16 research outputs found
Collaborative Estimation in Distributed Sensor Networks
Networks of smart ultra-portable devices are already indispensable in our lives, augmenting our senses and connecting our lives through real time processing and communication of sensory (e.g., audio, video, location) inputs. Though usually hidden from the user\u27s sight, the engineering of these devices involves fierce tradeoffs between energy availability (battery sizes impact portability) and signal processing / communication capability (which impacts the smartness of the devices). The goal of this dissertation is to provide a fundamental understanding and characterization of these tradeoffs in the context of a sensor network, where the goal is to estimate a common signal by coordinating a multitude of battery-powered sensor nodes. Most of the research so far has been based on two key assumptions -- distributed processing and temporal independence -- that lend analytical tractability to the problem but otherwise are often found lacking in practice. This dissertation introduces novel techniques to relax these assumptions -- leading to vastly efficient energy usage in typical networks (up to 20% savings) and new insights on the quality of inference. For example, the phenomenon of sensor drift is ubiquitous in applications such as air-quality monitoring, oceanography and bridge monitoring, where calibration is often difficult and costly. This dissertation provides an analytical framework linking the state of calibration to the overall uncertainty of the inferred parameters.
In distributed estimation, sensor nodes locally process their observed data and send the resulting messages to a sink, which combines the received messages to produce a final estimate of the unknown parameter. In this dissertation, this problem is generalized and called collaborative estimation , where some sensors can potentially have access to the observations from neighboring sensors and use that information to enhance the quality of their messages sent to the sink, while using the same (or lower) energy resources. This is motivated by the fact that inter-sensor communication may be possible if sensors are geographically close. As demonstrated in this dissertation, collaborative estimation is particularly effective in energy-skewed and information-skewed networks, where some nodes may have larger batteries than others and similarly some nodes may be more informative (less noisy) compared to others. Since the node with the largest battery is not necessarily also the most informative, the proposed inter-sensor collaboration provides a natural framework to route the relevant information from low-energy-high-quality nodes to high-energy-low-quality nodes in a manner that enhances the overall power-distortion tradeoff.
This dissertation also analyzes how time-correlated measurement noise affects the uncertainties of inferred parameters. Imperfections such as baseline drift in sensors result in a time-correlated additive component in the measurement noise. Though some models of drift have been reported in the literature earlier, none of the studies have considered the effect of drifting sensors on an estimation application. In this dissertation, approximate measures of estimation accuracy (Cramer-Rao bounds) are derived as a function of physical properties of sensors -- namely the drift strength, correlation (Markov) factor and the time-elapsed since last calibration. For stationary drift (Markov factor less than one), it is demonstrated that the first order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. When the drift is non-stationary (Markov factor equal to one), it is established that the constant part of a signal can only be estimated inconsistently (with non-zero asymptotic variance). The results help quantify the notions that measurements taken sooner after calibration result in more accurate inference
Optimal Identical Binary Quantizer Design for Distributed Estimation
We consider the design of identical one-bit probabilistic quantizers for
distributed estimation in sensor networks. We assume the parameter-range to be
finite and known and use the maximum Cram\'er-Rao Lower Bound (CRB) over the
parameter-range as our performance metric. We restrict our theoretical analysis
to the class of antisymmetric quantizers and determine a set of conditions for
which the probabilistic quantizer function is greatly simplified. We identify a
broad class of noise distributions, which includes Gaussian noise in the
low-SNR regime, for which the often used threshold-quantizer is found to be
minimax-optimal. Aided with theoretical results, we formulate an optimization
problem to obtain the optimum minimax-CRB quantizer. For a wide range of noise
distributions, we demonstrate the superior performance of the new quantizer -
particularly in the moderate to high-SNR regime.Comment: 6 pages, 3 figures, This paper has been accepted for publication in
IEEE Transactions in Signal Processin
Cram\'er-Rao Bounds for Polynomial Signal Estimation using Sensors with AR(1) Drift
We seek to characterize the estimation performance of a sensor network where
the individual sensors exhibit the phenomenon of drift, i.e., a gradual change
of the bias. Though estimation in the presence of random errors has been
extensively studied in the literature, the loss of estimation performance due
to systematic errors like drift have rarely been looked into. In this paper, we
derive closed-form Fisher Information matrix and subsequently Cram\'er-Rao
bounds (upto reasonable approximation) for the estimation accuracy of
drift-corrupted signals. We assume a polynomial time-series as the
representative signal and an autoregressive process model for the drift. When
the Markov parameter for drift \rho<1, we show that the first-order effect of
drift is asymptotically equivalent to scaling the measurement noise by an
appropriate factor. For \rho=1, i.e., when the drift is non-stationary, we show
that the constant part of a signal can only be estimated inconsistently
(non-zero asymptotic variance). Practical usage of the results are demonstrated
through the analysis of 1) networks with multiple sensors and 2) bandwidth
limited networks communicating only quantized observations.Comment: 14 pages, 6 figures, This paper will appear in the Oct/Nov 2012 issue
of IEEE Transactions on Signal Processin
Spatial Whitening Framework for Distributed Estimation
Designing resource allocation strategies for power constrained sensor network
in the presence of correlated data often gives rise to intractable problem
formulations. In such situations, applying well-known strategies derived from
conditional-independence assumption may turn out to be fairly suboptimal. In
this paper, we address this issue by proposing an adjacency-based spatial
whitening scheme, where each sensor exchanges its observation with their
neighbors prior to encoding their own private information and transmitting it
to the fusion center. We comment on the computational limitations for obtaining
the optimal whitening transformation, and propose an iterative optimization
scheme to achieve the same for large networks. We demonstrate the efficacy of
the whitening framework by considering the example of bit-allocation for
distributed estimation.Comment: 4 pages, 2 figures, this paper has been presented at CAMSAP 2011;
Proc. 4th Intl. Workshop on Computational Advances in Multi-Sensor Adaptive
Processing (CAMSAP 2011), San Juan, Puerto Rico, Dec 13-16, 201