Energy-Efficient Signal Processing and Communication Algorithms for Scalable Distributed Fusion

Wireless Sensor Networks for Fusion Sensor networks for environmental monitoring chemical/biological hazard detection surveillance and reconnaissance target detection and tracking

Smart Dust: Large Networks of Miniature Sensors Proposed Setting: Large collections of inexpensive miniature sensors randomly distributed integrated sensing, on-board processing (limited) wireless communication between nodes limited battery power per node and/or external powering Advantages: coverage; spatially diverse/rich sets of measurements potential for: fault-tolerant, readily scalable data collection systems long-term on-demand sensing with low-power designs

Signal Processing and Communication Challenges System constraints limited energy (and bandwidth) resources per sensor need for power-efficient processing algorithms and communication protocols limitations in sensing and on-board processing equipment limitations in type and rate of processing interested in ensembles of measurements (e.g., maximum, average) need for algorithms that obtain the fusion objective, not all individual measurements large networks; changes in network topology real-time knowledge of global topology impractical  locally constructed algorithms Additional requirements scalability fault-tolerance algorithms that can compute (reduced) fusion objective over reduced topologies

Objectives Desired Tasks computation of statistics of the measurements over very large networks of wireless sensors maximum, average, locally-averaged (in space) signal estimates Algorithmic Objectives algorithms for data processing, and communication, and relaying across the network  locally constructed, yet reliable  exploit compression benefits via distributed local fusion  designed for energy-efficient on-board processing and communication

Communication Protocols Objectives Reliable point-to-point communication source-encoding of analog signals in digital form channel coding for reliable transmission of underlying analog signals need for unequal error protection modulation via FSK Multiple access TDMA-FDMA protocol nodes are multiplexed in both time and frequency each node has a unique time-frequency slot for transmission during any time slot, each node can receive at most at one frequency slot need for algorithms for time-frequency slot allocation (with reuse) need for frame-synchronization signals

Hierarchical Networks Setting hierarchical protocol for data communication and fusion Advantages bandwidth efficient readily scalable hierarchy Disadvantages unequal distribution of resources often power usage inefficiency sensitivity to fusion node failures  robustness asymmetry

Ad-hoc Networks Setting two-way local communication between closely located (“connected”) sensors each sensor node receives messages sent by connected nodes each sensor broadcasts messages to connected nodes Advantages robust, readily scalable space-uniform resource usage transmit power efficient Issues need for networking

Ad hoc Networks for Fusion Related work ad hoc networks, amorphous computing Distinct features in fusion problem interested in underlying signal in data (e.g, target location, average temperature), not data info about signal “spread” over many nodes multiple destinations Remarks Advantages: data compression in fusion, inherent scalability Key problem: communication loops (contamination of information)

Computation of Global Maximum Objective compute maximum among measurements Approach sequence of local maximum computations sensor State=current maximum estimate communication step: each node broadcasts its state fusion step: new state at each node = maximum of all received states Resulting dynamics each node state converges to the global maximum (in finite number of steps) provided network is connected

Computation of Weighted Averages Applications large class of estimation, detection, and classification problems linear estimation, spatial matched filtering for signal detection surveillance: source localization and tracking Remarks not all local averaging fusion rules yield global average (data contamination) Approach locally constructed fusion rules can be designed [Scher03] which asymptotically compute weighted averages of functions of the individual measurements (e.g. average, power, variance of measurements) Advantages distributed, robust, readily scalable can address non-contributing node problem

Computation of Averages: Example Network of 200 sensors randomly placed on a circle Probabilistic model for connectivity between nodes (function of their distance)

1 st -Order Fusion Rules Nomenclature: Locally constructed fusion rule Rule properties z= 1 is eigenvector of W=I+  with eigenvalue 1 proper choice of   all eigenvalues of W except one are less than 1 in magnitude results in convergence of each node state to average with increasing n good choices of  can be selected locally via macroscopic quantities

Convergence of 1 st -Order Fusion Rules Performance Metric: RMSE depends on choice of parameter 

Improved Higher-Order Fusion Rules Filtering at each node via Eigenvalue shaping:

Eigenmode Reshaping via Filtering Method reduces magnitude of high-magnitude modes at expense of low- magnitude modes Convergence-mode histograms top-left: 1 st -order rule top-right: filtered rule with c=0.1 bottom-left: filtered rule with c=0.3 bottom-right: filtered rule with c=0.6

RMSE of Filtered Rules Relative MSE vs. number of iterations

RMSE Improvements due to Filtering Filtering can reduce number of iterations needed to achieve a target RMSE level, often by an order of magnitude Convergence improvement Metric: Iteration gain factor: ratio of number of iterations needed by 1 st order rule vs. number of iterations needed by associated filtered rule to achieve target RMSE (20dB-60dB)

Non-Contributing Nodes Techniques can be extended to compute averages with non-contributing nodes extra info required: each node knows contribution status of its immediately connected nodes 200-node example: 100 Contributing nodes Pairwise connections: solid: contributor pair dashed: contributor-noncontributor dotted: noncontributor pair

Non-Contributing Nodes Connections between contributors and noncontributors can be exploited to improve convergence RMSE comparison of 1 st -order rules: 100 out of 200 nodes are contributors

Project Objectives Remarks Finite delays and limitations in available energy and on-board processing  finite-time approximate computations Analysis and Optimization Design energy-efficient methods for approximate computation of maxima, averages and other measurement statistics Determine trade-offs on-board processing and communication power, delays and quality of computation Non-contributing nodes  need for power-efficient data relaying