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Hermitian Symmetric DFT Codes: A New Class of Complex DFT Codes

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第5期60卷 2396-2407页

作者： Kumar, A. Anil Makur, Anamitra Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

We introduce a new class of real number codes derived from DFT matrix, Hermitian symmetric DFT (HSDFT) codes. We propose a new decoding algorithm based on coding-theoretic as well as subspace based approach. Decoding of HSDFT codes requires only real arithmetic operations and smaller dimension matrices compared to the decoding of the state-of-art real BCH DFT (RBDFT) class of codes. HSDFT codes will also be shown to have more burst error correction capacity. For a Gauss-Markov source, on a binary symmetric channel at lower to moderate bit error rates (BERs), HSDFT codes show better performance than RBDFT codes, and on a Gilbert-Elliot channel HSDFT codes consistently perform better than RBDFT codes.

关键词： DFT codes joint source and channel coding real number codes subspace algorithms

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A Majorize-Minimize Memory Gradient method for complex-valued inverse problems

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SIGNAL PROCESSING 2014年 103卷 285-295页

作者： Florescu, Anisia Chouzenoux, Emilie Pesquet, Jean-Christophe Ciuciu, Philippe Ciochina, Silviu Univ Politehn Bucuresti Dept Telecommun Bucharest Romania Univ Paris Est UMR CNRS 8049 LIGM Champs Sur Marne France CEA NeuroSpin Ctr INRIA Saclay PARIETAL Team Gif Sur Yvette France

Complex-valued data are encountered in many application areas of signal and image processing. In the context of the optimization of functions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize-Minimize Memory Gradient (3MG) algorithm. Important practical applications of these results arise in inverse problems. Here, we focus on image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). The linear operator involved in the observation model then includes a subsampling operator over the k-space (2D Fourier domain) the choice of which is analyzed through our numerical results. In addition, sensitivity matrices associated with the multiple channel coils come into play. Comparisons with existing optimization methods confirm the better performance of the proposed algorithm. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Complex-valued signals Optimization subspace algorithms Descent methods Majorization-minimization Image reconstruction Inverse problems Magnetic resonance imaging Sampling Proximal methods

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DIRECTION FINDING OF MULTIPLE WIDE-BAND EMITTERS USING STATE-SPACE MODELING

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SIGNAL PROCESSING 1994年第1期40卷 39-52页

作者： VANPOUCKE, F MOONEN, M DEPRETTERE, EF [a]ESAT Katholieke Universiteit Leuven Kard. Mercierlaan 94 3001 Leuven Belgium [b]Department of Electrical Engineering Delft University of Technology Mekelweg 4 2628 CD Delft Netherlands

Estimating the angles-of-arrival of wide-band emitters is an important problem in array processing. This paper introduces a novel method which is applicable if the sensor array consists of doublets and if the wide-band signals can be accurately modeled as the output of a linear time-invariant system driven by white noise. The novelty in our approach lies in the use of state-space descriptions for the sensor outputs. We present two algorithms. The first is a simple nonrecursive algorithm. The second is a recursive algorithm with reduced computational complexity. Due to its regular parallel structure this algorithm is well suited for parallel implementation, e.g. in real-time applications requiring high throughput.

关键词： WIDE-BAND DIRECTION-OF-ARRIVAL ESTIMATION DOUBLETS subspace algorithms ADAPTIVE SVD PARALLEL algorithms

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Closed-Form Estimation of Normal Modes From a Partially Sampled Water Column

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IEEE JOURNAL OF OCEANIC ENGINEERING 2020年第4期45卷 1574-1582页

作者： Gazzah, Houcem Jesus, Sergio M. Univ Algarve LARSyS P-8005139 Faro Portugal

The output of a vertical linear array is used to infer about the parameters of the normal mode model that describes acoustic propagation in a shallow water. Existing subspace algorithms perform singular vector decomposition of the array data matrix to estimate the sampled model functions. Estimates are exact only if the sensing array is totally covering the water column. We design a new subspace algorithm free from this very restrictive requirement. We use two short hydrophone arrays and activate a monochromatic source at different depths. Estimates of both the modal functions and the wave numbers are obtained in a fully automatic and search-free manner. The algorithm can be qualified as truly high resolution in the sense that, while using short sensing arrays, estimation error becomes arbitrarily low if observation noise is arbitrarily low. This method compares advantageously to existing subspace techniques, as well as transform-domain techniques that require impulsive sources, among other constraints. With two (eigen and singular) vector decompositions, the proposed technique has the complexity of a regular subspace algorithm.

关键词： Arrays Transmission line matrix methods Estimation Signal processing algorithms Mathematical model Data models Sensors Normal modes shallow water subspace algorithms vertical linear arrays

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A parametric estimation method for dynamic factor models of large dimensions

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JOURNAL OF TIME SERIES ANALYSIS 2009年第2期30卷 208-238页

作者： Kapetanios, George Marcellino, Massimiliano Bocconi Univ European Univ Inst Univ London Dept Econ London E1 4NS England

The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, because of the increased availability of large data sets. In this article we propose a new parametric methodology for estimating factors from large data sets based on state-space models and discuss its theoretical properties. In particular, we show that it is possible to estimate consistently the factor space. We also conduct a set of simulation experiments that show that our approach compares well with existing alternatives.

关键词： Factor models principal components subspace algorithms C32 C51 E52

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Cointegration analysis with state space models

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ASTA-ADVANCES IN STATISTICAL ANALYSIS 2010年第3期94卷 273-305页

作者： Wagner, Martin Inst Adv Studies Dept Econ & Finance A-1060 Vienna Austria Frisch Ctr Econ Res Oslo Norway

This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration, and polynomial cointegration are defined. Based upon these definitions, the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By detailing the cases most relevant for empirical applications, the I(1), multiple frequency I(1), and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly discussed.

关键词： State space models Unit roots Cointegration Polynomial cointegration Pseudo maximum likelihood estimation subspace algorithms

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Choosing Integer Parameters in subspace Methods: A Survey on Asymptotic Results

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IFAC Proceedings Volumes 2003年第16期36卷 1741-1746页

作者： Dietmar Bauer Institute for Econometrics Operations Research and System Theory TU Wien Argentinierstr. 8 A-1040 Vienna Austria

When using subspace methods, the user has to specify a number of integer parameters. This paper surveys the literature on results relating to strategies for these choices and the consequences thereof. All results are asymptotic in nature and relate either to consistency questions or to the asymptotic covariance matrix of the estimated systems.

关键词： subspace algorithms asymptotic theory linear dynamical systems

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Closed-Loop PARSIMonious subspace Identification: Theory and Application to MPC

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IFAC Proceedings Volumes 2010年第5期43卷 361-366页

作者： Gabriele Pannocchia Mirco Calosi Dept. of Chem. Engineering (DICCISM) Univ. of Pisa Pisa Italy AspenTech S.r.l. Lungarno Pacinotti 47. Pisa Italy

We propose in this paper a novel subspace identification method, based on PARSIMonious parameterization (Qin et al., 2005), and we show that such algorithm guarantees consistent estimates of the Markov parameters with open-loop and closed-loop data. The method uses the predictor form and it effectively exploits in all steps the Toeplitz structure of the Markov parameters' matrices. After evaluation of ( A K = A – KC, C ) from the identified observability matrix, the method computes ( B K = B – KD, D, K ) and the initial condition by solving a single (well conditioned even for unstable systems) Least Squares problem. We use such method to obtain linear models for MPC design, and we show how the proposed method compares favorably with other existing subspace algorithms in two examples.

关键词： Closed-loop identification subspace algorithms MPC process control

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COMPARISONS OF subspace IDENTIFICATION METHODS FOR SYSTEMS OPERATING ON CLOSED-LOOP

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IFAC Proceedings Volumes 2005年第1期38卷 494-499页

作者： Weilu Lin S. Joe Qin Lennart Ljung Department of Chemical Engineering The University of Texas at Austin Austin Texas 78712 USA Department of Electrical Engineering Linköping University SE-581 83 Linköping Sweden

In this paper, we analyze two recently proposed closed-loop subspace identification methods, referred to as innovation estimation method and whitening filter approach respectively. The similarity and difference between them are investigated in detail. It turns out that all closed-loop subspace identification methods can be classified as one-step, two-step, or multi-stage projection methods. A SISO closed-loop simulation shows that to identify a consistent model the whitening filter approach might require longer future and past horizons than the innovation estimation method.

关键词： Closed-loop Identification subspace algorithms

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ON THE ROLE OF FUTURE HORIZON IN CLOSED-LOOP subspace IDENTIFICATION

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IFAC Proceedings Volumes 2006年第1期39卷 1080-1084页

作者： S. Joe Qin Lennart Ljung Department of Chemical Engineering The University of Texas at Austin Austin TX 78712 USA Department of Electrical Engineering Linköping University SE-581 83 Linköping Sweden

Closed loop subspace identification has become a focus of interest with several recent developments. Notably are the innovation estimation approach (Qin and Ljung, 2003), the state space approach with ARX pre-estimates (SSARX, (Jansson, 2003)), and the whitening filter approach (Chiuso and Picci, 2004). All these approaches use an extended future horizon to form the projection or regression from which an observable subspace is extracted. Yet there are other methods such as OKID of (Phan and Longman, 1992) and that of (Ljung and McKelvey, 1996) that do not use an extended horizon in the projection or regression step. Instead, a single high order ARX model is used. A natural question is whether the future horizon is necessary and if so what role does it play in these steps. In this paper we investigate the role of the future horizon using the whitening filter approach of (Chiuso and Picci, 2004), which works for both open-loop and closed-loop data. We conclude that the role of future horizon in this algorithm is merely extending the order of a bank of already high order ARX models. The difference from a single ARX model is insignificant if the ARX order or past horizon is sufficiently high. The role of future horizon is mainly in the model reduction step where it serves to elevate the order of the Hankel matrix. We complement the analysis with simulations.

关键词： Closed-loop identification subspace algorithms future horizon

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