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ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones Professor George H. Born Lecture 25: Kalman Filter Case Study. Announcements. Homework 8 Due Friday Lecture Quiz Due by 5pm on Wednesday Exam 2 – Friday, November 8
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ASEN 5070: Statistical Orbit Determination I Fall 2013 Professor Brandon A. Jones Professor George H. Born Lecture 25: Kalman Filter Case Study
Announcements • Homework 8 Due Friday • Lecture Quiz • Due by 5pm on Wednesday • Exam 2 – Friday, November 8 • Covers material through the end of this week • Accumulative in the sense that some topics, e.g., probability and statistics, used in the sequential filters
Example – Problem Statement • Ballistic trajectory with unknown start/stop • Red band indicates time with available observations Obs. Stations Start of filter
Example – Problem Statement • Object in ballistic trajectory under the influence of drag and gravity • Nonlinear observation model • Two observations stations
Filter Characterization • 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
Filter Residuals over Time Station 1 Station 2 • Blue – Range • Green – Range-Rate
Observation Residual Histograms Postfits Prefits
State Error and Uncertainty Velocity Position
What are some of the things we may want to consider adding to our filter?
Process Noise • 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 in November)
State Estimate with Process Noise Velocity Position
Residuals with Process Noise Station 1 Station 2
Residual Histogram with Process Noise Postfits Prefits
Process Noise • Compute the prefit residual variance via • An observation is not processed in the filter if:
Residuals with Observation Editing Station 1 Station 2
Residual Histograms w/ Editing Postfits Prefits
Filter Accuracy w/ Editing Velocity Position
Bias Estimation • To estimate the bias, we add it to the estimated state vector
Residual Histograms w/o Bias Estimation Postfits Prefits
Residual Histograms w/ Bias Estimation Postfits Prefits
Residuals without Bias Estimation Station 1 Station 2
Residuals w/ Bias Estimation Station 1 Station 2
Accuracy w/ Bias Estimation Velocity Position
Accuracy w/o Bias Estimation Velocity Position
Filter Estimated State Correlation Proc. Noise, Editing, Bias Est. No Augmentation