Asymptotic Design of Quantizers for Decentralized MMSE Estimation

Maranò, Stefano; Matta, Vincenzo; Willett, Peter

doi:10.1109/tsp.2007.898755

Cited by 31 publications

(24 citation statements)

References 32 publications

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“…We will delay discussion of DFSQ for Section II-C and instead focus on related works. The use of high-resolution for computation has been considered in detection and estimation problems [15]- [18]. In the scalar setting, the scenario where the computation is unknown but is drawn from a set of possibilities has been studied [19].…”

Section: A Previous Workmentioning

confidence: 99%

Distributed Functional Scalar Quantization Simplified

Sun

Misra

Goyal

2013

IEEE Trans. Signal Process.

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Abstract-Distributed functional scalar quantization (DFSQ) theory provides optimality conditions and predicts performance of data acquisition systems in which a computation on acquired data is desired. We address two limitations of previous works: prohibitively expensive decoder design and a restriction to source distributions with bounded support. We show that a much simpler decoder has equivalent asymptotic performance to the conditional expectation estimator studied previously, thus reducing decoder design complexity. The simpler decoder features decoupled communication and computation blocks. Moreover, we extend the DFSQ framework with the simpler decoder to source distributions with unbounded support. Finally, through simulation results, we demonstrate that performance at moderate coding rates is well predicted by the asymptotic analysis, and we give new insight on the rate of convergence.

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Section: A Previous Workmentioning

confidence: 99%

Distributed Functional Scalar Quantization Simplified

Sun

Misra

Goyal

2013

IEEE Trans. Signal Process.

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“…Following a similar development as in [6], the quantity E (Sc − Sq) 2 will be analyzed. Sc is the score function for estimation based on continuous measurements Sc = ∂ log f (y;x) ∂x .…”

Section: Asymptotic Approximationmentioning

confidence: 99%

“…A high-rate approximation is also proposed in [6], where the problem of estimating a random parameter based on scalarly quantized measurements is considered. The optimal companding function (quantizer input nonlinear function) and mean squared estimation errors are obtained considering that the quantizers output entropy sum is minimized, thus giving a characterization of the rate-distortion function for Bayesian estimation under the high-rate regime.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic approximation of optimal quantizers for estimation

Farias

Brossier

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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In this paper, the asymptotic approximation of the Fisher information for the estimation of a scalar parameter based on quantized measurements is studied. As the number of quantization intervals tends to infinity, it is shown that the loss of Fisher information due to quantization decreases exponentially as a function of the number of quantization bits. The optimal quantization interval density and the corresponding maximum Fisher information are obtained. Comparison between optimal nonuniform and uniform quantization for the location estimation problem indicates that nonuniform quantization is slightly better. At the end of the paper, an adaptive algorithm for jointly estimating and setting the thresholds is used to show that the theoretical results can be approximately obtained in practice.

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“…Lam and Reibman [9] discussed construction of optimal quantization partitions for quantizer design in distributed estimation systems. In the high resolution regime, asymptotic quantizer designs for distributed estimation were derived in terms of the point density function which is the limiting density of quantizer partitions [13], [14]. The necessary conditions for optimal quantization rules and linear estimation fusion rules were derived and shown to be searched simultaneously by using an iterative algorithm [17].…”

Section: Introductionmentioning

confidence: 99%

Region-Based Distributed Estimation Using Quantized Data

Kim

2014

IEICE Trans. Inf. & Syst.

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SUMMARYIn this paper, we consider distributed estimation where the measurement at each of the distributed sensor nodes is quantized before being transmitted to a fusion node which produces an estimate of the parameter of interest. Since each quantized measurement can be linked to a region where the parameter is found, aggregating the information obtained from multiple nodes corresponds to generating intersections between the regions. Thus, we develop estimation algorithms that seek to find the intersection region with the maximum likelihood rather than the parameter itself. Specifically, we propose two practical techniques that facilitate fast search with significantly reduced complexity and apply the proposed techniques to a system where an acoustic amplitude sensor model is employed at each node for source localization. Our simulation results show that our proposed algorithms achieve good performance with reasonable complexity as compared with the minimum mean squared error (MMSE) and the maximum likelihood (ML) estimators. key words: distributed estimation, maximum a posteriori (MAP), quantization, source localization, sensor networks

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Asymptotic Design of Quantizers for Decentralized MMSE Estimation

Cited by 31 publications

References 32 publications

Distributed Functional Scalar Quantization Simplified

Distributed Functional Scalar Quantization Simplified

Asymptotic approximation of optimal quantizers for estimation

Region-Based Distributed Estimation Using Quantized Data

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