Transcript Lecture 39
ASEN 5070: Statistical Orbit Determination I Fall 2015 Professor Brandon A. Jones Lecture 39: Combining State Estimates and Measurement Modeling University of Colorado Boulder No lecture quiz next week. Exam 3 posted today by 5pm Final Project Due December 14 by noon Eduardo’s office hours next week: ◦ In-class Students: Due December 11 by 5pm ◦ CAETE Students: Due 11:59pm (Mountain) on 12/13 ◦ He will be out of town Thursday and Friday, but is available via e-mail. ◦ Office hours Thursday (2:30-4:30pm) have been moved to Tuesday (2:30-4:30pm in ECAE 1B44) University of Colorado Boulder 2 Your solutions must be uploaded to D2L as a searchable PDF Open-book, open notes You may use a computer, MATLAB, etc. Honor code rules apply The TA has been instructed to redirect all questions to the instructor I can answer questions to clarify what is being asked, but cannot provide guidance on solutions ◦ Same rules as homework apply in regards to format, code appendices, etc. ◦ Do not give or ask for help from your peers University of Colorado Boulder 3 Project Q&A University of Colorado Boulder 4 Combining State Estimates University of Colorado Boulder 5 A ground station in Maui observed our satellite several times over the past week ◦ Generated a filtered solution using their observations A ground station in Florida also observed the satellite several times over the past week ◦ Generated a filter solution using their observations What is the best approach to fusing this information? University of Colorado Boulder 6 Treat one solution as the a priori and the other as the observation ◦ Does it matter which one is which? For this case, H=I University of Colorado Boulder 7 Does not require the additional processing of observations University of Colorado Boulder 8 University of Colorado Boulder 9 Modeling Measurements Tapley, Schutz, and Born, Chapter 3 Montenbruck and Gill, Satellite Orbits, Chapter 6 University of Colorado Boulder 10 One-way Range ◦ Example: GNSS ◦ Signal travels to/from reference from/to satellite University of Colorado Boulder 11 Two-way Range ◦ Examples: SLR, DSN ◦ Satellite is a relay for signal University of Colorado Boulder 12 Multi-way Range ◦ Examples: DSN, TDRSS ◦ Multiple satellite and/or ground stations used University of Colorado Boulder 13 We have been using range and range-rate: In the real world, what is wrong with these equations? University of Colorado Boulder 14 At best, a signal travels at the speed of light We must approximate the signal propagation time δt Approximately 0.06 seconds for GPS signal to reach Earth A LEO spacecraft will have moved approximately 500 meters in that time University of Colorado Boulder 15 Assume we have estimates of our satellite trajectory and the reference station/satellite We need to solve for δt No analytic solution so we solve for the correction using iteration University of Colorado Boulder 16 Start with δt=0 Compute the distance with the satellite state at time t and the reference state at t-δt Given that distance, compute the light propagation time Δδt Set δt=δt+Δδt Continue until Δδt is sufficiently small University of Colorado Boulder 17 We have taken care of light-time correction assuming the speed of light in a vacuum. Any other things we should account for? ◦ Signal does not always propagate through a vacuum Ionosphere Troposphere Charged particle interactions Solar corona etc. ◦ Coordinate and time systems This requires a very careful treatment in the filter University of Colorado Boulder 18 Not including accurate coordinate system information creates systematic errors. ◦ Violates our assumption of random errors! ◦ Creates a time-varying bias in the measurement Table courtesy of Bradley, et al., 2011 University of Colorado Boulder 19 Is it possible to measure range-rate instantaneously? ◦ No! (at least not that I am aware of) ◦ We have to observe this indirectly Instead, we look at the change in a signal over time to approximate the range-rate University of Colorado Boulder 20 Satellite sends pulse at fixed interval University of Colorado Boulder 21 University of Colorado Boulder 22 Image Courtesy of WikiCommons The velocity of the spacecraft affects the frequency of any radar signal Requires us to observe the change in frequency over some period of time ◦ Known as integrated Doppler shift University of Colorado Boulder 23 Image Courtesy of WikiCommons The velocity of the spacecraft affects the frequency of any radar signal Requires us to observe the change in frequency over some period of time ◦ Known as integrated Doppler shift University of Colorado Boulder 24 Range-rate model assumes: ◦ Linear change in range over integration time ◦ Constant transmission frequency over integration time University of Colorado Boulder 25 Do I need to perform any light time correction? Is there anything different about this case when compared to range? University of Colorado Boulder 26 FCQs University of Colorado Boulder 27