Efficient Resource Management for Radar Tracking Systems

1. Jeffery P. Hansen Sourav Ghosh Raj Rajkumar John P. Lehoczky Resource Management of Highly Configurable Tasks April 26, 2004 Carnegie Mellon University

2. Outline • Radar Tracking Problem • Introduction to Q-RAM • Application of Q-RAM to Radar Tracking • Slope-Based Traversal • Fast Traversal • Experimental Results

3. Resource Management for Radar Tracking • For each target we need to choose: • Radar parameters such as dwell period, dwell time and transmit power. • Ship/antenna to use. • Signal processing algorithm to use. • CPU from processing bank to use. • While satisfying constraints on: • Power dissipation • Radar and CPU Utilization • Scheduling • We must quickly respond to: • Changes in target position • New target arrivals • Target departures

4. Radar Resource Management Approaches 100% 100% 50% 50% 0% 0% Priority-Based Allocation • Existing solutions use operational doctrine to make resource allocation decisions. • Resources allocated to tasks in order of importance based only on each task’s characteristics. • Some problems with this approach are: • Important tasks can starve tasks of slightly lower priority. • Does not make best use of resources. • Difficulty in predicting viable scenarios. • QoS-based optimization considers resource tradeoffs and relative task importance. • Resources allocated in proportion to importance. • Tasks can have unlimited access to resource when demand is low. • Tasks can not starve other tasks of similar importance. • Operator can dynamically change importance. QoS-Based Optimization

5. QoS Optimization with Q-RAM Frames/sec. Image Resolution • QoS modeled as an n-dimensional space • Each set-point in the space has an associated “utility” value representing user satisfaction. • Utility values can be assigned individually or via dimension-wise utility functions. • A single QoS set-point can be realized by multiple “Resource Options”. • Resource trade-offs • QoS Routing • Optimization goal is to maximize total system utility while meeting resource constraints. • Per-user weights give higher priority to “important” users. • Near optimal solution for search space of over a trillion QoS setpoint combinations found in under 1 sec.

6. QoS Model of Radar Tracking Problem Threat Assessment • Environment • Distance • Speed • Direction • Maneuvering • Counter Measures • Resources • Radar bandwidth • Short-term power • Long-term power • CPUs • Memory Marginal Utility Control • Operational Dimensions • Dwell Period • Dwell Time • Transmit Power • Tracking Algorithm • # of task replicas • QoS Dimensions • Track Error • Target Drop Probability • Reliability

7. QoS Setpoints CPU CPU CPU CPU CPU CPU 0.999 0.999 0.99999 0.99999 CPU CPU CPU CPU CPU CPU Resource Option 1 Resource Option 2 Utility QoS (0.0) (0.4) (0.6) (1.0)

8. Radar Constraint/Resource Model Utilization(Ui ) – Limit on fraction of time radar can be in continuous use. Heat (Hi ) – Limit on heat that can be dissipated per unit time. Power (Pmax) – Limit on power that can be provided to power radars. Computing (Cmax) – Limit on processing capabilities for tracking targets. Per Antenna Constraints: Global R1 R2 Global Constraints: …

9. Radar Model Error Estimation Tx Tx Rx Rx w w Radar tracking error is estimated by a function: Dwell Period Dwell Time Tx Time Tx Power Distance Environmental Dimensions Operational Dimensions Velocity Tracking Alg. Acceleration Target Type Noise r Radar Usage a v ξ n CPU Usage

10. Setpoint Explosion Problem One Dimension Two Dimensions Three Dimensions Four Dimensions • Concave majorant algorithm used by Q-RAM requires O(n ln n) and must examine every setpoint. • For applications with more than a few operational dimensions, the number of setpoints can be very large • With k dimensions having m settings, there are mk setpoints. • Even a linear algorithm may take a long time.

11. Q-RAM Overview Track 1 • Optimization goal: Maximize total system utility while meeting resource constraints. • Algorithm: • Generate concave majorant of utility/resource curve for each target. • Assign minimum resource allocation to all targets. • Increase allocation for target with the highest marginal utility. • Repeat until all resources have been allocated. • Solution Properties • Optimal in continuous case • Within a fixed distance of optimal in discrete case. Utility Dwell Period: 100ms Dwell Time: 1ms Power: 1.3 kW Tracking Alg.: Kalman Resources Track 2 Utility Resources

12. Slope Based Traversal • Algorithm • Determine minimum and maximum QoS points. • Eliminate points under the line connecting them. • Apply concave majorant to remaining points. • Initial scan is linear • Reduces number of points to which we must apply the concave majorant algorithm. • Some reduction in execution time. • But, still must examine every setpoint. Utility Compound Resource

13. Resource/utility values associated with setpoints are not random. Utilize structure in the resource management problem to reduce this complexity. For most operational dimensions, an increase in quality on any dimension results in: Non-decreasing resource consumption. Non-decreasing utility. We call dimensions with the above property “monotonic” dimensions. All other dimensions are called “non-monotonic” dimensions. Fast Convex Hull Algorithms Transmit Power U R U U R R Dwell Period

14. Fast Traversal Methods <3,5> <3,4> <2,4> <1,4> <3,*> Utility <2,*> <1,*> <1,3> <*,5> <*,4> <*,3> <*,2> <1,2> <*,1> Compound Resource <1,1> Observations of the points on the concave majorant have revealed that for monotonic dimensions: • Concave majorant is usually composed of sub-sequences of points differing in only one quality index. • Dimension that is changing may shift as the concave majorant is traversed. • May need to treat “non-monotonic” dimensions separately.

15. Fast Traversal Algorithms U R* U U R* R* U U R* R* U U U U U R* R* R* R* R* • FOFT: First Order Fast Traversal Algorithm: • Make the minimum QoS point the current point. • Examine points adjacent in the quality index space to the current point. • Choose next point with highest marginal utility. • Repeat until reaching maximum QoS point. • Apply concave majorant to resulting set of points. • Generates nearly the same set of points as full concave majorant. • Explicitly examines only a small subset of the possible setpoints. • Utility values within a few percent of standard Q-RAM algorithm. Transmit Power Dwell Period Utility Compound Resource

16. Higher Order Traversal Algorithms Transmit Power Transmit Power Dwell Period Dwell Period SOFT* - Modified Second Order Fast Traversal • Same as SOFT, but include points which increase in at least one dimension, but may decrease in the other. • Experimental results show that • SOFT* requires more execution time than FOFT and SOFT. • Resulting concave majorant is slightly better than FOFT. SOFT - Second Order Fast Traversal • Same as FOFT, but we include setpoints that increase in up to two dimensions. • Experimental results show that • SOFT requires more execution time than FOFT. • Resulting concave majorant is actually worse than FOFT.

17. Optimization with Non-Monotonic Dimensions Utility Compound Resource Algorithm Kalman αβγ Concave Majorant Generation with Non-Monotonic Dimensions • For each combination of non-monotonic parameters, apply the traversal algorithm. • Generate the concave majorant from the combined set of setpoints. Transmit Power Transmit Power Dwell Period Dwell Period

18. Concave Majorant Utility Compound Resource

19. Slope-Based Concave Majorant

20. FOFT Concave Majorant Approximation

21. 2-FOFT Concave Majorant Approximation

22. Global Utility

23. Number of Setpoint per Task

24. Total Optimization Time

25. Conclusion • Approach Overview • Leverage structure in the setpoint space to generate concave majorant approximation. • Concave majorant estimated by following the adjacent point on the monotonic dimension with the highest marginal utility. • Algorithm repeated for all combinations of non-monotonic dimensions. • Benefits of Approach • Significantly reduces the number of setpoints that must be examined to obtain a concave majorant estimate. • Complexity is sub-linear in the number of setpoints. • Works best when most operational dimensions are monotonic. • Results • No significant reduction in solution quality. • Order of magnitude reduction in optimization time.