An Agenda for Information Theory Research in Sensor Networks

Outline

• Introduction• The Conventional Paradigm• The Emerging Paradigm• New Theory Challenges

Greg Pottie

UCLA EE Department

Center for Embedded Networked Sensing

Pottie@icsl.ucla.edu

Introduction

• Much research has focused upon sensor networks with some alternative assumption sets:– Memory, processing, and sensing will be cheap, but

communications will be dear; thus in deploying large numbers of sensors concentrate on algorithms that limit communications but allow large numbers of nodes

– For the sensors to be cheap, even the processing should be limited; thus in deploying even larger numbers of sensors concentrate on algorithms that limit both processing and communications

• In either case, compelling theory can be constructed for random deployments with large numbers and flat architectures

Theory for Dense Flat Networks of Simple Nodes

• Redundant communications pathways given unreliable radios

• Data aggregation and distributed fusion– Combinations with routing, connections with network rate distortion

coding

• Scalability• Density/reliability/accuracy trades• Cooperative communication• Adaptive fidelity/network lifetime trades

What applications?

• Early research concentrated on short-term military deployments– Can imagine that leaving batteries everywhere is at least as

acceptable as leaving depleted uranium bullets; careful placement/removal might expose personnel to danger

– Detection of vehicles (and even ID of type) and detection of personnel can be accomplished with relatively inexpensive sensors that don’t need re-calibration or programming in the field

• Story was plausible…

But was this ever done?

• Military surveillance– Largest deployment (1000 nodes or so) was in fact hierarchical and

required careful placement; major issues with radio propagation even on flat terrain

– Vehicles are really easy to detect with aerial assets, and the major problem with personnel is establishment of intent; this requires a sequence of images

– Our major problems are not battles, but insurgencies, which demand much longer-term monitoring as well as concealment

• Science applications diverge even more in basic requirements– Scientists want to know precisely where things are; cannot leave

heavy metals behind; many other issues

• Will still want dense networks of simple nodes in some locations, but will be system component

Sampling and Sensor Networks

• Basic goal is to enable new science– Discover things we don’t know now– Do this at unprecedented scales in remote locations

• This is a data-driven process: measure phenomena, build models, make more measurements, validate or reject models, … continue

• Spatiotemporal sampling: a fundamental problem in the design of any ENS system– Spatial: Where to measure– Temporal: How often to measure

• (Nearly) all problems in ENS system design are related to sampling: coverage, deployment, time-sync, data-dissemination, sufficiency to test hypotheses, reliability…

Adaptive Sampling Strategies

• Over-deploy: focus on scheduling which nodes are on at a given time

• Actuate: work with smaller node densities, but allow nodes to move to respond to environmental dynamics

• Our apps are at large scales and highly dynamic: over-deployment not an option– Always undersampled with respect to some

phenomenon– Focus on infrastructure supported mobility– Passive supports (tethers, buoyancy)– Small number of moving nodes

• Will need to extend the limited sets of measurements with models

Evolution to More Intelligent Design

• Early sensor network research focused on resource constrained nodes and flat architecture– High density deployments with limited application set

• Many problems with this flat architecture– Software is nightmarish– Always undersample physical world in some respect– Logistics are very difficult; usually must carefully place, service,

and remove nodes

• The major constraint in sustained science observations is the sensor– Biofouling/calibration: must service the nodes

• Drives us towards tiered architecture that includes mobile nodes– Many new and exciting theory problems

Some Theory Problems

• Data Integrity– Sufficiency of network components/measurements to trust

results

• Model Uncertainty– Effects on deployment density, number of measurements

needed given uncertainty at different levels

• Multi-scale sensing– Information flows between levels; appropriate populations at

the different levels given sensing tasks– Local interactions assume increased importance

• Logistics management– Energy mules– Mobile/fixed node trades

Many Models

• Source Phenomena– Discrete sets vs. continuous, coupling to medium,

propagation medium, noise and interference processes

• Sensor Transduction– Coupling to medium, conversion to electrical signal, drift and

error sources

• Processing Abstractions– Transformation to reduced representations, fusion among

diverse sensor types

• System Performance– Reliability of components, time to store/transport data at

different levels of abstraction

Much Uncertainty

• Observations (Data)– Noisy, subject to imperfections of signal conversion,

interference, etc.

• Model Parameters– Weighting of statistical and deterministic components;

selection of model order

• Models– Particular probability density function family, differential

equation set, or in general combination of components

• Goals and System Interactions– Goals can shift with time, interactions with larger system not

always well-defined

Model and Data Uncertainty in Sensor Networks

• How much information is required to trust either data or a model?

• Approach: multi-level network and corresponding models; evaluation of sequence of observations/experiments

Multiple nodes observe source, exchangereputation information, and then interactwith mobile audit node

Data Uncertainty

How many nodes must sample a field to determine it is caused by one (or more) point sources?

Model Uncertainty

A Few Problems

• Validation (=debugging) is usually very painful– One part design, 1000 parts testing– Never exhaustively test with the most reliable method

• So how can we trust the result given all the uncertainties?– Not completely, so the design process deliberately minimizes the

uncertainties through re-use of trusted components

• But is the resulting modular model/design efficient?– Fortunately not for academics; one can always propose a more

efficient but untestable design

• Our goal: quantifying this efficiency vs. validation effort tradeoff in model creation for environmental applications

Universal Design Procedure

• Innovate as little as possible to achieve goals– Applies to surprisingly large number of domains of human

activity.

• Begin with what we know– E.g., trusted reference experiment, prior model(s)

• Validate a more efficient procedure– Exploit prior knowledge to test selected cases

• Bake-off the rival designs or hypotheses– Use your favorite measure of fitness

• Iterate– Result is usually a composite model with many components

Example: Radio Propagation

• Model from First Principles: Maxwell’s Equations– Complete description (until we get to the scale of quantum dynamics)

– Economy of principles

– Computationally intractable for large volumes

– Many parameters that must be empirically determined

• Practical approach: hybrid models– Start with geometric optics (rays+Huygen’s principle)

– Add statistical models for unobserved or dynamic factors in environment

– Choice of statistical models determined by geometric factors

– Deeper investigation as required using either extensive observations or occasional solution of Maxwell’s equations for sample volumes

– Level of detail in model depends on goals

Two-Level Models

• Each level in hierarchy contains reference experiments– Trusted, but resource intensive and/or limited to particular scales

• Higher level establishes context– Selects among set of models at lower level corresponding to each context

– Each of these sets contains a reference model/experimental procedure

• This system allows re-use of components– Limits validation requirements

– Extensible to new environments and scales by adding new modules

Example: Fiat Lux

• Top level: camera/laser mapper providing context and wider area coverage– Direct locations for PAR sensors to resolve ambiguities due to ground

cover

• Modular model construction– Begin with simple situations: pure geometric factors, calibration of

instruments

– Progress to add statistical components: swaying of branches, distributions of leaves/branches at different levels of canopy, ground cover

• Resulting model is hybrid combination of:– Deterministic causal effects

– Partially characterized causes (statistical descriptions)

• Level of detail depends on goals– Reconstruction, statistics or other function of observations

Early Experiments

• A homogeneous screen is placed to create a reflection Er proportional to incident light Ec.

• Camera captures the reflection on its CCD

• The image pixel intensity is transformed to Er using camera’s characteristic curve.

• Sensors with different modes and spatial resolutions– E.g. PAR sensor and camera– PAR measures local incident

intensity– Camera measures relative

reflected intensity

• Provides better spatial and temporal resolution, at cost of requiring careful calibration

• Analogous to remote sensing on local scales

Daily Average Temperature(Geostatistical Analyst)

Aspect(Spatial Analyst)

Slope(Spatial Analyst)

Elevation(Calculated from Contour Map)

Aerial Photograph(10.16cm/pixels)

If 2 levels are good, n levels are even better!

Hourly Temperature for June 5 2004

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Temperature

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3D Images

Graphs

Extend modelto include remotesensing;additional levels of “side information”and/or sources fordata fusion

Layers and Modules vs. Tabula Rasa Design

• Fresh approach (e.g. “cross-layer design”) allows optimization according to particular goals– Yields efficiency of operation

– But may lack robustness, and requires much larger validation effort each time new goals/conditions considered

– Size of model parameter set can be daunting

• Sequential set of experiments allows management of uncertainty at each step– Minimizes marginal effort; if each experiment or design in chain was of

interest, overall effort (likely) also minimized

– Naturally lends itself to Bayesian approach; many information theory opportunities

– But has an overhead in terms of components not required for given instantiation

• Research goal is quantification of efficiency/validation tradeoff

Conclusion

• Development of multi-layered systems– Physical phenomenon modeled at multiple abstraction layers

– Hardware has many levels from tags to mobile infrastructure

– Software abstractions and tools in support of this development

– Theoretical study of information flows among these levels

• New and interesting problems arise from real deployments– Even seemingly simple phenomena such as light patterns in forests

are amazingly complicated to model

– Approach through sequence of related experiments and models