Detection and Estimation in Wireless Sensor Networks İsrafil Bahçeci Department of Electrical Engineering TOBB ETÜ June 28, 2012 1 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 2 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 3 of 38
Wireless Sensor Networks Many nodes, preferably cheap Power/energy/bandwidth limited Wireless medium 4 of 38
Functionality and Utility Detection False alarm and detection probability Estimation Estimation error 5 of 38
Typical Problems Deployment optimization Node density Node location Wireless networking and communications Achievable rate/distortion regions Source/channel coding problems Quantization/coding/analog transmission Power control and interference management, energy efficiency Centralized vs. distributed Multiple access vs. Orthogonal access Single vs. multiple fusion center Path selection and shortest path algorithms Self-organization Node failure & self-healing Information security Access to information Node intrusion, e.g. Byzantine attack 6 of 38
Typical Network Configurations Parallel network Hierarchical network Serial network 7 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 8 of 38
System Model Let n 0, n 1,..., n N 1 denote the sensor nodes Let u i is the observed samples at node n i Let h i,j is the channel gain from n j to n i h i,j include the effect of antenna gains and long term channel losses For transmission from n m to n k, received signal: r k [t] = h k,m s m [t] + N 1 i=0,i m Transmitted signal at n m : s m [t] = g(u m, r m ) Bandwidth and energy constraints I i [t]h k,i s i [t] + w k [t] 9 of 38
Metrics Detection Detection probability (correct decision) False alarm/miss probability (erroneous decision) Estimation Mean-square error, E( ˆθ θ 2 ) 10 of 38
Observation Statistics Independent observations Correlated observations Dense deployment 11 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 12 of 38
Estimation Under Bandwidth Constraints I Universal estimation [1] Each sensor has 1 sample from a noisy observation and can send 1 bit (0 or 1 per local estimate u i = θ + n i, θ [ V, V] and n i f U (u), V = U if fu (u) µ is known, N 1 4ɛ 2 µ 2 if f U (u) is unknown, N U2 4ɛ, e.g., binary messaging requires only at 2 most 4 times more sensor nodes Sample mean estimation [2, 3] u i = θ + n i, n i N(0, σ 2 ) Maximum likelihood estimator available for both identical thresholds, non-identical thresholds Fixed step size difference, τk+1 τ k > σ equal to noise variance is close to optimality Parameter with a small dynamic range: 1 bit quantization is sufficient Relaxing 1 bit constraint, a step size equal to noise variance is good for practical cases 13 of 38
Estimation Under Bandwidth Constraints II Inhomogeneous environment [4] Local information compressed to a number of bits proportional to logarithm of its local observation SNR Fusion center only needs the received quantized messages and use the length of the message in final estimation No need for noise pdf at the FC, each sensor needs its local SNR The MSE of this estimator achieves 25/8 times the MSE of BLUE 14 of 38
Compression and Estimation The above bandwidth constrained schemes compress the signals to a few bits An overview of several cases of distributed estimation [5] Same order of MSE performance achieved by a centralized estimation is doable under various bandwidth constrained schemes under different knowledge levels for the observation noise statistics 15 of 38
Power Control for Distributed Estimation Estimation with digital modulation [6] Joint design of universal estimator and uncoded QAM modulation Optimal quantization and transmit power levels to minimize MSE Bah channel or bad observation lower quantization level, or inactive Estimation with analog modulation [7] Correlated data observation, e.g., a random field Non-linear measurement issues also considered Linear MMSE + numerical power control optimization 16 of 38
Source-Channel Coding for Distributed Estimation Wyner-Ziv source coding based strategies for a general tree network [8] Achievable region for a generic one-step communication with side-information Application of one-step solution to a tree network: A sensor uses its own observations, all messages it received + statistical information for the observation made by decoder and messages received by the decoder Rate-distortion bounds for the Quadratic Gaussian case is determined 17 of 38
CEO problem and distributed estimation CEO problem: Estimation with a parallel configuration Admissible sum-rate distortion regions [9] Local observations separately encoded and transmitted to a CEO Closed form solution to rate allocation for the Quadratic Gaussian CEO problem Rate-constrained estimation for CEO problem [10] 18 of 38
Distributed Quantization and Estimation Adaptive quantization [11] Bandwidth constraint, so only one bit quantization Dynamic adjustment of quantization threshold based on feedback from other sensor nodes Distributed Delta modulation Quantizer precision for large networks [12] xi = θ + n i for all nodes Identical, noncooperative uniform scalar quantization at each node achieves same asymptotics as optimal scheme If observation SNR is high, few nodes with fine quantization is better There exists an optimal number of sensors for this quantization, not all sensors needed 19 of 38
Cooperative Communications Cooperative diversity for distributed estimation [13] Several cooperative relaying schemes exists that achieve spatial diversity Multiple access channel, r[n] = N i=1 x i[n] + w[n] Amplify-forward or decode-forward based distributed estimation achieve same asymptotic performance Collection of correlated data: spatial sampling (one sensor out of a group of correlated sensor nodes) Selective transmission is good for loose distortion, but needs improved cooperation for strict distortion constraint 20 of 38
Linear Distributed Estimation Parallel configuration with all linear processing for a coherent Gaussian network with MAC [14] Linear observation model Linear encoding at the transmitter: MAC allows for a closed-form expression for encoding Linear MMSE at the fusion center Optimal power allocation allows distributed implementation 21 of 38
Estimation Diversity and Energy Efficiency Analog transmission of x i = θ i + n i, to a fusion center [15, 16] Fixed data vs. correlated data BLUE vs. MMSE Estimation outage and estimation diversity (slope of outage probability) Full diversity can be achieved on the number of sensor nodes Power control for fixed data vs. correlated data 22 of 38
Distributed Kalman Filtering Distributed estimation of a dynamically varying signal with a linear observation model [17] Need to exchange messages between neighbor nodes 2-step estimation Step 1: Kalman-like estimation based only on local observations Step 2: Information fusion via a consensus matrix after receiving messages from neighbors Design problems: Optimal Kalman gain, and consensus matrix, based on the amount of message exchange 23 of 38
Distributed Data Gathering with a Dense Sensor Network Estimation of a observable random field at a collector node [18] Transport capacity of many-to-one channel O(logN) can be achieved by an amplify-forward scheme, even under subject to total power constraint Unbounded transport capacity for many-to-one channel with only finite total average power Gaussian spatially bandlimited processes are observable (e.g., it can be estimated at a collector node with a finite MSE for a certain bandwidth and total average power level) This is true even for lossy source encoder composed of a single-dimensional quantization followed by a Slepian-Wolf encoder 24 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 25 of 38
Distributed Detection with Multiple Sensors An overview on various distributed detection strategies [19] Error-free transmission of local decisions to a fusion center Independent local observations Likelihood ratio tests, for both Neyman-Pearson and Bayes formulation, are optimal at both local sensor nodes and fusion centers 26 of 38
Bandwidth/Power Constrained Distributed Detection I Binary detection over a parallel network with MAC [20] Specifying the power, bandwidth, error tolerance fixed the information rates of sensors for this MAC Minimization of Chernoff exponent for the decision at the FC Asymptotically, for Gaussian and exponential observation, having R identical binary sensors, e.g., 1 bit/sensor for a rate-r MAC channel, is optimal Not true for some other statistical distributions Having more sensors is better than having detailed information from each node Asymptotic detection for power constrained network [21] Joint power constraint + AWGN at sensor-to-fusion center channel Having identical sensor nodes, e.g., each node using the same scheme, is asymptotically optimal Optimal transmission power levels for binary nodes observing Gaussian source 27 of 38
Energy Efficient Distributed Detection Energy and bandwidth constraints taken into account [22] Detection performance subject to system cost due to transmission power and measurement errors Randomization over the choice of measurements and when to send/no send Joint optimization over sensor nodes allows the optimization per node 28 of 38
Parallel and Serial Detection over Fading Channel The communications are all Rayleigh fading [23, 24] Binary detection and binary antipodal modulation for decision transmission Channel state information need to be obtained at the receiver node Suitable likelihood ratios at all nodes are optimal with known CSI 29 of 38
Optimal Distributed Detection over Noisy Channel Non-ideal channels to fusion center [25, 26] Detection at fusion center needs to consider the CSI in case of fading LRTs are shown to be optimal in the sense that they minimize error probability at the fusion center 30 of 38
Type-Based Distributed Detection Each local sensor generates a histogram, or type of its observation over time and forwards the type to fusion center [27, 28] MAC where fusion center receives a superposition of transmitted local signals attain a better detection performance relative to orthogonal MAC Histogram fusion at the fusion center is asymptotically optimal and observation statistics need to be known only at the fusion cener 31 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 32 of 38
Remarks Diverse applications and many research topics Many open problems Joint design of local/global processing and network operation, routing Cooperative sensing/routing Network life time maximization via data aggregation, joint source/channel coding, and power control New paradigms for detection estimation under constraints of WSNs Detection/estimation at multiple fusion center, distributed congestion control 33 of 38
Outline Introduction Problem Setup Estimation Detection Conclusions References 34 of 38
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