Transcript Lecture 29
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 29: Kalman Filter Case Study University of Colorado Boulder Exam 2 – Friday, November 6 Office hours this week: ◦ Prof. Jones – T/Th 12:30-1:30pm ◦ Eduardo – W 2-4pm, Th 2:30-4:30pm University of Colorado Boulder 2 Kalman Filter Case Study - Introduction University of Colorado Boulder 3 Obs. Stations Start of filter University of Colorado Boulder Ballistic trajectory with unknown start/stop Red band indicates time with available observations 4 Object in ballistic trajectory under the influence of drag and gravity Nonlinear observation model ◦ Two observation stations University of Colorado Boulder 5 University of Colorado Boulder 6 What should we look at to characterize the filter performance? ◦ Residuals (pre-/post-fit) ◦ Covariance ◦ State Estimate There are different ways to visualize these We will consider the case where we have a known truth for comparison University of Colorado Boulder 7 Station 1 Station 2 Blue – Range Green – Range-Rate University of Colorado Boulder 8 Prefits University of Colorado Boulder Postfits 9 Position University of Colorado Boulder Velocity 10 What are some of the things we may want to consider adding to our filter? University of Colorado Boulder 11 Kalman Filter Case Study – Filter Saturation University of Colorado Boulder 12 To prevent filter saturation, we add a constant term to the covariance time update to set a minimum value: This is usually referred to as process noise ◦ More typically based on stochastic acceleration (more on this next week) University of Colorado Boulder 13 Position University of Colorado Boulder Velocity 14 Station 1 University of Colorado Boulder Station 2 15 Prefits University of Colorado Boulder Postfits 16 Kalman Filter Case Study – Observation Editing University of Colorado Boulder 17 Compute the prediction residual variance via An observation may be ignored in the filter if (for example): University of Colorado Boulder 18 Station 1 University of Colorado Boulder Station 2 19 Prefits University of Colorado Boulder Postfits 20 Position University of Colorado Boulder Velocity 21 Kalman Filter Case Study – Bias Estimation University of Colorado Boulder 22 To estimate the bias, we add it to the estimated state vector University of Colorado Boulder 23 Prefits University of Colorado Boulder Postfits 24 Prefits University of Colorado Boulder Postfits 25 Station 1 University of Colorado Boulder Station 2 26 Station 1 University of Colorado Boulder Station 2 27 Position University of Colorado Boulder Velocity 28 Position University of Colorado Boulder Velocity 29 No Augmentation University of Colorado Boulder Proc. Noise, Editing, Bias Est. 30