An Agenda for Information Theory Research in Sensor Networks

1. 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

2. 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

3. 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

4. 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…

5. 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

6. 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…

7. 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

8. 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

9. 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

10. 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

11. 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

12. Model and Data Uncertainty in Sensor Networks Data Uncertainty • 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, exchange reputation information, and then interact with mobile audit node Model Uncertainty How many nodes must sample a field to determine it is caused by one (or more) point sources?

13. 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

14. 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

15. 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

16. 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

17. 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

18. Early Experiments • 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 • 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.

19. If 2 levels are good, n levels are even better! Daily Average Temperature (Geostatistical Analyst) Aspect (Spatial Analyst) Slope (Spatial Analyst) Elevation (Calculated from Contour Map) Aerial Photograph (10.16cm/pixels) Extend model to include remote sensing; additional levels of “side information” and/or sources for data fusion Graphs 3D Images

20. 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

21. 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