Cost minimization of measurement devices under estimation accuracy constraints in the presence of Gaussian noise

doi:10.1016/j.dsp.2012.04.009

Digital Signal Processing

Volume 22, Issue 5, September 2012, Pages 828-840

https://doi.org/10.1016/j.dsp.2012.04.009 Get rights and content

Abstract

Novel convex measurement cost minimization problems are proposed based on various estimation accuracy constraints for a linear system subject to additive Gaussian noise. Closed form solutions are obtained in the case of an invertible system matrix. In addition, the effects of system matrix uncertainty are studied both from a generic perspective and by employing a specific uncertainty model. The results are extended to the Bayesian estimation framework by treating the unknown parameters as Gaussian distributed random variables. Numerical examples are presented to discuss the theoretical results in detail.

Section snippets

Berkan Dulek received the B.S. and M.S. degrees with high honors in electrical engineering from Bilkent University, Turkey, in 2003 and 2006, respectively. He is currently studying toward the Ph.D. degree at Bilkent University. His research interests are in statistical signal processing and communications with emphasis on stochastic signaling, randomized detection and estimation under cost constraints.

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Power adaptation for vector parameter estimation according to Fisher information based optimality criteria
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Citation Excerpt :
In the following, we provide closed-form solutions for optimal power allocation problems by considering various estimation accuracy criteria based on the FIM in (4). The worst-case error variance criterion is a measure of robustness rather than average estimation accuracy and is associated with the maximum eigenvalue of the CRLB [27,30]. In order to reduce the worst-case error variance, the maximum eigenvalue of the CRLB can be minimized.
The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the parameter vector and an additive noise component with an arbitrary probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Via optimization theoretic approaches, various closed-form solutions are derived for the proposed problems. Also, the results are extended to cases in which nuisance parameters exist in the system model or certain types of nonlinear transformations are applied on the parameter vector. Numerical examples are presented to investigate performance of the proposed power allocation strategies.
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Detection and estimation problems considering system resource constraints have extensively been studied in the literature [4–22]. In [4], measurement cost minimization is performed under various estimation accuracy constraints. In [5], optimal distributed detection strategies are studied for wireless sensor networks by considering network resource constraints, where it is assumed that observations at the sensors are spatially and temporally independent and identically distributed (i.i.d.).
Optimal detection performance of centralized and decentralized detection systems is investigated in the presence of cost constrained measurements. For the evaluation of detection performance, Bayesian, Neyman–Pearson and J-divergence criteria are considered. The main goal for the Bayesian criterion is to minimize the probability of error (more generally, the Bayes risk) under a constraint on the total cost of the measurement devices. In the Neyman–Pearson framework, the probability of detection is to be maximized under a given cost constraint. In the distance based criterion, the J-divergence between the distributions of the decision statistics under different hypotheses is maximized subject to a total cost constraint. The probability of error expressions are obtained for both centralized and decentralized detection systems, and the optimization problems are proposed for the Bayesian criterion. The probability of detection and probability of false alarm expressions are obtained for the Neyman–Pearson strategy and the optimization problems are presented. In addition, J-divergences for both centralized and decentralized detection systems are calculated and the corresponding optimization problems are formulated. The solutions of these problems indicate how to allocate the cost budget among the measurement devices in order to achieve the optimum performance. Numerical examples are presented to discuss the results.
Estimate accuracy versus measurement cost saving in continuous time linear filtering problems
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We address the problem of defining a good trade off between reducing the cost of measurement and keeping the estimate accuracy within acceptable levels for continuous time linear system filtering problems. A measurement procedure which modifies the classical Kalman filter is proposed, allowing a sensible reduction of the measurement time intervals. This procedure is tested with satisfactory results against stable and unstable linear systems.
Power adaptation for vector parameter estimation according to Fisher information based optimality criteria
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Sinan Gezici received the B.S. degree from Bilkent University, Turkey in 2001, and the Ph.D. degree in electrical engineering from Princeton University in 2006. From 2006 to 2007, he worked at Mitsubishi Electric Research Laboratories, Cambridge, MA. Since February 2007, he has been an Assistant Professor in the Department of Electrical and Electronics Engineering at Bilkent University. Dr. Geziciʼs research interests are in the areas of detection and estimation theory, wireless communications, and localization systems. Among his publications in these areas is the book Ultra-wideband Positioning Systems: Theoretical Limits, Ranging Algorithms, and Protocols (Cambridge University Press, 2008).

^☆: Part of this work is presented at IEEE International Workshop on Signal Processing Advances for Wireless Communications (SPAWC), June 2012.

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Cost minimization of measurement devices under estimation accuracy constraints in the presence of Gaussian noise☆

Abstract

Section snippets

Signal recovery with cost-constrained measurements

IEEE Trans. Signal Process.

An Introduction to Signal Detection and Estimation

Energy-efficient detection in sensor networks

IEEE J. Sel. Areas Commun.

Bandwidth-constrained distributed estimation for wireless sensor networks—Part I: Gaussian case

IEEE Trans. Signal Process.

Power scheduling of universal decentralized estimation in sensor networks

IEEE Trans. Signal Process.

Estimation diversity and energy efficiency in distributed sensing

IEEE Trans. Signal Process.

Rate-constrained distributed estimation in wireless sensor networks

IEEE Trans. Signal Process.

Dynamic field estimation using wireless sensor networks: Tradeoffs between estimation error and communication cost

IEEE Trans. Signal Process.

Sensor selection and power allocation for distributed estimation in sensor networks: Beyond the star topology

IEEE Trans. Signal Process.

Constrained decentralized estimation over noisy channels for sensor networks

IEEE Trans. Signal Process.

Sensor selection via convex optimization

IEEE Trans. Signal Process.

Optimal sensor selection in binary heterogeneous sensor networks

IEEE Trans. Signal Process.

Average Fisher information maximisation in presence of cost-constrained measurements

Electron. Lett.