1. Scheduling Radar Warning Receivers (RWRs)
Scott R. Schultz
Mercer University / Mercer Engineering Research Center
F.M. Barron
Paul MacNeil
Eric Mullenax

2. About the Speaker
Dr. Scott Schultz – associate professor Mercer University, and consultant at Mercer Engineering Research Center.
Industry Experience:
13 years automotive experience – Ford Motor Company.
2 years furniture experience – Furniture Manufacturing Management center.
Consulting – manufacturing and military
Teaching Experience:
6 years as Industrial Engineer – Mercer Univ.
Simulation
Production, scheduling, inventory control
Operations Research
others…

3. Problem Statement
Develop an RWR scheduler that minimizes the time to detect multiple threats across multiple frequency bands.

4. RWR Scheduling Definitions
Revisit Time (RT) – time to rotate 360 degrees (rotating radar)
Illumination Time (IT) – function of RT and BW
Pulse Width (PW) – length of time while target is energized
Pulse Repetition Interval (PRI) – time between pulses
Beam Width (BW)
Revisit
Time (RT)
Pulse
Repetition
Interval (PRI)
Illumination
Time (IT)
Pulse Width (PW)
Time

5. Example RWR Schedule
RWR Schedule – a series of dwells on different frequency bands: sequence and length

6. RWR Scheduling Problem
Objective – detect all threats as fast as possible (protect the pilot)
How to sequence dwells?
How to determine dwell length?
How to evaluate / score schedules?
Meta-Heuristics
Simulation

7. RWR Scheduling Approach
Meta-Heuristics: Simulated Annealing (SA)
SA Components:
Solution representation
Neighborhood generation scheme
Solution evaluation/score

8. RWR Scheduling Approach
RWR SA Solution Representation:
Assumptions:
Unit Time
Idle Time fills space from end of last dwell to total cycle time.

9. RWR Scheduling Approach
RWR SA Neighborhood generation scheme:
Two Examples:
Add or Subtract a Unit of Time Split a Dwell

10. RWR Scheduling Approach
Solution Evaluation: Simulation Approach:
Given that the offset for each threat pulse train is unknown.
Determine: MTDAT - expected time to detect all threats,
MaxDAT - maximum time to detect all threats
Threat detected in cycle 1
Note different offsets
Threat detected in cycle 2

11. RWR Scheduling Approach
Objective: Evaluate / Score a single RWR schedule.
N – number of iterations
I – number of threats
i = 1
Generate offset for threat i ~ U(0,RTi)
Update MTDAT, MaxDAT
Determine time when RWR schedule coincides with threat i
n = n + 1
i = i + 1
Yes
i < I
n < N
Yes No No
Done

12. RWR Scheduling Approach
When does the MTDAT running average begin to converge?
MTDAT running average: 3 threats
MTDAT running average: 5 threats
MTDAT running average: 10 threats

13. Experimental Design Compare SA to Simple Heuristic:
Pre-determined Cycle Time Heuristic:
Set the number of dwells equal to the number of frequency bands,
Set the dwell time as calculated below:
dwell time = int((RWR cycle time – retune time * number of bands )/ number of bands)
Any time left over is assumed idle time and placed at the end of the schedule

14. Experimental Design Problem Parameters:
Retune Time: 1 Time Unit (msec)
RWR Cycle Times: Evaluate from 40 to 90 (msec)
Threat List: 5 Enemy Radars

15. Experimental Design Problem Parameters:
Retune Time: 1 Time Unit (msec)
RWR Cycle Times: Evaluate from 40 to 90 (msec)
Threat List: 5 Enemy Radars

16. Results
Results:
Note: MTDAT approaching infinity for pre-determined cycle time heuristic at some cycle times due to synchronization.

17. Results

18. Conclusions SA outperforms simple heuristic
SA approach presented for developing RWR schedules using the performance measure “mean time to detect all threats”, MTDAT.
SA will converge on an RWR schedule having a particular cycle time, however this is dependent on the initial cycle time and bounded by cycle times which are synchronized with a threat’s revisit time.
Synchronization poses an interesting challenge compared to many SA applications of discrete optimization problems which converge to a global optimal solution independent of the starting solution.

19. RWR Research - Status Future:
Investigate alternative means of generating scores to avoid costly simulation
Research literature identified
Compare to enhanced evaluator (simulator)
Assess impact of multiple radars in RWR platform
Replace single radar with one monitoring high frequencies and one monitoring lower frequencies
Math Model?

20. Research Sponsor Sponsors:
RAPCEval - collaborative Air Force and university education and research program to support advances in electronic combat technology. The RAPCEval program is overseen by a steering committee of scientists and engineers from the Air Force Research Laboratory at Wright Patterson AFB, the Warner Robins Air Logistics Center at Robins AFB, Mercer University, Mercer Engineering Research Center (MERC), Wright State University, and Rose-Hulman Institute of Technology who are charged with ensuring that student research is of sufficient interest to the USAF and also of high academic quality.
Mercer Engineering Research Center – located in Warner Robins, Georgia, a non profit operating unit of Mercer University. MERC employs over 150 engineers, scientists, and support staff. Engineering, Logistics, management, and educational services are provided to a wide range of government and commercial customers