and and from the consider covariance, . Also place the position and velocity errors on this plot.

  10. Example 6.9, page 420, Results

  11. Example 6.9, page 420, Results

  12. Example 6.9, page 420, Results

  13. Example 6.9, page 420, Results

  14. Example 6.9, page 420, Results

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