1. Progress in Sensor Management for Integrated Surveillance
MURI Meeting
David A Castañón
November 3, 2008

2. Key Challenges Heterogeneous multimodal Sensors
Challenging environments
Unconventional targets
Distributed, time-varying platform suites

3. Sensor Management Key focus: Multisensor, multitarget algorithms
Outline:
Performance prediction: multitarget multiplatform multifunction radar systems
Adaptive wide area search: sparsity-constrained multiresolution radar search
Constraint Generation and Integer Programming for Information-Theoretic Sensor Management
Castanon Topic
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

4. Paradigm: Multi-server Systems
Sensors as network providers of service, targets as jobs
Overlapping fields of regard, limited capacity
Optimize allocation of bundles of resources to jobs subject to capacity and reachability
Characterize achievable network performance
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

5. Multitarget multiplatform, multifunction radar management
Objectives:
Wide Area Search
Track Initiation
Track Updates
Classification
targets
time=t+
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

6. Objective: performance prediction
Radar constraints:
multipulse radar can be allocated to multiple tasks: target tracking, wide area search,...
number of radar pulses affect MSTE/ROC and time spent on a given task
Objective: predict overall system capabilities
maximum number of targets that can be reliably tracked with a given number of radars?
system loading and load margin available for other tasks (discrimination, kill assessment, search)?
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

7. APPROACH A guaranteed uncertainty management (GUM) framework
Radar system performance prediction determines level of effort per function (search, track update, classify)
Guarantee specified level of track/detection accuracy (std error of 2%, 5% FA and 1% M)‏
Scheduling allocates level of effort from available resources
Need to specify stable regime of system operation
An combination of information theoretic uncertainty management and prioritized longest queue (PLQ) resource allocation
Related to multiprocessor policy of Wasserman et al (’06) for multi-queuing systems.
Uses information analysis to link pulses to performance, uncertainty
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

8. Uncertainty management and PLQ
Service
Load
Target
Uncertainty
Policy is analogous to optimal processor
allocation in heterogeneous multiple queueing
systems (Wasserman&etal:2006)
PLQ: idle radar assigned to task that needs most
Resources (as measured by weighted service time)
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

9. PLQ Stability Analysis
Radar resource need for nth target after  secs elapsed (CT expected volume, C0 FOV)
As radar load grows super-linearly in time system stability is the central issue
Cumulative service time to revisit all N targets once (assuming order is preserved in growth of uncertainty)
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

10. Track-only stability condition
For stable operation of radar system
where (balance equation)‏
Track-only system capacity: = maximum number of targets for
which solution exists
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

11. Multi-tasking stability: load margin
Assuming radar operates below capacity, headroom exists for other tasks.
Search load:
Discrimination load:
Condition for stability with additional load 
Excess capacity and occupancy
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

12. Illustration: 24 Swerling II targets
C-band radar (4Mhz)‏
PRI=1ms (150km)‏
Range res=150m
# pulses=10
(Pf,Pd) = ( , )‏
Target speed=300m/s
Speed std error=30m/s
Direction std error=18deg
System is underprovisioned
Stable track maintenance impossible
Load curve lies above diagonal
Max number of trackable targets is 23
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

13. Illustration: 12 Swerling II targets
C-band radar (4Mhz)‏
PRI=1ms (150km)‏
Range res=150m
# pulses=10
(Pf,Pd) = ( , )‏
Target speed=300m/s
Speed std error=30m/s
Direction std error=18deg
System has excess capacity
Load margin is and occupancy is 70%
Track-only load curve below diagonal
Can handle up to 23 targets
With12 targets extra 0.2 secs to spare
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

14. Discussion
GUM performance prediction framework specifies capacity and stability of single and multiple radar systems
Can analyze different scheduling policies
Information theoretic analysis determines needed resources to maintain performance
The system capacity and stability depend on the prescribed maximum track and detect uncertainty
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

15. Adaptive wide area search
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

16. Problem Setup Set of all cells ROI ROI indicator
Spatio-temporal energy allocation policy
Observations
Uniform spatial allocation:
Ideal spatial allocation:
Optimal N-step: multistage stochastic control problem
Simpler: two-step optimal
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

17. Optimal Strategy: Adaptive Resource Allocation Policy (ARAP)
Assumptions:
Uniform prior on each cell
Infinitely divisible effort per cell
Algorithm:
Assume uniform effort e1* and collect
measurement y(t)
Process y(t) to derive posteriors on each cell
Allocate remaining effort optimally based
on posteriors
Result: ARAP
Can solve simultaneous equations to determine e1*
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

18. Comparisons Wide area SAR acquisition Optimal two step SAR acquisition
Overall energy allocated is identical in both cases
Wide area SAR
acquisition
Optimal two step SAR
acquisition
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

19. New Results: M-ARAP Extend ARAP to account for
time constraints (number of chips acquired)‏
radar beam shape (footprint)‏
extended targets
multi-resolution search implementation
Modified measurement model incorporates spatial point spread function H(t)‏
Features of two-step M-ARAP search algorithm
motivated by pooled statistical sampling
assigns energy to regions with high posterior probability of containing targets
is a multi-resolution extension of the ARAP search algorithm presented at last review.
Is low computational complexity - O(Q)‏
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

20. Simulation of M-ARAP for MTI
Uniformly attenuating beam pattern
FOV is 66 x 66 km with pixel dimensions of 20 × 20 m
Radar resolution cell is 100 × 100 × 150 m.
Sparsity level p = was selected Q = 4082
Identical targets with target reflection distribution modeling an aircraft similar to an Airbus A-320.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

21. M-ARAP for MTI tracking radar
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

22. Correct detection probability vs false discovery rate
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

23. Optimal energy allocation
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

24. Discussion
M-ARAP searches for P sparsely distributed but clustered targets over Q search cells with minimum time and energy constraints
Can attain 7dB MSE reduction at SNR of 5 dB using only N=Q/P samples
Objective function J is related to the KL information divergence and the Fisher information under a Gaussian measurement model
J only depends on the cumulative energy allocated to each voxel in the image volume (deferred reward)‏
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

25. Multisensor Information Theoretic Allocation using Integer Programming

26. Selection structures
Problem: Select group of measurements to allocate to each target
One common selection structure allows you to select any K observations from a larger set (“K-element subset selection”)
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

27. Selection structures
Another common selection structure is one involving a number of sets, in which you may select one or more observations from each set
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

28. Submodularity
Earlier work: developing computable bounds for greedy information gathering.
Greedy generation of constraint sets
Computable bound gives guarantee on performance relative to an upper bound on optimal constraint generation.
Steps:
1. Definition of MI
2. Observations zC are independent of zB conditioned on X
3. Conditioning reduces entropy
4. Definition of MI
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

29. Directed search Due to submodularity:
A family of tighter upper bounds: ( denotes the observations corresponding to the elements in set )
We utilize this concept by using a collection of candidate subsets and exploration subsets
Suppose we want to find an upper bound to the reward of this subset of observations. We can easily do so by applying the chain rule, and then dropping some subset of conditionings. Here we have removed all conditionings. The fewer conditioning observations we drop, the tighter upper bound we obtain.
Here we’ve obtained an upper bound as the reward of subset A plus the incremental reward of each element in the difference set B\A conditioned on only subset A (it is an upper bound as we have dropped the conditioning on the previous elements in the sum). Since we can choose any set A < B, this provides a family of upper bounds, which becomes tighter as A grows closer to B.
We exploit this family of upper bounds by constructing a solution which utilizes candidate subsets — these sets A for which we have evaluated the true reward, and exploration subsets — additional elements that can be added to a given candidate subset, and for which we have evaluated the incremental reward conditioned on the candidate subset A.
Notice that if there is only one element in B\A, the upper bound is tight; otherwise we need to grow A closer to B to make the bound closer to tight.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

30. Integer programming formulation
Assign bundles of measurements to objects
Each measurement can only be in one bundle
Every object must receive a bundle
Value is additive across objects
This is the integer program that we would ideally like to solve. The variables over which we are optimizing are these binary indicator variables; omegaiAi is one if we select subset Ai for object i and zero otherwise; this constraint requires that exactly one subset should be selected for each object. The reward is the sum of the rewards for the subsets selected for each object.
This constraint requires that each resource is used at most once. The structure of the integer program is similar to an assignment problem, assigning subsets to objects. However, in general each subset utilizes multiple resources, so the structure required for efficient solution is not present. Furthermore, the number of subsets from which we will be choosing will be prohibitively large for problems of realistic size.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

31. Iterative integer programing formulation
Assign from existing
bundle list plus add individual assignments
Use information theory upper bound to value incrementing a bundle with additional assignments
To address this difficulty, we solve a series of integer programs which exploit the structure examined a couple of slides ago. Each integer program is an upper bound to the optimal solution, and an algorithm uses the results of each integer program to tighten the upper bounds.
The integer program is very similar to the previous one except that rather than explicitly enumerating all possible subsets, we use a compact representation consisting of candidate subsets script T, which may be combined with exploration subset elements.
Again, each resource can be used at most once, either by a candidate subset or an exploration subset element, and exactly one candidate subset must be chosen for each object. This additional constraint specifies that the exploration subset elements corresponding to a given candidate subset can only be selected if the candidate subset is selected.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

32. Comments
At every iteration, the solution of the integer program for that iteration is an upper bound to the optimal reward.
The bound becomes tighter with each iteration.
At termination an optimal solution is found.
We can also add a small number of constraints to the integer program to find an auxiliary problem that provides a lower bound to the optimal reward, which also becomes tighter with each iteration and converges to the optimum.
The important results of the integer program is that at it provides an upper bound to the optimal reward. The update algorithm which uses the results of the integer program ensures that the bound tightens with each iteration, and converges to the optimal solution. We can also add a small number of constraints to the integer program to find an auxiliary problem that provides a lower bound, along with a solution attaining that lower bound, which also becomes tighter with each iteration and converges to the optimal reward. By combining the upper and lower bounds, we can terminate when we are within a desired fraction of optimality. In our experiments, we terminate when we are within 5% of optimality.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

33. Experiment Tracking 50 objects
Sensor can provide (for any single object) either
Azimuth and range
Azimuth and range rate
Sensor moves in a race-track pattern, azimuth noise varies with actual azimuth (smallest when object is broadside)
Observation noise increases when objects are closely spaced
The sensor can also obtain a more accurate azimuth/range or azimuth/range rate observation in 3 time steps
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

34. Results – performance
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

35. Results – computation time
Brute force for 20 steps requires >> 1040 reward evaluations
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

36. Experiment Tracking 50 objects for 50 time slots
The initial uncertainty of the first 25 objects is slightly lower
Any object can be observed in any time slot
The observation noise for the first 25 objects increases by a factor of 106 half-way through the simulation
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

37. Results – performance
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

38. Multisensor Feedback Sensor Management

39. Previous Work Classification with distributed multi-mode radars
Vehicles with multiple sensors, multiple modes
Stationary objects of unknown type
Choose how to use sensors (modes), + where to point them
Known object locations, widely spaced (one object, one beam)
Want: adaptive policies to allocate resources for optimization of classification accuracy given resource constraints
Previous Results
Bounds on achievable performance based on expansion of admissible feedback policies
Characterization of optimal policies for performance bounds
Approximate policies with performance close to bounds
Simple demonstrations using simulation
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

40. Approach: Pricing Algorithms for Scalable Sensor Management
Avoids exponential explosion in
Scenario states
Potential sensor actions Not suitable for real-time
Uses prices for sensor utility based on scenario information to coordinate solution of subproblems
Pricing problem is linear programming problem using column generation
Resource
Price
Update
Resource
Utilization
Prices
Target 1
Subproblem
Target N
Subproblem
Strategy for target subproblems used to estimate utilization for price updates
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

41. Key Extensions Needed Improved inference models
Expand from conditionally independent classifications to feature-based observations
Objects = frames of scattering centers (Moses/Potter model)
Intrinsic orientation-related quality for class separation
More comprehensive missions
Target dynamics, detection, tracking, classification
Time-varying sensor observability
Focus on this topic
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

42. Initial Extension: Target Arrivals
Objects may be located in discrete cells
Cell contents unknown, may be empty
Have search modes for detection in addition to different classification modes
Empty cells may have new targets arriving as function of time: Hidden Markov Model
Need to keep revisit to detect new arrivals
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

43. Initial Extension: Target Arrivals
SAM
Truck
Car
Empty
1.0
0.80
0.10
0.06
0.04
Cell states are no longer stationary
Model state changes with HMM
Add extra state to statespace
X := X  {empty}
Add extra action
A := A  {wait}
Now must choose between:
Waiting to take measurements in case target shows up
Taking no measurements at all (deciding apriori)
Making use of all available time to take as many measurements as possible
Note: actions are not ‘taken off the table’ over time!
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

44. Model Consequences
Main decomposition result derived previously is no longer valid!
Previously, optimal strategies were “local” in that actions chosen per objects depended only on knowledge about that object, and not other objects
Performance was invariant to order of actions across objects –> easy “stitching”
Problem: when search is included, need to consider total schedule across sensor actions for different cells to evaluate the effect of searching a potentially empty cell
“When” needs to be absolute in HMM
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

45. Improved Model
Bin sensor time into discrete time bins and impose sensor resource constraint for each discrete bin
Allows for time-varying performance model for sensors
Obscuration, temporal performance variations, …
Can now develop approach as before, with explicit discrete time
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

46. Results Lower bound results from constraint relaxation
Lower bound problem can be solved with “separable” or “local” feedback strategies using pricing
However, prices now are indexed by Sensor and discrete time
Larger-dimensional optimization in price space  Robust code developed using column generation + LP solver and POMDP
Optimal mixed strategies are mixtures of larger number of strategies
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

47. Example: Search and Classify
100 cells, 10 known target locations, plus 90 cells with potential target arrivals
3 types of objects: Cars, Trucks, TELs
5 discrete time periods
2 similar sensors, with different fields of regard
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

48. Example: Search and Classify
Sensor Model for
Set likelihoods for search to not discriminate between targets
Ex. consider 3 modes {search, mode1, mode2} and 4 target types: {empty, car, truck, TEL}
Make search action much cheaper than other actions
Now POMDP can first use ‘search’ to detect if a target is present
Then follow-up with mode1 / mode2 to determine type
Empty
Car
Truck
TEL
Search Action
Mode1 Action
Mode2 Action
Should comment on the difference between mode1 and mode2.
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

49. Policy Graphs with Arrivals + Search
90 never-before-seen objects and 10 with prior info, K=1, M=4
Strategy 1: mixture weight 0.726
Strategy 2: mixture weight 0.274
X =
{military,
truck,
car,
empty}
i[0..9]
./column_gen -dom_check true -method grid -fg_type search -fg_purge normal_prune -proj_purge domonly -fg_epsilon 1.0e-9 -fg_points scenario_filename ../../sensor_management/searchAndExploitColumnGen_ver2.data -pomdp ../../sensor_management/searchAndExploit_ver2.POMDP
Horizon(6) NumRuns(1) NumTargets(100) NumSensors(1) NumSensorActions(4) NumDecisions(3) NumResLevels(1) MaxMDToFARatio(1)
States: { military, truck, car, empty}
Actions: { wait, search, mode1, mode2}
Observations: { obsNothing, obsNonMilitary, obsMilitary}
SensorTimeCost:
initLambda: 0.001
ResLevel0( )
Initial Hyperplane 0 declareEmpty (-1.000, , , 0.000)
Initial Hyperplane 1 declareNonMil (-1.000, 0.000, 0.000, )
Initial Hyperplane 2 declareMil (0.000, , , )
TaskList(0:9) P[class type]: (0.100, 0.200, 0.600, 0.100)
TaskList(10:99) P[class type]: (0.020, 0.060, 0.120, 0.800)
# Transition probabilities
T: * : military
T: * : truck
T: * : car
T: * : empty
# Observations obsNothing obsNonMilitary obsMilitary
O: wait uniform
O: search : military
O: search : truck
O: search : car
O: search : empty
O: mode1 : military
O: mode1 : truck
O: mode1 : car
O: mode1 : empty
O: mode2 : military
O: mode2 : truck
O: mode2 : car
O: mode2 : empty
Final Simulation Results:
C C C C C C C7
Minimize
R <= 100
R = 1
Actual values of the variables: C C C C C C C
Lambda Trajectory:
Finished ComputeBestStrategies: userTime(8.830) systemTime(0.370) !
TaskList(0) Value(0.2000) avg_J_classify(0.1242) avg_J_measure(0.0000, , , )
Column(5): initNode(5) J_classify(0.1242) J_measure( , , , )
Column(7): initNode(6) J_classify(0.1242) J_measure( , , , )
P[class type]: (0.100, 0.200, 0.600, 0.100)
TaskList(50) Value(0.3810) avg_J_classify(0.0949) avg_J_measure(0.0000, , , )
Column(5): initNode(43) J_classify(0.0834) J_measure( , , , )
Column(7): initNode(18) J_classify(0.1253) J_measure( , , , )
P[class type]: (0.020, 0.060, 0.120, 0.800)
BestCosts = [[ ]];
i[10..99]
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

50. ROC Curves For Example Resources = 300 vs (150,150) Resources =
Plots of J vs. MD = [1..80] with FA = 1, (K=1 M = 2) vs (K=2, M = 1)
Resources =
300 vs (150,150)
Resources =
500 vs (250,250)
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

51. ADD WORDS HERE THAT MAKE SENSE
Summary
ADD WORDS HERE THAT MAKE SENSE
MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation