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Iterative signal-order and noise estimation for multivariate data

ELECTRONICS LETTERS 2001年第2期37卷 134-135页

作者： Lee, J Staelin, DH MIT Elect Res Lab Cambridge MA 02139 USA

The iterative order and noise (ION) estimation algorithm estimates the signal order of multivariate data, e.g. using a scree plot [1], and the unknown noise variances, e.g. using the expectation-maximisation (EM) algo... 详细信息

关键词： filtering theory multivariate data scree plot Filtering methods in signal processing iterative methods iterative signal-order estimation linear regression principal component analysis principal component analyses unknown noise variances Wiener filtering Signal processing theory Interpolation and function approximation (numerical analysis) expectation-maximisation algorithm Wiener filters noise estimation signal resolution Other topics in statistics

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Gaussian mixture model approximation of total spatial power spectral density for multiple incoherently distributed sources

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IET SIGNAL PROCESSING 2013年第4期7卷 306-311页

作者： Wang, Huigang Li, Shanlong Li, Huxiong Shi, Yang Northwestern Polytech Univ Coll Marine Xian 710072 Peoples R China Wenzhou Univ Sch Comp Engn Wenzhou Peoples R China Univ Victoria Dept Mech Engn Victoria BC V8N 3P6 Canada

Practically, the spatial power spectral density (PSD) of single or multiple incoherently distributed (ID) sources is often unknown, and the total spatial PSD is suitable to model the spatial distribution characteristic of signals if the number of multiple ID sources is also unknown. In this study, the Gaussian mixture model (GMM) is employed to characterise the total spatial PSD of multiple ID sources, and two algorithms are proposed to estimate the parameters of the GMM. The first one is the covariance fitting method for multiple ID sources with Gaussian PSD, and the other is the iterative expectation maximisation (EM) algorithm. Simulation studies demonstrate that the EM algorithm outperforms other methods in approximating the shape of the total spatial PSD, especially for small spatial spread.

关键词： expectation-maximisation algorithm IDAHO OPERATIONS OFFICE Gm(m)

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Attitude determination method integrating square-root cubature Kalman filter with expectation-maximization for inertial navigation system applied to underwater glider

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REVIEW OF SCIENTIFIC INSTRUMENTS 2019年第9期90卷 095001-095001页

作者： Huang, Haoqian Shi, Rengdu Zhou, Jun Yang, Yuan Song, Rui Chen, Jianfeng Wu, Guoqing Zhang, Jiajin Hohai Univ Coll Energy & Elect Engn Nanjing 211100 Jiangsu Peoples R China Southeast Univ Sch Instrument Sci & Engn Nanjing 210096 Jiangsu Peoples R China Nankai Univ Inst Robot & Automat Informat Syst Tianjin 300457 Peoples R China Jiangsu Univ Automot Engn Res Inst Zhenjiang 212013 Jiangsu Peoples R China China Ship Sci Res Ctr Wuxi 214100 Jiangsu Peoples R China Fujian Inst Oceanog Fujian Prov Key Lab Coast & Isl Management Techno Xiamen 361013 Fujian Peoples R China

The uncertainty, complexity, and variability of the marine environment inevitably lead to a change in the measurement error resulting in erroneous estimation of navigation information. To solve this problem, this paper proposes a novel method integrating the square-root cubature Kalman filter (SCKF) with the expectation-maximization (EM) algorithm. The proposed new SCKF (NSCKF) algorithm makes better use of the advantages of SCKF and the EM online algorithm. The performance of NSCKF is verified theoretically and evaluated by experiments. The results indicate that the proposed NSCKF algorithm can better estimate predicted error covariance and measurement noise than two other comparison methods owing to the online EM method so that the more accurate attitude estimation can be obtained by the NSCKF algorithm although the measurement error has a great variation. Moreover, the accuracy and efficiency can be guaranteed by employing the SCKF. Experimental results demonstrate that the NSCKF can provide a more stable attitude estimation in different cases of measurement errors. Therefore, the NSCKF is more suitable to be used in underwater navigation than other comparison methods because of higher accuracy, more efficiency, and better robustness.

关键词： attitude measurement covariance analysis expectation-maximisation algorithm inertial navigation Kalman filters measurement errors underwater equipment

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Estimation of target states and signal strength in the probabilistic multiple hypothesis tracking framework

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IET RADAR SONAR AND NAVIGATION 2014年第6期8卷 565-574页

作者： Choi, Won-Yong Hong, Sun-Mog Kyungpook Natl Univ Sch Elect Engn Taegu South Korea

An approach is presented for simultaneously estimating target states and signal-to-noise ratio (SNR) in the framework of the probabilistic multiple hypothesis tracking (PMHT). The approach, named PMHT-S, utilises the expectation-maximisation (EM) algorithm to obtain the maximum a posteriori estimates of target states and SNR's of multiple targets in the presence of false measurements. The missing data of the EM algorithm consists of measurement-to-target assignments as well as a set of fictitious geometric and signal strength measurements each associated with a target under the hypothesis that the target has been undetected. This formulation creates new algorithmic approaches for solving PMHT problems such that information on missed targets may be exploited. It is shown that the auxiliary function of the PMHT-S is additively separable as the sum of a function of target states and a function of target SNR's. The pair, as a result, can be independently maximised in each EM iteration to update target states and SNR's. The computational advantage of the separation is substantial even for a small number of targets. Explicit expressions of the auxiliary function of the PMHT-S are given. Monte Carlo simulations were performed to assess estimation performance of the PMHT-S for target tracking examples.

关键词： expectation-maximisation algorithm Monte Carlo methods probability signal processing state estimation target tracking target state estimation probabilistic multiple hypothesis tracking framework SNR signal-to-noise ratio PMHT-S expectation-maximisation algorithm EM algorithm maximum a posteriori estimation measurement-to-target assignments signal strength measurements auxiliary function EM iteration Monte Carlo simulations target tracking

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Tracking and length estimation of underwater acoustic target

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ELECTRONICS LETTERS 2017年第17期53卷 1224-1226页

作者： Yu, Liang Cheng, Yongmei Li, Song Liang, Yan Wang, Xiaoxu Northwestern Polytech Univ Sch Automat Xian 710072 Peoples R China

Underwater acoustic multi-target tracking using bearing, Doppler and a conventional filtering method to determine the target location has problems such as low precision and inaccurate identification. Target echo time broadening is used first for the tracking process. The length of the target can be derived from the echo broadening, and the target length is obtained as a parameter by expectation-maximisation derivation, thereby increasing the dimension of the measurement for the estimation. Simulation results show that this method has higher tracking accuracy and target recognition accuracy than do other feature-aided tracking methods.

关键词： underwater acoustic communication tracking expectation-maximisation algorithm length estimation underwater acoustic target underwater acoustic multitarget tracking filtering method Doppler method tracking process echo broadening expectation-maximisation derivation target recognition tracking methods

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IMAGE IDENTIFICATION AND RESTORATION IN THE SUBBAND DOMAIN (VOL 3, PG 312, 1994)

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1994年第6期3卷 873-873页

作者： KIM, JM Center for Image Processing Research and Electrical Computer and Systems Engineering Department Rensselaer Polytechnic Institute Troy NY USA

When faced with a large support point spread function (PSF), the iterative expectation-maximization (EM) algorithm, which is often used for PSF identification, is very sensitive to the initial PSF estimate. To deal with this problem, the authors propose to do EM image identification and restoration in the subband domain. After the image is first divided into subbands, the EM algorithm is applied to each subband separately. Since the PSF can be taken to have smaller support in each subband, these subbands should be less of a problem with the EM model identification. They also introduce an adaptive subband EM method for use in the upper frequency subbands.

关键词： restoration bearing point subband Subbands expectation-maximisation algorithm Point spread function Image recognition

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Adjust quality scores from alignment and improve sequencing accuracy

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NUCLEIC ACIDS RESEARCH 2004年第17期32卷 5183-5191页

作者： Li, M Nordborg, M Li, LM Univ So Calif Los Angeles CA 90033 USA

In shotgun sequencing, statistical reconstruction of a consensus from alignment requires a model of measurement error. Churchill and Waterman proposed one such model and an expectation-maximization (EM) algorithm to estimate sequencing error rates for each assembly matrix. Ewing and Green defined Phred quality scores for base-calling from sequencing traces by training a model on a large amount of data. However, sample preparations and sequencing machines may work under different conditions in practice and therefore quality scores need to be adjusted. Moreover, the information given by quality scores is incomplete in the sense that they do not describe error patterns. We observe that each nucleotide base has its specific error pattern that varies across the range of quality values. We develop models of measurement error for shotgun sequencing by combining the two perspectives above. We propose a logistic model taking quality scores as covariates. The model is trained by a procedure combining an EM algorithm and model selection techniques. The training results in calibration of quality values and leads to a more accurate construction of consensus. Besides Phred scores obtained from ABI sequencers, we apply the same technique to calibrate quality values that come along with Beckman sequencers.

关键词： expectation-maximisation algorithm Sequencing Alignment error model DNA Sequence Analysis sequencer Error measure model selection Analyses, Sequence

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A constrained EM algorithm for principal component analysis

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NEURAL COMPUTATION 2003年第1期15卷 57-65页

作者： Ahn, JH Oh, JH Pohang Univ Sci & Technol Dept Phys Pohang South Korea

We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.

关键词： post-treatment Symmetric matrix Factor analysis component analysis expectation-maximisation algorithm downward mining diagonalization

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Statistical trajectory of an approximate EM algorithm for probabilistic image processing

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2007年第37期40卷 11285-11300页

作者： Tanaka, Kazuyuki Titterington, D. M. Tohoku Univ Grad Sch Informat Sci Aoba Ku Sendai Miyagi 9808579 Japan Univ Glasgow Dept Stat Glasgow G12 8QQ Lanark Scotland

We calculate analytically a statistical average of trajectories of an approximate expectation-maximization ( EM) algorithm with generalized belief propagation ( GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations.

关键词： GENERALIZED BELIEF PROPAGATION GRAPHICAL MODELS HYPERPARAMETER ESTIMATION FREE-ENERGY RESTORATION MECHANICS CORRECTNESS CODES restoration Belief propagation Approximate Free energy expectation-maximisation algorithm Mechanics cluster variation method Image processing Probability density function Graphical models Codes trajectory RECURSIVE FUNCTIONS

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BINARY CLASSIFICATION BY STOCHASTIC NEURAL NETS

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1995年第2期6卷 488-491页

作者： NADAS, A IBM Research Division IBM Thomas J. Watson Research Center Yorktown Heights NY USA

We classify points in R(d) (feature vectors) by functions related to feedforward artificial neural networks (ANN's). These functions, dubbed ''stochastic neural nets,'' arise in a natural way from probabilistic as well as statistical considerations. The probabilistic idea is to define a classifying bit locally by using the sign of a hidden state-dependent noisy linear function of the feature vector as a new;d + 1st coordinate of the vector. This d + 1-dimensional distribution is approximated by a mixture distribution. The statistical idea-is that the approximating mixtures, and hence the a posteriori class probability functions (stochastic neural nets) defined by them, can be conveniently trained either by maximum likelihood or by a Bayes criterion through the use of an appropriate expectation-Maximization (EM) algorithm.

关键词： Probability functions Eigenvector maximum likelihood Stochastic expectation-maximisation algorithm Neural network

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