Transcript Lecture 9
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 9: Batch Estimator and Weighted LS University of Colorado Boulder Homework 3 – Due September 18 Lecture Quiz 3 Due Friday by 5pm Future Lectures ◦ Lecture 10 – Monday 9/14 @ 4pm ◦ Lecture 11 – Monday 9/21 @ 9am ◦ Lecture 12 – Monday 9/21 @ 4pm University of Colorado Boulder 2 Batch Estimator University of Colorado Boulder 3 University of Colorado Boulder 4 Straightforward way to estimate the state at a time that matches the observations What about when the observations cover multiple points in time? University of Colorado Boulder 5 What can we do to estimate the state x0 when we have observations at multiple points in time? ◦ What tool(s) do we have available to alter the formulation? ◦ Given result from above, how might we alter the formulation to use a single relationship of the form: University of Colorado Boulder 6 University of Colorado Boulder 7 University of Colorado Boulder 8 Process all observations over a given time span in a single batch ◦ The alternative sequential methods will be discussed later What are the shortcomings of such a formulation? University of Colorado Boulder 9 University of Colorado Boulder 10 University of Colorado Boulder 11 University of Colorado Boulder 12 Process all observations over a given time span in a single batch University of Colorado Boulder 13 No weighting of observations ◦ How do we account for different sensors with different accuracies? No incorporation of previous information ◦ Known a a priori state information ◦ How do we include this in the filter? University of Colorado Boulder 14 Weighted Least Squares Estimation University of Colorado Boulder 15 For each yi, we have some weight wi University of Colorado Boulder 16 Consider the case with two observations (m=2) If w2 > w1, which εi will have a larger influence on J(x) ? Why? University of Colorado Boulder 17 University of Colorado Boulder 18 For the weighted LS estimator: How do we find W ? University of Colorado Boulder 19 University of Colorado Boulder 20 University of Colorado Boulder 21 Weighted Least Squares w/ A Priori University of Colorado Boulder 22 A priori ◦ Relating to or denoting reasoning or knowledge that proceeds from theoretical deduction rather than from observation or experience We have: University of Colorado Boulder 23 As you will show in the homework: University of Colorado Boulder 24 University of Colorado Boulder 25