Transcript Lecture 22
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 22: Further Discussions of the CKF University of Colorado Boulder Homework 7 Due Friday Lecture Quiz ◦ Due by 5pm on Friday 10/23 University of Colorado Boulder 2 The Kalman Filter – Implementation Discussion University of Colorado Boulder 3 Does not map to epoch time! Note the use of Htilde University of Colorado Boulder 4 Like the batch processor, we need to use linearization and a reference trajectory ◦ This gives us the STM and we use it to evaluate Htilde At any point in time, we have an estimate of the state: University of Colorado Boulder 5 Reinitialize integrator after each observation: Alternatively, if we want to use one call to the integrator, we can use already generated output: University of Colorado Boulder 6 In the CKF presented, we have to invert a p×p matrix, which is more efficient and (likely) stable than the n×n matrix inversion for the batch Can we further reduce the computation overhead? Yes – under certain conditions… University of Colorado Boulder 7 University of Colorado Boulder 8 Home Exercise: Prove to yourself that the scalar update is equivalent to the original form if Rk is diagonal. University of Colorado Boulder 9 Whitening Transformation Use new values in Kalman filter University of Colorado Boulder 10 Whitening Transformation University of Colorado Boulder 11 University of Colorado Boulder 12 The Kalman Filter – Prediction Residuals University of Colorado Boulder 13 Previously, we have discussed the pre-fit and post-fit residuals: What else might we consider in the context of the CKF? University of Colorado Boulder 14 At each measurement time in the CKF, we can take a look at the prediction residual (sometime called innovation): Covariance of the prediction residual: University of Colorado Boulder 15 What would the predicted residual PDF be useful for? University of Colorado Boulder 16 If we take another look at the Kalman gain equation: University of Colorado Boulder 17 If we take a closer look, the CKF is using the predicted residual PDF at each time to update the state: In other words, the CKF estimate of the state is a weighted sum of the a priori and a correction due to the predicted residual and its statistics University of Colorado Boulder 18 University of Colorado Boulder 19 Comparison of Kalman and Batch University of Colorado Boulder 20 University of Colorado Boulder 21 University of Colorado Boulder 22 University of Colorado Boulder 23 University of Colorado Boulder 24 University of Colorado Boulder 25 What are the similarities between the batch and the sequential processor (as discussed up until now)? What are the differences between the batch and the sequential processor (as discussed up until now)? University of Colorado Boulder 26