Progress in Sensor Management for Integrated Surveillance

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. Service Load Target Uncertainty Uncertainty management and PLQ 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) = (0.000001, 0.9999)‏ • 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) = (0.000001, 0.9999)‏ • Target speed=300m/s • Speed std error=30m/s • Direction std error=18deg • System has excess capacity • Load margin is 0.176 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 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 • 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)‏ • 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)‏ 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 = 0.0007 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. 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

24. Multisensor Information Theoretic Allocation using Integer Programming

25. 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

26. 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

27. 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. MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

28. 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 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

29. 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 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

30. 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 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

31. 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. MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

32. 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

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

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

35. Multisensor Adaptive Dynamic Sensor Management

36. 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

37. 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

38. 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

39. 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

40. 1.0 1.0 1.0 0.80 SAM Truck Car Empty 0.04 0.06 0.10 Initial Extension: Target Arrivals • 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

41. 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

42. 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

43. 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

44. 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

45. Search Action Mode1 Action Mode2 Action Empty Car Truck TEL 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 MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

46. i[0..9] i[10..99] 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} MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation

47. ROC Curves For Example • 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

48. Future Directions • Multi-task multi-platform guaranteed uncertainty sensor management (SM) • Multistatic sensor management for tomographic target recognition • Integration of improved information theoretic performance models into SM • Multiplatform trajectory optimization for SM • Distributed SM algorithms • Performance bounds for layered ATE systems MURI: Integrated Fusion, Performance Prediction, and Sensor Management for Automatic Target Exploitation