ASEN 5050 SPACEFLIGHT DYNAMICS Spacecraft Navigation Prof. Jeffrey S. Parker University of Colorado...

ASEN 5050SPACEFLIGHT DYNAMICS

Spacecraft Navigation

Prof. Jeffrey S. Parker

University of Colorado – Boulder

Lecture 36: Navigation 1

Announcements• FCQs today! End of class.

• STK Lab 3 due riiiiiight now!

• STK Lab 4 due 12/12

• Final Exam on 12/12, due 12/18– Take-home, open book open notes

• Final project and exam due 12/18Lecture 36: Navigation 2

Schedule from here out


• 12/5: Spacecraft Navigation

• 12/8: Final Review, part 1• 12/10: Final Review, part 2• 12/12: Small Body Missions

Space News• Orion’s Exploration Flight Test 1: Friday 12/5 at 7:05 am

Eastern Time (5:05 am Mountain!). Duration: 4.5 hours.



Navigation




Spacecraft Navigation

• Mission Design– Define trajectories, error tolerances, navigation strategies, tracking

strategies, science requirements, etc.• Launch

– Launch targets, guidance, tracking, performance estimation• Hand-off to the spacecraft operators

– Best estimate of the spacecraft’s state and associated uncertainty• Tracking and orbit determination

– Ground station tracking and maybe other sources of tracking (GNSS, TDRSS, LiAISON, SoOp, etc)

– Satellite telemetry– Estimate the spacecraft’s state and associated uncertainty

• Maneuver design and execution– Maneuver guidance (attitude, timing, propulsion, execution)– Maneuver execution estimation


Spacecraft State

• The “State” ( X ) describes anything that the satellite operators wish to estimate, with associated uncertainties. Example state parameters:– Satellite’s position and velocity (6 parameters)– Satellite’s mass, Cd, Cr, and other similar parameters– Maneuver execution parameters

– Science• Atmospheric density profile (GOCE, DANDE, etc)• Gravity signatures (GRACE)

– Others as needed


Spacecraft State Uncertainty

• The state is estimated and an uncertainty is associated with that estimate.– State = X

– Uncertainty = P, the variance-covariance matrix


Useful variation, showing only the correlations in the lower-left

Symmetric matrix

Orbit Determination

• The art of estimating the state of a satellite in the presence of a great deal of uncertainty.

• We start with either no information or an estimate of the state.

• We model the dynamics (gravity, SRP, drag, etc)• We acquire tracking data, including noise and

systematic errors• Filter the data and generate an estimate of the state.• Take ASEN 5070 for a lot more information.Lecture 36: Navigation 9

Tracking Data

• Ground stations– 1-way, 2-way, 3-way– Range, Doppler, RA, Dec– Delta-DOR– Other beacons, Laser reflectors

• Satellite tracking– TDRSS, GNSS, LiAISON

• Telemetry information– Gyros, accelerometers, propulsion system data

• Other– OpNav, SoOps, X-Ray Pulsar, Radar, Lidar, etc.


Lecture 36: Navigation11

Methods of Initial Orbit Determination• Observations of range, azimuth, and elevation• Angles-only observations

– Laplace’s Method– Gauss’s Technique– Double r-iteration

• Mixed Observations– Range and Range-Rate Processing– Range-only Processing

• Three Position Vectors and Time– Gibbs Method– Herrick-Gibbs

• Two Position Vectors and Time Lambert’s Problem– Minimum Energy– Gauss’s Solution– Universal Variables– Battin Method


Range, Azimuth, Elevation


Range, Azimuth, and Elevation

Angles-Only Observations



Three Positions and TimeProblem Statement: Given three time-sequential position vectors, determine the velocity vector corresponding to the 2nd position vector. Note that determining the position and velocity vectors at the 2nd time essentially completely determines the orbit, and they may be converted into a complete set of orbital elements.


Gibbs MethodWe have covered a lot of equations here, so lets summarize the Gibbs Method:

Given:

Determine:

Algorithm:

Check if coplanar:

Check if too close together:


Gibbs Method

Compute velocity:


Lambert’s Problem

Given two positions and the time-of-flight between them, determine the orbit between the two positions.

Orbit Determination

• If your state has 6 parameters and you get 6 pieces of information, you can estimate each parameter – but you are very vulnerable to modeling and measurement errors!

• Standard OD methods involve collecting as much data as possible and using a least-squares estimate to fit the state to the data.– i.e., 106 pieces of information, including noise and errors!– Batch processor– Kalman Filters



Orbit Determination

Things to Note

• Not all observations are created equal.– Range and Doppler data only provides line-of-sight

information.

– Angular data – or data over a long arc – may be very useful to improve the observability of the state.

• Clean data should be weighted higher than noisy data.

• The satellite is never where you think it is. Pay attention to the covariance matrix!


Maneuver Planning

• Once you have an estimate of your state, you may require a maneuver downstream in order to achieve the mission’s requirements.

• What are your acceptable error corridors for each orbital element / state parameter?


Maneuver Execution Error

• Maneuvers are never performed perfectly– Though they’re getting better and better.

• There is typically a minimum expected execution error – you can’t perform better without switching to a different system / nozzle / flow rate.

• There is also typically a proportional error that grows with the maneuver’s duration / magnitude.


Maneuver Navigation

• Gates Model, describing maneuver execution errors.– C. R. Gates, “A Simplified Model of Midcourse Maneuver Execution

Errors,” Tech. Rep. 32-504, JPL, Pasadena, CA, October 15, 1963.

• Error in pointing of the burn

• Error in magnitude direction of burn

• Sample these errors and apply them to Monte Carlo simulations.


Gates Model

• Error in pointing of the burn

• Error in magnitude direction of burn


Gates Model

• Now, define a coordinate frame, where z is aligned with the commanded Delta-V direction:


Gates Model

• Sample a simple Gaussian distribution three times to generate

• Execution errors, in maneuver frame:

• Finally, rotate them into any useful frame.


Navigation


• Example Gates Model inputs into a navigation study:

• Good practices in spaceflight navigation

– Practice! Tune your filter on all kinds of data. Be ready for a wide variety of data.

– Perform lots of solutions and compare them.• Solutions over different arcs of time, long and short• Solutions with different data types• Solutions with different parameters, consider parameters, process noise, etc.

– Present the information in a manager-friendly format, but understand the details.

• B-Plane, error ellipses, covariance, residuals

– Look at that covariance in different ways.

– Don’t neglect the numerical details.29

Flight Operations

• All of them.

30

Missions that require navigation

• All spacecraft require OD– For communication

• Most spacecraft require OD for other reasons– For science

– For mission planning

– For maneuver design

31

Spacecraft missions


FCQs




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ASEN 5050 SPACEFLIGHT DYNAMICS Spacecraft Navigation Prof. Jeffrey S. Parker University of Colorado...

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