Transcript Lecture 36
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 36: SNC Example and Solution Characterization University of Colorado Boulder Homework 11 due on Friday 12/4 ◦ Sample solutions will be posted online Exam 3 Posted On Friday 12/4 ◦ In-class Students: Due December 11 by 5pm ◦ CAETE Students: Due 11:59pm (Mountain) on 12/13 Final Project Due December 14 by 12noon University of Colorado Boulder 2 Homework 11 University of Colorado Boulder 3 Leverage code from HW10 ◦ New data set generated with a different force model ◦ Otherwise, same format, data noise, etc. Process observations in existing filter ◦ Do not add J3 to your filter model! ◦ Observe the effects of such errors on OD ◦ Add process noise to improve state estimation accuracy University of Colorado Boulder 4 University of Colorado Boulder 5 University of Colorado Boulder 6 University of Colorado Boulder 7 Application of SNC to Ballistic Trajectory University of Colorado Boulder 8 Obs. Stations Start of filter University of Colorado Boulder Ballistic trajectory with unknown start/stop Red band indicates time with available observations 9 Object in ballistic trajectory under the influence of drag and gravity Nonlinear observation model ◦ Two observations stations University of Colorado Boulder 10 University of Colorado Boulder 11 Outliers ◦ Mitigate through prediction residual 3σ editing An observation bias in Station 1 range ◦ Still estimating the bias in the filter University of Colorado Boulder 12 Now use an EKF We will vary the truth model to study the benefits of SNC ◦ Look at two cases: Run each with and without a process noise model Error in gravity (g = 9.8 m/s vs. 9.9 m/s) Error in drag (b = 1e-4 vs. 1.1e-4) University of Colorado Boulder 13 Station 1 Station 2 Blue – Range Green – Range-Rate University of Colorado Boulder 14 University of Colorado Boulder 15 Added SNC to the filter: Why is the term for the x-acceleration smaller? University of Colorado Boulder 16 Station 1 Station 2 Blue – Range Green – Range-Rate University of Colorado Boulder 17 178.26 vs. 0.85 meters RMS University of Colorado Boulder 18 Station 1 Station 2 Blue – Range Green – Range-Rate University of Colorado Boulder 19 University of Colorado Boulder 20 Added SNC to the filter: University of Colorado Boulder 21 Station 1 Station 2 Blue – Range Green – Range-Rate University of Colorado Boulder 22 27.63 vs. 1.26 meters RMS University of Colorado Boulder 23 Mitigation of the gravity acceleration error yielded better results than the drag error case. Why could that be? University of Colorado Boulder 24 Solution Characterization University of Colorado Boulder 25 Truncation error (linearization) Round-off error (fixed precision arithmetic) Mathematical model simplifications (dynamics and measurement model) Errors in input parameters (e.g., J2) Amount, type, and accuracy of tracking data University of Colorado Boulder 26 For the Jason-2 / OSTM mission, the OD fits are quoted to have errors less than centimeter (in radial) ◦ How do they get an approximation accuracy? ◦ Residuals? Depends on how much we trust the data Provides information on fit to data, but solution accuracy? ◦ Covariance Matrix? How realistic is the output covariance matrix? (Actually, I can make the output matrix whatever I want through process noise or other means.) University of Colorado Boulder 27 Characterization requires a comparison to an independent solution ◦ Different solution methods, models, etc. ◦ Different observations data sets: Global Navigation Satellite Systems (GNSS) (e.g., GPS) Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) Satellite Laser Ranging (SLR) Deep Space Network (DSN) Delta-DOR Others… Provides a measure based on solution precision University of Colorado Boulder 28 Jason-2 / OSTM positions solutions generated by/at: ◦ JPL – GPS only ◦ GSFC – SLR, DORIS, and GPS ◦ CNES – SLR, DORIS, and GPS Algorithms/tools differ by team: ◦ Different filters ◦ Different dynamic/stochastic models ◦ Different measurement models University of Colorado Boulder 29 Image: Bertiger, et al., 2010 1 Cycle = approximately 10 days Differences on the order of millimeters University of Colorado Boulder 30 Compare different fit intervals: University of Colorado Boulder 31 Consider the “abutment test”: University of Colorado Boulder 32 Each data fit at JPL uses 30 hrs of data, centered at noon This means that each data fit overlaps with the previous/next fit by six hours Compare the solutions over the middle four hours ◦ Why? University of Colorado Boulder 33 Image: Bertiger, et al., 2010 Histogram of daily overlaps for almost one year Imply solution consistency of ~1.7 mm This an example of why it is called “precise orbit determination” instead of “accurate orbit determination” University of Colorado Boulder 34 In some case, we can leverage observations (ideally not included in the data fit) to estimate accuracy How might we use SLR to characterize radial accuracy of a GNSS-based solution? University of Colorado Boulder 35 Image: Bertiger, et al., 2010 Results imply that the GPS-based radial error is on the order of millimeters Why is the DORIS/SLR/GPS solution better here? University of Colorado Boulder 36 Must consider independent state estimates and/or observations Not an easy problem, and the method of characterization is often problem dependent ◦ How do you think they do it for interplanetary missions? University of Colorado Boulder 37