A New Class of Bayesian Cyclic Bounds for Periodic Parameter Estimation

Nitzan, Eyal; Routtenberg, Tirza; Tabrikian, Joseph

doi:10.1109/tsp.2015.2478758

Cited by 20 publications

(11 citation statements)

References 50 publications

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“…This distribution was studied in directional statistics and is a close approximation to wrapped normal distribution, which is in turn the circular/periodic analog of the normal distribution (Mardia, 1972). Therefore, it is particularly appropriate to characterize the parameter of interestcircular frequency since it is wrapped around [−𝜋, 𝜋] (Nitzan, 2016). The pdf of von Mises distributed parameter, 𝜃, is given as (Fisher, 1993)…”

Section: A Priori Distribution Of Circular Frequency: Von Mises Distr...mentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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The crystallization kinetics and melting behavior of nylon 10,10 in neat nylon 10,10 and in nylon 10,10 -montmorillonite (MMT) nanocomposites were systematically investigated by differential scanning calorimetry. The crystallization kinetics results show that the addition of MMT facilitated the crystallization of nylon 10,10 as a heterophase nucleating agent; however, when the content of MMT was high, the physical hindrance of MMT layers to the motion of nylon 10,10 chains retarded the crystallization of nylon 10,10, which was also confirmed by polarized optical microscopy. However, both nylon 10,10 and nylon 10,10 -MMT nanocomposites exhibited multiple melting be-havior under isothermal and nonisothermal crystallization conditions. The temperature of the lower melting peak (peak I) was independent of MMT content and almost remained constant; however, the temperature of the highest melting peak (peak II) decreased with increasing MMT content due to the physical hindrance of MMT layers to the motion of nylon 10,10 chains.

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Section: A Priori Distribution Of Circular Frequency: Von Mises Distr...mentioning

confidence: 99%

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Zhuang

Huang

et al. 2019

Mathematical Biosciences and Engineering

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“…Additionally, the classical CRLB applies on the MSE (Euclidean metric), while this criterion may not be the most appropriate for characterizing the performance when parameters are living in a manifold. For example [6][7][8][9] proposed CRLBs for periodic error costs, more suited to angle estimation problems. In our context, a lower bound on the mean natural Riemannian distance can be more relevant and also reveal hidden properties of estimators.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Cramér–Rao Bounds for Scatter and Shape Matrices Estimation in CES Distributions

Breloy

Ginolhac

Renaux

et al. 2019

IEEE Signal Process. Lett.

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Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramér-Rao bounds are derived for the problem of scatter and shape matrices estimation with samples following a Complex Elliptically Symmetric distribution. The Fisher Information Metric and its associated Riemannian distance (namely, CES-Fisher) on the manifold of Hermitian positive definite matrices are derived. Based on these results, intrinsic Cramér-Rao bounds on the considered problems are then expressed for three different distances (Euclidean, natural Riemannian and CES-Fisher). These contributions are therefore a generalization of Theorems 4 and 5 of [1] to a wider class of distributions and metrics for both scatter and shape matrices.

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“…1 Our derivation of the WWB uses the MSE also for the phase, although a cyclic cost like the Mean-Cyclic-Error (MCE) [23] is a good alternative. 2 For the optimization we selected…”

Section: B Design Cost Functionmentioning

confidence: 99%

Constrained optimal design of automotive radar arrays using the Weiss-Weinstein Bound

González-Huici

Mateos-Nunez

Greiff³

et al. 2018

2018 IEEE MTT-S International Conference on Microwaves for Intelligent Mobility (ICMIM)

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We propose a design strategy for optimizing antenna positions in linear arrays for far-field Direction of Arrival (DoA) estimation of narrow-band sources in collocated MIMO radar. Our methodology allows to consider any spatial constraints and number of antennas, using as optimization function the Weiss-Weinstein bound formulated for an observation model with random target phase and known SNR, over a pre-determined Field-of-View (FoV). Optimized arrays are calculated for the typical case of a 77GHz MIMO radar of 3Tx and 4Rx channels. Simulations demonstrate a performance improvement of the proposed arrays compared to the corresponding uniform and minimum redundancy arrays for a wide regime of SNR values.

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A New Class of Bayesian Cyclic Bounds for Periodic Parameter Estimation

Cited by 20 publications

References 50 publications

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

School of Mechanical Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China

Intrinsic Cramér–Rao Bounds for Scatter and Shape Matrices Estimation in CES Distributions

Constrained optimal design of automotive radar arrays using the Weiss-Weinstein Bound

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