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 networksConclusions: Steps to application

Overview of Approaches

We develop heuristics more powerful than greedy, not compromising speedExact methods tuned for domain structureOverall 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

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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

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Initial Assumptions

Each sensor can only track one target at a time 3 sensors are required to track a target

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Initial Graph Model

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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

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Constrained Graph Modelsensors targets

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possible solution

Description of Experiments

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Start with square area with unit sidesPlace sensors and targets randomly in area

sensorsensor

targettarget

Create communication graph based on range C

sensorsensor

targettarget

CC

Create communication graph based on range C

sensorsensor

targettarget

CC

Create communication graph based on range C

sensorsensor

targettarget

CC

Create visibility graph based on radar range R

sensorsensor

targettarget

RR

Create visibility graph based on radar range R

sensorsensor

targettarget

RRRR

Create visibility graph based on radar range R

sensorsensor

targettarget

RR

Combine the communication and visibility graphs

sensorsensor

targettarget

Limit cases

Phase Transition w.r.t. Communication Range:

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Experiments with a configuration of 9 sensors and 3 targets such that there is a communication channel between two sensors with probability p

Pro

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all

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Communication edge probability p

Insights into the designand operation of sensor networks w.r.t. communication range

Special case:all targets arevisible to all sensors

Phase Transition w.r.t. Radar Detection Range

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Experiments with a configuration of 9 sensors and 3 targets such that each sensor is able to detect targets within a range R

Pro

babili

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all

targ

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Normalized Radar Range R

Insights into the designand operation of sensor networks w.r.t. radar detection range

Special case: all nodes cancommunicate

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 functionDefine such that each sensor, with info from its 1-hop neighbors, can determine which target to trackPotential 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 www.cs.huji.ac.il/~jsch/beautifulmovies/movies.html(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 P1, P2, … Pn , one for each agent There are intra-agent constraints and inter-

agent constraints

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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.)

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Computational ComplexityComputational Complexity: total computation cost for all agents

Communication ComplexityCommunication 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

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Communication vs. Radar Range vs. Computation

Average Complexity (target-centered)

• 5 targets and 17 sensors

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Mean computational cost

Probability of Tracking

Average Complexity (target-centered)

• 5 targets and 17 sensors

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Probability of Tracking Mean 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 costsRealistic criterion for successful trackingSpecialize to a plausible, full-scale deployed system

Dynamic Bayesian Model

Joint work with Matt Thomas, AFRLCreate 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?

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Summary

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.

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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

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