Launch COLA
Dr. Salvatore Alfano
Outline
 Problem Statement
– Space Object Environment
 Standard formulation
– Description
– Issues
 JSPOC use case
 AGI’s patented solution method
– Re-formulate the problem
 Questions and answers
2
Problem statement Find permissible launch times
 Given
– Launch trajectory
 Designed in the Earth Fixed frame
 Motion characterized in MET (Mission Elapsed Time)
– MET = seconds past Launch time
– Satellite Catalog
 Given in the Earth Centered Inertial (ECI) frame
 Motion characterized in civil time
– Launch window
 Time interval in civil time (absolute time scale)
 Example: 12 Feb 09 05:00:00 to 12 Feb 09 11:00:00 UTC
 Launch may occur anytime during this window
3
Problem Statement (Cont’d)
 Concern: close approaches with space objects
– Launching missile won’t be able to perform avoidance
maneuver
– Satellite object may not be able to move (debris)
– Satellite object unaware of launch
– Satellite object unwilling to move
 Which time intervals in the launch window are
NOT safe for launch?
– These are the Launch Blackout intervals
4
Space object environment
 12,000+ objects (publicly) cataloged by
USSTRATCOM
– Mostly debris with significant ephemeris uncertainty
(3-20km)
 Object ephemeris modeling
– SGP4 using a TLE
 Analytic routine (fast)
 Accurate for short durations (days)
 Each object’s TLE is routinely updated every few days
– SP (Special Perturbations propagator)
 Numerically integrated trajectories
5
Definitions
 Primary
 Secondaries
 Close Approach
 Designed launch trajectory
 Other space objects
 range < given threshold
Compute
All time intervals during the launch window for which
the primary will have a close approach with some
secondary if launched during that interval
6
Standard formulation
 Identify the set of secondaries to consider
– Use ephemeris generated near launch window time
– Filter out secondaries based upon apogee of launch trajectory
 Choose a sampling of times within the launch window
– Every 60 sec, 10 sec, 1 sec, etc.
 For each sampled time
– Transform launch trajectory to inertial frame
 sampled time = launch time
– Perform close approach to secondaries
– If close approaches are detected, then sampled time is in Blackout
interval
7
Standard formulation (cont’d)
 Do analysis in civil time
– Convert MET incrementally for each launch time
 Do analysis in ECI frame
– Transform MET incrementally for each launch time
 Will probably want to gather some further
results
– Close approach objects, minimum approach
distance
 Assimilate all results
8
Issues
 Sampling rate
– Events occur over short durations (seconds)
 Argues for using small time steps
– Launch Window is long (hours)
– May need to do many cases to assess entire
window
 Large number of cases
– More cases means more computational time
– More cases means more results to process when
determining the Blackout windows
9
Issues (cont’d)
 Accuracy requires timely data
– Ephemerides may not be valid for long times
– Argues for doing the analysis close to the time of
launch window itself
Can all the cases be computed and
assessed at a time close to the launch
window but before it starts?
10
Still need to investigate
 Planning
– How to plan months in advance of the launch
window?
 Launch trajectory design
– How can one assess the impact of trajectory
changes knowing the computations may take a long
time?
 Resetting the Launch Window
– Slips occur for lots of reasons
– How fast can a new assessment be made for the
new window?
11
JSPOC Use Case
 AGI In-House Hardware Configuration
– Intel® Xeon® CPU – 8 cores @ 2.13 GHz
– 24 GB RAM
– All tests results obtained using only 1 core
 Launch Window Example Configuration
– 6 hour launch window
– Primary trajectory MET duration ~ 15 min
– Conjunction range threshold – 40 km
 Example Catalog
– ~12,000 secondaries using ephemeris files
generated from publicly available TLEs
– Method not limited to TLEs
12
Results
Launch
Window
Sampling
Strategy
Fixed at Fixed at Fixed at Fixed at
AGI
60 sec 10 sec
1 sec 0.5 sec Launch
COLA
Conjunctions
Detected
< 1%
5.4 %
50 %
>99 %
100 %
Compute
Time
40 min
4 hrs
46.7 hrs
108.8
hrs
3.1 min
 Found 573 conjunctions
 Shortest blackout interval ~ 0.2 sec
 Smallest minimum range ~ 22 m
13
AGI Launch COLA papers
 “Determination of Close Approaches for
Earth Fixed Launch Trajectories”
– Jim Woodburn, AAS 98-134, 1998.
– http://www.stk.com/downloads/resources/userresources/downloads/whitepapers/CloseAppToEFL
aunch.pdf
 US Patent 6,102,334 Issued 15 Aug 2000
– “METHOD AND APPARTATUS FOR
DETERMINING CLOSE APPROACHES FOR
EARTH-FIXED LAUNCH TRAJECTORIES” by Jim
Woodburn of AGI
14
AGI-Patented solution strategy
 Transform the analysis space
– Use Earth-fixed frame rather than Inertial frame
– Use MET in addition to civil time
 Each MET time value
– Locates a single Earth-fixed position of launch
trajectory
– Corresponds to the considered interval (in civil time)
 Start: Launch window start + MET
 Stop: Launch window stop + MET
– The considered interval determines an arc of each
secondary’s trajectory
15
AGI-Patented solution strategy
 Take advantage of conjunction metrics that
are well behaved in MET in Earth-fixed
frame
– No need to sample at small steps to detect short
conjunctions
– Use small number of samples for determining
functional trends
– Accurately identify extrema and threshold crossing
events by iteratively sub-sampling as needed
 Convert MET events into launch times (civil
times)
16
Minimum possible range
Secondary Trajectory
Secondary position
at given civil time
Minimum
Possible
Range
Range Sample
Launch vehicle position
at a given MET
17
Solution strategy (cont’d)
 Is secondary’s arc within range threshold
at this position in the launch trajectory?
– No: no close approach at this MET
– Yes: secondary does have close approach
 If Yes:
– Determine time interval within the considered
interval for which range < threshold (i.e.,
conjunction time interval)
– Convert this conjunction time interval into a time
interval in the launch window when primary must
have launched for the close approach to have
occurred
18
Conjunction time interval
 Sample each secondary’s arc
 Use event detection routine to look for
threshold crossing
– Identifies a conjunction time interval within
considered interval
Range Sample
Range
Threshold
time-into-considered-interval
Conjunction
time interval
19
Computation Strategy
 Filter out secondaries based upon perigee
 For each secondary not filtered out
– Judiciously sample launch trajectory in MET
– Compute conjunction intervals at each sample,
where range < threshold
 This itself requires judicious sampling and iterative subsampling
– Iteratively sub-sample in MET to precisely
determine the envelope of all conjunction intervals
for this secondary
– Convert envelope boundary time interval into timeinto-launch-window interval (thus, blackout interval)
20
Conjunction Timing
Just Touches
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MET conjunctions
Shape of mapping is important
Latest end time
Blackout start time
Blackout end time
Earliest start time
Conjunction Timing
Touches twice
1
2
23
MET conjunctions
Shape of mapping is important
Latest end time
2
1
Blackout start time
Blackout end time
Earliest start time
24
Conjunction Timing
Touches twice
1
2
25
MET conjunctions
Shape of mapping is important
Latest end time
2
1
Blackout start time
Blackout end time
Earliest start time
26
MET conjunctions
Shape of mapping is important
= 1.6 s
DTwindow
Blackout
Latest end time
Blackout start time
Blackout end time
Earliest start time
MET = 1.2 s
27
Concerns addressed
 AGI Launch COLA:
– Can make plans in advance and continually update
the results
– Can easily account for changes to launch trajectory
design
– Can easily account for resetting the launch window
– Can be run very close to launch window start, using
the best available data as of that time for best
prediction accuracy
28
JSPOC Use Case Extended – Part 1
Extension from a single launch to
multiple simultaneous launches from nearby sites
 Which time intervals in the launch window
are NOT safe for launch from any of the
given launch sites?
– These are the Launch Blackout intervals for the
entire set of multiple simultaneous launches
29
Problem Statement
 Given
– Launch trajectories and launch window as before
– Launch sites are close and trajectories remain in close
proximity
 Simultaneous launches from all launch sites may
occur anytime during the launch window
 AGI Solution - treat trajectories as a cluster
– Generate single reference trajectory for the entire cluster
– Create new conservative range threshold for the entire cluster
– Compute conservative blackout intervals for reference
trajectory using conservative range threshold
– Refine blackout intervals for individual trajectories
30
Reference for multiple launches
Define single reference launch site and trajectory, e.g.
average of all launch trajectories in Earth-fixed frame in MET
Reference trajectory
Launch sites
Reference launch site
31
Max dispersion distance
Determine maximum distance of any launch vehicle
from the reference position at any time in MET
Positions at
some MET
Positions at
MET=0
Maximum
dispersion
distance at MET
32
Filter using reference trajectory
Compute conservative blackout intervals using reference
launch trajectory with range threshold set to
max dispersion distance + original range threshold + additional “pad”
Conservative
range threshold
sphere
Additional “pad”
Original range
threshold sphere
33
Individual trajectory processing
 Filtered conservative blackout intervals are
refined using launch window analysis of
actual individual trajectories
– Computational savings result from using filtered
blackout intervals which are typically much shorter
than the overall launch window
34
JSPOC Use Case Extended – Part 2
Extension from a finite set of launch sites to launches
from anywhere within a continuous area
 Which time intervals in the launch window
are NOT safe for launch from anywhere
within given area?
– These are the Launch Blackout intervals for the
entire area
35
Problem Statement
 Given
– Launch trajectory and launch window as before
– Method for changing Earth-fixed MET trajectory
from one launch site to another within specified
area
 Launch may occur anytime during the
launch window and anywhere within the
specified area
36
Area Launch Definition
 Rectangular area in lat-lon space
 Earth-fixed MET trajectory is defined for
some launch site within the area (e.g. its
center)
 Trajectory is modified when moved to a
different launch site within the area, e.g.
– Same trajectory in local topocentric frame
– Same Earth-fixed MET burnout point
– Other methods are possible
37
Area Launch – Same Trajectory
Trajectories are fixed in MET in local topocentric
frame for each launch site
A lot of samples to
cover the area
38
Area Launch – Same Burnout Point
Burnout point fixed in MET in Earth-fixed frame is
the same for any launch site
A lot of samples to
cover the area
39
Standard formulation
 Sample launch area at some acceptable
resolution
 For each sample launch site
– Perform launch window analysis
– Accumulate results
 Report accumulated results from all sampled
sites
40
Issues
 How to determine acceptable area resolution?
 Fine resolution over large area = many launch
sites = many analyses to run
– 100 km x 100 km at 10 km resolution = 100 launches
 It may be difficult to obtain answers that are
both timely and accurate
41
Primary Trajectory Surface at MET
 At a given MET, positions of all possible primary
trajectories starting within specified launch area
make up primary trajectory surface
Primary Trajectory Surface at a given MET
Launch Area (MET = 0)
42
Minimum possible range to surface
Sample on secondary trajectory
Corresponding Min Range point on Primary trajectory surface
Secondary Trajectory
Primary trajectory surface
at a given MET
Minimum Possible
Range for entire
surface at a given MET
43
AGI Solution
 Start using approach similar to clustered
trajectories case
– Generate reference trajectory for the area
– Create conservative padded range threshold
– Compute conservative blackout intervals
 Refine blackout intervals
– Replace range computation to a single position at MET with
range computation to the nearest point on the surface at MET
– Nearest point is found using judicious sampling and iterative
sub-sampling of surface points
– Clearing any and all points on the surface means clearing the
nearest point
44
Judicious Area Sampling
Judicious sampling works well for areas of various size
Initial samples
45
Results Extended
Launch AGI Launch
Window
COLA
Sampling
Strategy
Compute
Time
3.1 min
AGI Launch
COLA
for 18
trajectories
AGI Clustered
Launch COLA
for 18
trajectories
AGI Area
Launch
COLA
Rectangular
Area 100 x
100 km
23.9 min
3.2 min
3.7 min
 Fixed computational cost is associated with loading
secondary ephemeris files for processing
– independent from the number of primary trajectories
46
Metrics
 12,000 ephemeris files generated from TLEs
– 35 minutes on a 1-core PC for all objects for 5 days
– 90 points per orbit
 Apply perigee filter to all 12,000
– 11,000 satellites eliminated (1,000 left)
 Run launch COLA for 100km x 100km case
–
–
–
–
–
6 hour launch window
Primary trajectory MET duration ~ 15 min
Conjunction range threshold – 40 km
4 minutes processing time
Conjunctions found ~ 600
47
Video of multiple launches
COLA_Red.wmv
48
Results Combined
49
50
Questions & answers