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  • 1.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Spectral Analysis of Nonuniformly Sampled Data and Applications2012Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets.

    The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters.

    The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.

  • 2.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Gudmundson, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Automatic cepstrum-based smoothing of the periodogram via cross-validation2008In: Proc. 16th European Signal Processing Conference, European Association for Signal Processing , 2008Conference paper (Refereed)
  • 3.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Gudmundson, Erik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Optimal Preconditioning for Interpolation of Missing Data in a Band-Limited Sequence2008In: Proc. 42nd Asilomar Conference on Signals, Systems and Computers, Piscataway, NJ: IEEE , 2008, p. 561-565Conference paper (Refereed)
  • 4.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Pelckmans, Kristiaan
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    Linear Systems, Sparse Solutions, and Sudoku2010In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 1, p. 40-42Article in journal (Refereed)
  • 5.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    A combined linear programming-maximum likelihood approach to radial velocity data analysis for extrasolar planet detection2011In: ICASSP2011, the 36th International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic, 2011, p. 4352-4355Conference paper (Refereed)
    Abstract [en]

    In this paper we introduce a new technique for estimating the parameters of the Keplerian model commonly used in radial velocity data analysis for extrasolar planet detection. The unknown parameters in the Keplerian model, namely eccentricity e, orbital frequency f, periastron passage time T, longitude of periastron., and radial velocity amplitude K are estimated by a new approach named SPICE (a semi-parametric iterative covariance-based estimation technique). SPICE enjoys global convergence, does not require selection of any hyperparameters, and is computationally efficient (indeed computing the SPICE estimates boils down to solving a numerically efficient linear program (LP)). The parameter estimates obtained from SPICE are then refined by means of a relaxation-based maximum likelihood algorithm (RELAX) and the significance of the resultant estimates is determined by a generalized likelihood ratio test (GLRT). A real-life radial velocity data set of the star HD 9446 is analyzed and the results obtained are compared with those reported in the literature.

  • 6.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Comments on "Iterative Estimation of Sinusoidal Signal Parameters"2010In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 12, p. 1022-1023Article in journal (Refereed)
  • 7.
    Babu, Prabhu
    et al.
    Department of Electronic and Computer Engineering, HKUST, Hong Kong.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Connection between SPICE and Square-Root LASSO for sparse parameter estimation2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 95, p. 10-14Article in journal (Refereed)
    Abstract [en]

    In this note we show that the sparse estimation technique named Square-Root LASSO (SR-LASSO) is connected to a previously introduced method named SPICE. More concretely we prove that the SR-LASSO with a unit weighting factor is identical to SPICE. Furthermore we show via numerical simulations that the performance of the SR-LASSO changes insignificantly when the weighting factor is varied. SPICE stands for sparse iterative covariance-based estimation and LASSO for least absolute shrinkage and selection operator.

  • 8.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Sparse spectral-line estimation for nonuniformly sampled multivariate time series: SPICE, LIKES and MSBL2012In: 2012 Proceedings Of The 20th European Signal Processing Conference (EUSIPCO), 2012, p. 445-449Conference paper (Refereed)
    Abstract [en]

    In this paper we deal with the problem of spectral-line analysis ofnonuniformly sampled multivariate time series for which we introduce two methods: the first method named SPICE (sparse iterativecovariance based estimation) is based on a covariance fitting framework whereas the second method named LIKES (likelihood-basedestimation of sparse parameters) is a maximum likelihood technique. Both methods yield sparse spectral estimates and they donot require the choice of any hyperparameters. We numericallycompare the performance of SPICE and LIKES with that of the recently introduced method of multivariate sparse Bayesian learning(MSBL).

  • 9.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Spectral analysis of nonuniformly sampled data — a review2010In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 20, no 2, p. 359-378Article in journal (Refereed)
  • 10.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    University of Florida.
    Modeling radial velocity signals for exoplanet search applications2010In: The 7th International Conference on Informatics in Control, Automation and Robotics, Madeira, Portugal, 2010Conference paper (Refereed)
  • 11.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    Chen, Zhaofu
    Ge, Jian
    Analysis of radial velocity data by a novel adaptive approach2010In: Astronomical Journal, ISSN 0004-6256, E-ISSN 1538-3881, Vol. 139, no 2, p. 783-793Article in journal (Refereed)
  • 12.
    Babu, Prabhu
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Marzetta, Thomas L.
    An IQML type algorithm for AR parameter estimation from noisy covariance sequences2009In: Proc. 17th European Signal Processing Conference, European Association for Signal Processing , 2009, p. 1022-1026Conference paper (Refereed)
  • 13. Sandgren, Niclas
    et al.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On moving average parameter estimation2012Conference paper (Refereed)
    Abstract [en]

    Estimation of the autoregressive moving average (ARMA)parameters of a stationary stochastic process is a problemoften encountered in the signal processing literature. It iswell known that estimating the moving average (MA) parameters is usually more difficult than estimating the autoregressive (AR) part, especially if the zeros are located close tothe unit circle. In this paper, we present four linear methodsfor MA parameter estimation (i.e., methods that involve onlylinear operations) and compare their performances first in acase when the zeros are located far away from the unit circleand secondly in a presumably harder case when the zeros arelocated very close to the unit circle

  • 14.
    Stoica, Anca-Juliana
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computing Science.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Quantitative framework for managing software life cycle2011In: The Open Software Engineering Journal, ISSN 1874-107X, E-ISSN 1874-107X, Vol. 5, p. 1-18Article in journal (Refereed)
  • 15.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Algebraic Derivation of Elfving Theorem on Optimal Experiment Design and Some Connections With Sparse Estimation2010In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 8, p. 743-745Article in journal (Refereed)
  • 16.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Maximum-likelihood nonparametric estimation of smooth spectra from irregularly sampled data2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 12, p. 5746-5758Article in journal (Refereed)
  • 17.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Department of Electronic and Computer Engineering, HKUST, Hong Kong.
    Model order estimation via penalizing adaptively the likelihood (PAL)2013In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 11, p. 2865-2871Article in journal (Refereed)
    Abstract [en]

    This paper introduces a novel rule for model order estimation based on penalizingadatively the likelihood (PAL). The penalty term of PAL, which is data adaptive (as the name suggests), has several unique features: it is "small" (e.g. comparable to AIC penalty) for modelorders, let us say n(0), less than or equal to the true order, denoted by no, and it is "large" (e.g. of the same order as BIC penalty) for n > n(o); furthermore this is true not only as the data sample length increases (which is the case most often considered in the literature) but also asthe signal-to-noise ratio (SNR) increases (the harder case for AIC, BIC and the like); and this "oracle-like" behavior of PAL's penalty is achieved without any knowledge about n(0). Thepaper presents a number of simulation examples to show that PAL has an excellent performance also in non-asymptotic regimes and compare this performance with that of AIC and BIC. 

  • 18.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    On the Exponentially Embedded Family (EEF) Rule for Model Order Selection2012In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 19, no 9, p. 551-554Article in journal (Refereed)
    Abstract [en]

    Model selection is an important task in many signal processing applications. In this letter, we present a generalized likelihood ratio (GLR)-based derivation of the recently proposed EEF rule in an attempt to cast EEF in the main stream of model order selection approaches and provide further insights into its theoretical foundations. We also show that EEF can be expected to behave asymptotically (in the number of data samples) similarly to the Bayesian information criterion (BIC). To evaluate the finite sample performance we consider two numerical examples, including the selection of the number of components in a Gaussian mixture model (GMM), by means of which we show that EEF behaves similarly to BIC.

  • 19.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    On the LIMES approach to spectral analysis of irregularly sampled data2012In: Electronics Letters, ISSN 0013-5194, E-ISSN 1350-911X, Vol. 48, no 4, p. 218-219Article in journal (Refereed)
    Abstract [en]

    LIMES (LIkelihood-based Method for Estimation of Spectra) is a recently introduced non-parametric approach for the spectral analysis of regularly or irregularly sampled data. While LIMES is a statistically powerful approach (owing to its maximum-likelihood character), it is computationally rather intensive for large data sets; additionally, the variance of its estimation errors increases somewhat fast as the size of the data set decreases. Provided are simple practical solutions to these two problems of LIMES.

  • 20.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    On the Proper Forms of BIC for Model Order Selection2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 9, p. 4956-4961Article in journal (Refereed)
    Abstract [en]

    The Bayesian Information Criterion (BIC) is often presented in a form that is only valid in large samples and under a certain condition on the rate at which the Fisher Information Matrix (FIM) increases with the sample length. This form has been improperly used previously in situations in which the conditions mentioned above do not hold. In this correspondence, we describe the proper forms of BIC in several practically relevant cases that do not satisfy the above assumptions. In particular, we present a new form of BIC for high signal-to-noise ratio (SNR) cases. The conclusion of this study is that BIC remains one of the most successful existing rules for model order selection, if properly used.

  • 21.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Parameter estimation of exponential signals: a system identification approach2013In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 23, no 5, p. 1565-1577Article in journal (Refereed)
    Abstract [en]

    Exponential signals occur in extremely diverse applications and estimation of their parameters is one of the basic problems in applied sciences. Nevertheless there are only a handful of methods for exponential analysis that are recommended in the literature, and even those methods have relatively mediocre performance in more difficult scenarios. In this paper we attempt to correct this situation by making use of a system identification approach. The proposed methodology, which we call EASI (Exponential Analysis via System Identification), is shown to have a satisfactory performance (i.e., high resolution and small statistical variability) for practical data lengths, and this not only for white measurement noise but also in cases with highly correlated noise (which were rarely considered in the previous literature).

  • 22.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Sparse estimation of spectral lines: Grid selection problems and their solutions2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, p. 962-967Article in journal (Refereed)
    Abstract [en]

    Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid how should one select the number of grid points, K? We first present a simple practical rule for choosing an initial value (or initial values) of K in a given situation. Then, we go on to explain how the estimation results corresponding to different values of K can be compared with one another and therefore how to select the "best" value of K among those considered. Furthermore, we introduce a method for detecting when a grid is "too rough" and for obtaining refined parameter estimates in such a case.

  • 23.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    SPICE and LIKES: Two hyperparameter-free methods for sparse-parameter estimation2012In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 92, no 7, p. 1580-1590Article in journal (Refereed)
    Abstract [en]

    SPICE (SParse Iterative Covariance-based Estimation) is a recently introduced method for sparse-parameter estimation in linear models using a robust covariance fitting criterion that does not depend on any hyperparameters. In this paper we revisit the derivation of SPICE to streamline it and to provide further insights into this method. LIKES (LIKelihood-based Estimation of Sparse parameters) is a new method obtained in a hyperparameter-free manner from the maximum-likelihood principle applied to the same estimation problem as considered by SPICE. Both SPICE and LIKES are shown to provide accurate parameter estimates even from scarce data samples, with LIKES being more accurate than SPICE at the cost of an increased computational burden.

  • 24.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    The Gaussian data assumption leads to the largest Cramér-Rao bound2011In: IEEE signal processing magazine (Print), ISSN 1053-5888, E-ISSN 1558-0792, Vol. 28, no 3, p. 132-133Article in journal (Refereed)
  • 25.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    A sparse covariance-based method for direction-of-arrival estimation2011In: ICASSP2011, the 36th International Conference on Acoustics, Speech and Signal Processing, Prague, Czech Republic., 2011, p. 2844-2847Conference paper (Refereed)
    Abstract [en]

    In this paper we present a new sparse iterative covariance-based estimation approach, called SPICE, to the direction of arrival estimation problem. SPICE is obtained by the minimization of a statistically well motivated covariance matrix fitting criterion and can be used in both single and multiple-snapshot cases. Some of the unique features enjoyed by SPICE are : it takes account of the noise in the data in a natural manner, it does not require selection of any hyperparameters, and it has global convergence properties.

  • 26.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 1, p. 35-47Article in journal (Refereed)
  • 27.
    Stoica, Peter
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Li, Jian
    SPICE: A Sparse Covariance-Based Estimation Method for Array Processing2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 2, p. 629-638Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel SParse Iterative Covariance-based Estimation approach, abbreviated as SPICE, to array processing. The proposed approach is obtained by the minimization of a covariance matrix fitting criterion and is particularly useful in many-snapshot cases but can be used even in single-snapshot situations. SPICE has several unique features not shared by other sparse estimation methods: it has a simple and sound statistical foundation, it takes account of the noise in the data in a natural manner, it does not require the user to make any difficult selection of hyperparameters, and yet it has global convergence properties.

  • 28. Wahlberg, Bo
    et al.
    Stoica, Peter
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    Babu, Prabhu
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.
    On estimation of cascade systems with common dynamics2009In: 15th IFAC Symposium on System Identification, Saint-Malo, France, 2009, 2009Conference paper (Refereed)
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