Distributed Data Association for Multi-Target Tracking in Sensor Networks

1. Distributed Data Association for Multi-Target Tracking in Sensor Networks Alan S. Willsky SensorWeb MURI Review Meeting December 2, 2005

2. A Notional Example Multiple sensors with one or more bearing or location measurements Possibly additional signal features Challenge: Scalable and resource-aware algorithms for data association and tracking/estimation under network constraints

3. Reminder of where we were last year • Inference algorithms for graphical models • Exploitation of embedded tractable subgraphs • Truly optimal algorithms through “tree-reweighting” • Formulation of approaches to data association as problems in inference for graphical models • Automatic construction of sensor-target-region graphical models • Communication-sensitive message passing protocol • Experimental results demonstrating the power of this method and a performance-versus-comms-load threshold effect • Demonstration of scalability • New approach to inference for continuous variables: Non-parametric Belief Propagation (NBP)

4. What we’ve done lately • Important new approaches to high-performance inference for graphical models • Recursive Cavity Modeling for near-optimal inference • Walk-sum analysis of message-passing algorithms • Neither will be discussed today • Substantial extension of our graphical model-based methods for multi-target tracking • A new approach to dynamic hypothesis management for multitarget tracking • New graphical model structure • Use of NBP to manage hypotheses • Natural accommodation of late-arriving data

5. Distributed data association using advanced methods for graphical models • Why graphical models? • Natural match to sensor networks • A variety of parallel message-passing algorithms that provide basis for comms-constrained solutions and tradeoff analysis • How do data association problems map to graphical model inference problems? • Several approaches, which highlight key issues • Careful “hybrid” organization of hypotheses • Different approaches for “organized” networks and networks requiring some degree of organization

6. Data association in an organized network

7. Graphical models for organized networks - I • Sensor-oriented modeling • Nodes correspond only to sensors – GOOD! • Node variables correspond to associations of measurements for each individual sensor • Trouble if > 2 sensors cover same region – BAD! • Leads to complex, messaging among many sensors • Target-oriented modeling • Nodes correspond to targets – BAD! • Has straightforward, graphically simple messaging structure – GOOD!

8. Graphical models for organized networks - II • Hybrid models • Start from sensor-based model • Introduce target nodes only for targets seen by more than two sensors • Leads to models with pairwise cliques only • Mapping of inference computations and messages to physical nodes and comms • “Maximally explicit” • Makes crystal clear an important issue related to target handoff (which node takes responsibility for which target) • Easy to construct automatically and efficiently

9. Region-based representation when self-organization needs to be accomplished • Elementary variables are the numbers of objects in each of a set of disjoint subregions covering the surveillance region • Each subregion is that surveilled by a specific subset of sensors • For simplicity, assume sensors are very simple “proximity” indicators • Local signal processing provides likelihood function for the number of targets present within the range of that sensor • Effects of individual false alarms and missed detections are captured in these local likelihood functions

10. Algorithmic Complexity • In fully asynchronous, comms-unconstrained implementation • Complexity per sensor per iteration is constant • This is the key to scalability • The value of that constant depends on sensor/target densities: • Number of targets seen by each sensor • Number of targets seen by more than two sensors • Number of sensors which all overlap the same subregion

11. Communications-sensitive message-passing • Objective: • Provide each node with computationally simple (and completely local) mechanism to decide if sending a message is worth it • Need to adapt the algorithm in a simple way so that each node has a mechanism for updating its beliefs when it doesn’t receive a full set of messages • Simple rule: • Don’t send a message if the K-L divergence from the previous message falls below a threshold • If a node doesn’t receive a message, use the last one sent (which requires a bit of memory: to save the last one sent)

12. Experiments to assess tradeoff of comms vs performance • 25 sensors • ~40-75 targets (2-4 seen by each sensor) • Results: • Sharp transitions in tradeoff as a function of message tolerance threshold • Provides rational basis for setting threshold • When using suboptimal inference algorithms (e.g., loopy BP): • Stopping messaging can improve performance! • Dynamics of messaging provides scenario-dependent adaptivity automatically

13. Typical example for organized network data association

14. Illustrating comms-sensitive message-passing dynamics Self-organization with region-based representation Organized network data association

15. “Partially-Organized” Network • Include sensor, target, and region nodes • Sensors linked to regions (which measurements go with which region?) • Targets are linked to regions (in which region is each target?)

16. N-Scan Tracking and Data Association • Widely used in multiple hypothesis tracking • Defer making hypothesis decisions about target tracks until additional information is available • Usual “track-based” approach has exponential complexity

17. An Equivalent Graphical Representation • Add nodes that allow us to separate target dynamics from discrete data associations • Perform explicit data association within each frame (using evidence from other frames) • Stitch across time through temporal dynamics

18. Hybrid Message Passing - I • Discrete BP in the discrete subgraph for each scan • NBP for the continuous tracking • Distribution for each target at each time is a sum of many terms (corresponding to all of the possible measurement associations) • However, one key is that NBP samples these distributions

19. Hybrid Message Passing - II • Stitching discrete and continuous nodes • Discrete-to-continuous node messages • Mixtures weighted by current discrete-node probabilities for alternate association hypotheses • Continuous-to-discrete node messages • Updated evidence from current continuous-node track distribution for alternate association hypotheses

20. Hybrid Message Passing - III • The big win: • We still maintain explicit data association at each frame • However, we avoid the computationally disastrous problem of enumerating all data associations across time • Instead, we let NBP-based sampling provide statistically significant evidence for enhanced data association through the use of multiple scans

21. An Example: 20 targets, 25 sensors • Each sensor has ~ 5 targets within its coverage region (and sensors are also subject to false alarms and missed detections)

22. A small example

23. The Way Ahead - I • Further savings over standard MHT: • Hypothesis pruning • Use K-L divergence to decide when there is no more evidence to enhance particular data associations • Hypothesis merging • Use K-L divergence to decide when two or more alternate data association hypotheses lead to nearly identical target track distributions

24. The Way Ahead - II • More detailed look at comms-sensitive message-passing • Depends on where non-sensor node computations are done • Messages internal to a single processor should be censored only for the control of hypothesis explosion (which might have a different threshold) • This begs the question of how one assigns inference responsibilities to nodes • AND to the question of how these are handed off as tracks move • There’s a comms cost of handoff!

25. The Way Ahead - III • Enhancing performance through the use of our emerging, new methods for inference in graphical models • Recursive cavity modeling • Involve propagating information out radially from initiating nodes (and then back toward these nodes) • Walk-sum-based algorithms • Takes greater advantage of local memory at each processing node