Wireless Distributed Sensor Tracking: Computation and Communication Bart Selman, Carla Gomes, Scott Kirkpatrick, Ramon Bejar, Bhaskar Krishnamachari, Johannes Schneider Intelligent Information Systems Institute, Cornell University & Hebrew University Autonomous Negotiating Teams Principal Investigators' Meeting, Dec. 17, 2001

Outline Overview of our approaches Ants - Challenge Problem (Sensor Array) Exact methods  Determination of the phase diagram Results from physical model (annealing) Distributed CSP model Dynamic Bayesian networks Conclusions: Steps to application

Overview of Approaches We develop heuristics more powerful than greedy, not compromising speed Exact methods tuned for domain structure Overall theme --- Identification of domain structural features  tractable vs. intractable subclasses  phase transition phenomena  backbone Goal:  Principled, controlled, hardness-aware systems

ANTs Challenge Problem Multiple doppler radar sensors track moving targets Energy limited sensors Communication constraints Distributed computation Dynamic system IISI, Cornell University

Models Start with a simple graph model Refine in stages to approximate the real situation: Static weakly-constrained model Add communication, target range constraints Physical model allows full range of real constraints, incorporate target acquisition… Distributed constraint satisfaction model Goals: Algorithms that scale for this problem Understand the sources of complexity IISI, Cornell University

Initial Assumptions Each sensor can only track one target at a time 3 sensors are required to track a target IISI, Cornell University

Initial Graph Model IISI, Cornell University The initial model presented is a bipartite graph, and this problem can be solved using a maximum flow algorithm in polynomial time Results incorporated into framework developed by Milind Tambe’s group at ISI, USC Joint work in progress Sensor nodes Target nodes

IISI, Cornell University Constrained Graph Model sensors targets communication links possible solution

Description of Experiments IISI, Cornell University Start with square area with unit sidesPlace sensors and targets randomly in areasensor target Create communication graph based on range Csensor target C sensor target C sensor target C Create visibility graph based on radar range R sensor target R sensor target RR sensor target R Combine the communication and visibility graphssensor target

Limit cases

Phase Transition w.r.t. Communication Range: IISI, Cornell University Experiments with a configuration of 9 sensors and 3 targets such that there is a communication channel between two sensors with probability p Probability( all targets tracked ) Communication edge probability p Insights into the design and operation of sensor networks w.r.t. communication range Special case: all targets are visible to all sensors

Phase Transition w.r.t. Radar Detection Range IISI, Cornell University Experiments with a configuration of 9 sensors and 3 targets such that each sensor is able to detect targets within a range R Probability( all targets tracked ) Normalized Radar Range R Insights into the design and operation of sensor networks w.r.t. radar detection range Special case: all nodes can communicate

The full picture Communication vs. Radar Range vs. Performance

Performance and Phase Boundaries Natural units: sensors/target, sensors within range of a target, sensors communicating with a sensor 19 sensors, 5 targets

Phase diagram for the sensor array 3D phase diagram is bounded by: 3+ sensors/target 3+ sensors within range of each target 2+ one-hop neighbors for each sensor

Physical model (and annealing) Represent acquisition and tracking goals in terms of a system objective function Define such that each sensor, with info from its 1- hop neighbors, can determine which target to track Potential per target depends on # of sensors tracking

More on annealing Target Cluster (TC) is >2 1-hop sensors tracking the same target – enough to triangulate and reach a decision on response. Classic technique – Metropolis method simulates asynchronous sensor decision, thermal annealing allows broader search (with uphill moves) than greedy, under control of annealing schedule. Our results on the unconstrained problem validate the objective function, converge with as few as three iterations per sensor.

Moving targets, tracking and acquisition 100 sensors, t targets (t=5-30) incident on the array, curving at random. Movies of 100 frames for each of several values of (sensors in range)/target and (1- hop neighbors)/sensor. Sensors on a regular lattice, with small irregularities. Between each frame a “bounce,” or partial anneal using only a low temperature, is performed to preserve features of the previous solution as targets move.

Moving Targets -- Movies Conventions: Targets Target range Sensors  Sector active Target Clusters Coverage

Analyzing the movies Summary frames: easy case (10 targets) hard case (30 targets) color code: red (1 TC), green (2 TCs), blue (3 TCs), purple (4TCs), …

Examples of physical model solutions See (these are 12-20MB animated gif files, so I will run my examples from local copies) Three lattices (hex, square, triangular) Target detection range = 1.5, 2, 3, 4x nngbr dist. Avg. # of neighboring sensors from 4.5 (hex) to 7 (triangular) examples:

Analysis of physical model results When t targets arrive at once, perfect tracking can take time to be achieved. Target is considered “tracked” when a TC of 3+ sensors keeps it in view continuously. We analyze each movie for longest continuous period of coverage of each target, report minimum and average over all targets.

Results with moving targets Target visibility range and targets/sensor bounds seen:

Distributed Computational Model In a Distributed Constraint Satisfaction Problem (DCSP), variables and constraints are distributed among multiple agents. It consists of: A set of agents 1, 2, … n A set of CSPs P 1, P 2, … P n, one for each agent There are intra-agent constraints and inter-agent constraints IISI, Cornell University

DCSP Models With the DCSP models, we study both per-node computational costs as well as inter-node communication costs DCSP algorithms: DIBT (Hamadi et al.) and ABT (Yokoo et al.) IISI, Cornell University

Computational Complexity Computational Complexity: total computation cost for all agents Communication Complexity Communication Complexity: total number of messages sent by all agents Communication range / Sensor (radar) range provides 3rd dimension. These measures can vary for the same problem when using different DCSP models IISI, Cornell University Communication vs. Radar Range vs. Computation

Average Complexity (target-centered) 5 targets and 17 sensors IISI, Cornell University Mean computational costProbability of Tracking

Average Complexity (target-centered) 5 targets and 17 sensors IISI, Cornell University Probability of TrackingMean communication cost

Next Steps

Physical Model Increased realism in the objective function Energy costs of excessive coverage – handoff policy Sector switching – delay and energy costs Geometrical constraints for accurate tracking Continuous asynchronous tracking More accurate model of target acquisition Optimize to reduce communication costs Realistic criterion for successful tracking Specialize to a plausible, full-scale deployed system

Dynamic Bayesian Model Joint work with Matt Thomas, AFRL Create dynamic Bayes network (with probabilistic information about domain state) within traditional influence diagram. Use this approach to handle turning off sensors as much as possible for energy conservation.

Dynamic DCSP Model Further refinement of the model: incorporate target mobility The graph topology changes with time What are the complexity issues when online distributed algorithms are used? IISI, Cornell University

Summary

Graph-based and physical models capture the ANTs challenge domain Results on the tradeoffs between: Computation, Communication, Radar range, and Performance are captured in phase diagram. Results enable a more principled and efficient design of distributed sensor networks. Techniques handle realistic constraints, fast enough for use in real distributed system. IISI, Cornell University

Collaborations / Interactions ISI: Analytic Tools to Evaluate Negotiation Difficulty Design and evaluation of SAT encodings for CAMERA’s scheduling task. ISI: DYNAMITE Formal complexity analysis DCSP model (e.g., characterization of tractable subclasses). UMASS: Scalable RT Negotiating Toolkit Analysis of complexity of negotiation protocols.

The End IISI, Cornell University