Centroid Estimation Research Articles

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.

Stars’ Centroid Determination Using PSF-Fitting Method

AbstractThis paper presents an algorithm for restoring telescope images corrupted by turbulence effects and readout noise of a telescope system in order to determine centroid positions of stars, especially the position of a reference star. A computation method employing an accurate centroid estimation algorithm reconstructing apoint spread function(PSF) from the recorded astronomical images has been used. Minimisation of turbulence effects and telescope control system noise in long exposure images acquired and recorded by the ground telescope is proposed. As a solution of the distortion error a minimisation signal is dedicated to GoTo calibration procedures built in control mechanisms of the electromechanical telescope system. The proposed method has been verified in the Matlab environment for real deep sky images recorded by the ground telescope system.

A Localization Method for Multistatic SAR Based on Convex Optimization.

In traditional localization methods for Synthetic Aperture Radar (SAR), the bistatic range sum (BRS) estimation and Doppler centroid estimation (DCE) are needed for the calculation of target localization. However, the DCE error greatly influences the localization accuracy. In this paper, a localization method for multistatic SAR based on convex optimization without DCE is investigated and the influence of BRS estimation error on localization accuracy is analysed. Firstly, by using the information of each transmitter and receiver (T/R) pair and the target in SAR image, the model functions of T/R pairs are constructed. Each model function’s maximum is on the circumference of the ellipse which is the iso-range for its model function’s T/R pair. Secondly, the target function whose maximum is located at the position of the target is obtained by adding all model functions. Thirdly, the target function is optimized based on gradient descent method to obtain the position of the target. During the iteration process, principal component analysis is implemented to guarantee the accuracy of the method and improve the computational efficiency. The proposed method only utilizes BRSs of a target in several focused images from multistatic SAR. Therefore, compared with traditional localization methods for SAR, the proposed method greatly improves the localization accuracy. The effectivity of the localization approach is validated by simulation experiment.

Practical signal processing algorithm for wide‐area surveillance‐GMTI mode

On the basis of the real data acquired with an X-band airborne wide-area surveillance (WAS)-GMTI radar, a practical signal processing algorithm for WAS-GMTI mode is proposed, and it is simple and effective for real-time processing. The key feature of the new algorithm is that the spatial steering vector and fixed channel error are estimated according to the result of the Doppler centroid estimation. This is due to the fact that the angle corresponding to the Doppler centroid is just the antenna look direction. In this study, the detailed description of the algorithm is presented with four steps: pre-processing, clutter suppression, constant false alarm rate detection and parameter estimation. Besides, to observe the effect of the proposed algorithm, the real data processing results are shown after each step. Finally, moving target positioning results of five successive scan periods is presented to demonstrate the effectiveness of the new algorithm.

Simple and robust baseline estimation method for multichannel SAR-GMTI systems

ABSTRACTIn this paper, the authors propose an approach of estimating the effective baseline for ground moving target indication (GMTI) mode of synthetic aperture radar (SAR), which is different from any previous work. The authors show that the new method leads to a simpler and more robust baseline estimate. This method employs a baseline search operation, where the degree of coherence (DOC) is served as a metric to judge whether the optimum baseline estimate is obtained. The rationale behind this method is that the more accurate the baseline estimate, the higher the coherence of the two channels after co-registering with the estimated baseline value. The merits of the proposed method are twofold: simple to design and robust to the Doppler centroid estimation error. The performance of the proposed method is good. The effectiveness of the method is tested with real SAR data.

High-precision and real-time algorithms of multi-object detection, recognition and localization toward ARVD of cooperative spacecrafts

The spacecraft pose estimation based on vision measurement is widely used as an effective method for proximity operation in autonomous rendezvous and docking (ARVD). In order to estimate pose parameters more effectively, it is necessary to achieve high-precision object localization in video images. However, there are some difficulties to satisfy precision and real-time requirements simultaneously for the localization of multiple objects. In this paper, high-precision and real-time algorithms are proposed for multi-object detection, recognition and localization toward ARVD of cooperative spacecrafts. At first, through the denoise and characteristic analysis of video images, an object detection method is proposed based on adaptive threshold segmentation by threshold optimization with the variances of inter-classes and intra-class; then a recognition algorithm of multi-object is proposed by self-organization clustering; moreover, a high-precision localization algorithm of multi-object is proposed based on bilinear interpolation, which can achieve sub-pixel precision for object centroid estimation. A series of experimental results demonstrate that the proposed algorithms can achieve excellent object detection accuracy of 100% within 120m, high-precision object localization of 0.004–0.43pixel at 0.3–150m distance, and is also characterized with strong anti-disturbance and well real-time of 22ms average runtime so as to make a sound basis for further engineering tests.

Compromising polarity and waveform constraints in focal-mechanism solutions; the Mara Rosa 2010 Mw 4 central Brazil earthquake revisited

Focal-mechanism determination of weak events recorded in sparse networks is challenging. First-motion polarities are often available at relatively distant stations, and waveforms only at a few near stations can be modeled. A two-step approach of how to combine such data has been suggested recently (Cyclic Scanning of the Polarity Solutions, or CSPS method; Fojtíková and Zahradník, 2014). It starts with creating a suite of first-motion polarity solutions, which is often highly non-unique. The next step consists of repeating full waveform inversion for all polarity solutions. Even few stations may efficiently reduce the non-uniqueness of the polarity solutions. Centroid depth, time, scalar moment and uncertainty estimate of the well-fitting double-couple solutions are obtained. The CSPS method has been extended in this paper by adding a new feature, i.e. repeated inversions using multiple first-motion polarity sets. The polarity sets are created by projecting the stations on focal sphere in several available velocity models, thus accounting for the takeoff angle uncertainty. The multiple polarity sets provide assessment of the CSPS solution stability. These ideas are demonstrated on a comprehensive analysis of a rare event in central Brazil. It is the Mw ∼4 mainshock of the Mara Rosa 2010 earthquake sequence (Barros et al., 2015, Carvalho et al., 2015). We employ polarities at 11 stations (distances < 730 km) and invert full waveforms at two stations (CAN3 and BDFB at distances ∼120 and 240 km), for 0.1–0.2 and 0.05–0.125 Hz, respectively. Six polarity sets reflect the takeoff angle uncertainty. The obtained CSPS results are very stable across all the polarity sets (in terms of depth, Mw, and strike/dip/rake angles). It is found that the Mara Rosa mainshock mechanism deviated from the composite solution of the whole sequence by 38°. The paper also includes a test simulating situations at which just a single waveform is used, and how it negatively affects the solution stability.

Validation of a method for combining biplanar radiography and magnetic resonance imaging to estimate knee cartilage contact

Combining accurate bone kinematics data from biplane radiography with cartilage models from magnetic resonance imaging, it is possible to estimate tibiofemoral cartilage contact area and centroid location. Proper validation of such estimates, however, has not been performed under loading conditions approximating functional tasks, such as gait, squatting, and stair descent. The goal of this study was to perform an in vitro validation to resolve the accuracy of cartilage contact estimations in comparison to a laser scanning gold standard. Results demonstrated acceptable reliability and accuracy for both contact area and centroid location estimates. Root mean square errors in contact area averaged 8.4% and 4.4% of the medial and lateral compartmental areas, respectively. Modified Sorensen-Dice agreement scores of contact regions averaged 0.81 ± 0.07 for medial and 0.83 ± 0.07 for lateral compartments. These validated methods have applications for in vivo assessment of a variety of patient populations and physical activities, and may lead to greater understanding of the relationships between knee cartilage function, effects of joint injury and treatment, and the development of osteoarthritis.

RCE-Kmeans Method for Data Clustering

There have been many methods developed to solve the clustering problem. One of them is method in swarm intelligence field such as Particle Swarm Optimization (PSO). Rapid Centroid Estimation (RCE) is a method of clustering based Particle Swarm Optimization. RCE, like other variants of PSO clustering, does not depend on initial cluster centers. Moreover, RCE has faster computational time than the previous method like PSC and mPSC. However, RCE has higher standar deviation value than PSC and mPSC in which has impact in the variance of clustering result. It is happaned because of improper equilibrium state, a condition in which the position of the particle does not change anymore, when the stopping criteria is reached. This study proposes RCE-Kmeans which is a method applying K-means after the equilibrium state of RCE reached to update the particle's position which is generated from the RCE method. The results showed that RCE-Kmeans has better quality of the clustering scheme in 7 of 10 datasets compared to K-means and better in 8 of 10 dataset then RCE method. The use of K-means clustering on the RCE method is also able to reduce the standard deviation from RCE method.

A novel SAR interferometry processing method in high resolution spotlight SAR

Synthetic Aperture Radar Interferometry (InSAR) can produce accurate Digital Elevation Model (DEM), and a novel spotlight SAR can get higher azimuth resolution than conventional strip-map SAR. Hence, the combination of InSAR and spotlight SAR techniques implies the potential to obtain higher resolution DEMs which will show more tiny terrain variations. However, in spotlight InSAR processing, additional azimuth interferometric fringes and misregistration decorrelation will be induced by conventional co-registration methods which ignore azimuth varied Doppler centroids in interpolations. Meanwhile, because interferometric fringes in regions with high resolution terrain variations can easily be damaged by random phase noise, there will generate more unreliable unwrapped phase areas with conventional phase unwrapping methods. To eliminate residual azimuth fringes, misregistration decorrelation and unreliable unwrapped phase areas, this paper firstly proposes a novel spotlight SAR interferometry processing method based on co-registration related to two-dimensional Doppler centroid estimation and joint phase unwrapping, and it is validated by using TerraSAR-X spotlight data. The final generated 4 m × 4 m grid space DEM not only preserves high resolution, but also has low root mean square error and absolute mean error which are less than 3 m with respect to the Google earth DEM.

Unsupervised feature selection using swarm intelligence and consensus clustering for automatic fault detection and diagnosis in Heating Ventilation and Air Conditioning systems

Various sensory and control signals in a Heating Ventilation and Air Conditioning (HVAC) system are closely interrelated which give rise to severe redundancies between original signals. These redundancies may cripple the generalization capability of an automatic fault detection and diagnosis (AFDD) algorithm. This paper proposes an unsupervised feature selection approach and its application to AFDD in a HVAC system. Using Ensemble Rapid Centroid Estimation (ERCE), the important features are automatically selected from original measurements based on the relative entropy between the low- and high-frequency features. The materials used is the experimental HVAC fault data from the ASHRAE-1312-RP datasets containing a total of 49 days of various types of faults and corresponding severity. The features selected using ERCE (Median normalized mutual information (NMI)=0.019) achieved the least redundancies compared to those selected using manual selection (Median NMI=0.0199) Complete Linkage (Median NMI=0.1305), Evidence Accumulation K-means (Median NMI=0.04) and Weighted Evidence Accumulation K-means (Median NMI=0.048). The effectiveness of the feature selection method is further investigated using two well-established time-sequence classification algorithms: (a) Nonlinear Auto-Regressive Neural Network with eXogenous inputs and distributed time delays (NARX-TDNN); and (b) Hidden Markov Models (HMM); where weighted average sensitivity and specificity of: (a) higher than 99% and 96% for NARX-TDNN; and (b) higher than 98% and 86% for HMM is observed. The proposed feature selection algorithm could potentially be applied to other model-based systems to improve the fault detection performance.

Pixel response function experimental techniques and analysis of active pixel sensor star cameras

The pixel response function (PRF) of a pixel within a focal plane is defined as the pixel intensity with respect to the position of a point source within the pixel. One of its main applications is in the field of astrometry, which is a branch of astronomy that deals with positioning data of a celestial body for tracking movement or adjusting the attitude of a spacecraft. Complementary metal oxide semiconductor (CMOS) image sensors generally offer better radiation tolerance to protons and heavy ions than CCDs making them ideal candidates for space applications aboard satellites, but like all image sensors they are limited by their spatial frequency response, better known as the modulation transfer function. Having a well-calibrated PRF allows us to eliminate some of the uncertainty in the spatial response of the system providing better resolution and a more accurate centroid estimation. This paper describes the experimental setup for determining the PRF of a CMOS image sensor and analyzes the effect on the oversampled point spread function (PSF) of an image intensifier, as well as the effects due to the wavelength of light used as a point source. It was found that using electron bombarded active pixel sensor (EBAPS) intensification technology had a significant impact on the PRF of the camera being tested as a result of an increase in the amount of carrier diffusion between collection sites generated by the intensification process. Taking the full width at half maximum (FWHM) of the resulting data, it was found that the intensified version of a CMOS camera exhibited a PSF roughly 16.42% larger than its nonintensified counterpart.

Imaging method with low data rate for autonomous star trackers based on compressive sensing

Compressive sensing (CS) theory is popular and has led to the development of new imaging methods in many fields. Specifically, CS theory can reduce the sampling rate of a high-accuracy star tracker and maintain the quality of star images. However, the imaging system of a star tracker contains certain properties that cannot correspond to conventional measurement architectures. Thus, a compressive imaging system that is suitable for the star trackers used in space missions is proposed. First, the CS framework is briefly introduced and the feasibility of typical measurement architectures is analyzed. Second, an imaging method with a low data rate and based on deterministic phase modulation (DPM) is presented to form a weight block circulant matrix (WBCM) of deterministic measurement. The advantage of the proposed imaging method is determined by comparing it with the typical measurement architectures. Third, numerical simulations are conducted to investigate the performance of the proposed method. Results show that the reconstruction quality of the DPM architecture is close to that of random phase modulation architecture. Meanwhile, the WBCM measurement is better than the conventional block circulant matrix measurement. Furthermore, the statistical result significantly ensures accurate star centroid estimation and confirms the feasibility of CS application to star tracker imaging at low data rates.

Automatic bearing fault diagnosis using particle swarm clustering and Hidden Markov Model

Ball bearings are integral elements in most rotating manufacturing machineries. While detecting defective bearing is relatively straightforward, discovering the source of defect requires advanced signal processing techniques. This paper proposes an automatic bearing defect diagnosis method based on Swarm Rapid Centroid Estimation (SRCE) and Hidden Markov Model (HMM). Using the defect frequency signatures extracted with Wavelet Kurtogram and Cepstral Liftering, SRCE+HMM achieved on average the sensitivity, specificity, and error rate of 98.02%, 96.03%, and 2.65%, respectively, on the bearing fault vibration data provided by Case School of Engineering of the Case Western Reserve University (CSE) which warrants further investigation.

Kalman Filtering–Based Probabilistic Nowcasting of Object-Oriented Tracked Convective Storms

AbstractThe weather radar–based object-oriented convective storm tracking is a standard approach for analyzing and nowcasting convective storms. However, the majority of current storm-tracking algorithms provide nowcasts only in a deterministic fashion with limited ability to estimate the related uncertainties.This paper proposes a method for probabilistic nowcasting of convective storms that addresses the issue of uncertainty of nowcasts. The approach first utilizes a two-dimensional radar-based storm identification and tracking algorithm in conjunction with the Kalman filtering of noisy measurements of storm centroid with the continuous white noise acceleration model. The resulting smoothed estimates of storm centroid and velocity components and their error covariance values are then applied to nowcast the probability of storm occurrence.To verify the approach, 20–60-min nowcasts were computed every 5 min using composite weather radar data in Finland including approximately 22 000 tracked storms. The verification shows that the algorithm is applicable in both deterministic and probabilistic manner. Moreover, the forecast probabilities are consistent with observed frequencies of the storms, especially with 20- and 30-min nowcasts. The accuracy of the probabilistic nowcasts was evaluated through the Brier skill score with respect to the deterministic nowcasts and nowcasts based on observation persistence and sample climatology. The results show that the proposed nowcasting method has an improved accuracy over all of the reference forecast types.

Optimization of the autocorrelation weighting function for the time-domain calculation of spectral centroids.

Spectral centroid from the backscattered ultrasound provides important information about the attenuation properties of soft tissues and Doppler effects of blood flows. Because the spectral centroid is originally determined from the power spectrum of backscattered ultrasound signals in the frequency domain, it is natural to calculate it after converting time-domain signals into spectral domain signals, using the fast Fourier transform (FFT). Recent research, however, derived the time-domain equations for calculating the spectral centroid using a Parseval's theorem, to avoid the calculation of the Fourier transform. The work only presented the final result, which showed that the computational time of the proposed time-domain method was 4.4 times faster than that of the original FFT-based method, whereas the average estimation error was negligible. In this paper, we present the optimal design of the autocorrelation weighting function, which is used for the timedomain spectral centroid estimation process, to reduce the computational time significantly. We also carry out a comprehensive analysis of the computational complexities of the FFTbased and time-domain methods with respect to the length of ultrasound signal segments. The simulation results using numerical phantoms show that, with the optimized autocorrelation weighting function, we only need approximately 3% of the full set of data points. In addition to that, because the proposed optimization technique requires a fixed number of data points to calculate the spectral centroid, the execution time is constant as the length of the data segment increases, whereas the execution time of the conventional FFT-based method is increased. Analysis of the computational complexities between the proposed method and the conventional FFT-based method presents O(N) and O(Nlog2N), respectively.

Robust Clutter Suppression and Moving Target Imaging Approach for Multichannel in Azimuth High-Resolution and Wide-Swath Synthetic Aperture Radar

This paper describes a clutter suppression approach and the corresponding moving target imaging algorithm for a multichannel in azimuth high-resolution and wide-swath (MC-HRWS) synthetic aperture radar (SAR) system. Incorporated with digital beamforming processing, MC-HRWS SAR systems are able to suppress the Doppler ambiguities to allow for HRWS SAR imaging and null the clutter directions to suppress clutter for ground moving target indication. In this paper, the degrees of freedom in azimuth for the multichannel SAR systems are employed to implement clutter suppression. First, the clutter and moving target echoes are transformed into the range compression and azimuth chirp Fourier transform frequency domain, i.e., coarse-focused images formation, when the clutter echoes are with azimuth Doppler ambiguity. Considering that moving targets are sparse in the imaging scene and that there is a difference between clutter and a moving target in the spatial domain, a series of spatial domain filters are constructed to extract moving target echoes. Then, using an extracted moving target echo, two groups of signals are formed, and slant-range velocity of a moving target can be estimated based on baseband Doppler centroid estimation algorithm and multilook cross-correlation Doppler centroid ambiguity number resolving approach. After the linear range cell migration correction and azimuth focus processing, a well-focused moving target image can be obtained. In addition, the proposed clutter suppression and imaging approach is not only adapted for uniformly displaced phase center sampling but also for the nonuniform sampling cases. Some simulation experiments are taken to demonstrate our proposed algorithms. Finally, some real measured data results are presented to validate the theoretical investigations and the proposed approaches.

Outlier Detection Using Improved Genetic K-Means

The outlier detection problem in some cases is similar to the classification problem. For example, the main concern of clustering-based outlier detection algorithms is to find clusters and outliers, which are often regarded as noise that should be removed in order to make more reliable clustering. In this article, we present an algorithm that provides outlier detection and data clustering simultaneously. The algorithm improves the estimation of centroids of the generative distribution during the process of clustering and outlier discovery. The proposed algorithm consists of two stages. The first stage consists of improved genetic k-means algorithm (IGK) process, while the second stage iteratively removes the vectors which are far from their cluster centroids.

Maximum‐likelihood‐based Doppler centroid estimation algorithm for MC‐HRWS SAR system

For the multi-channel in azimuth high-resolution and wide-swath (MC-HRWS) synthetic aperture radar (SAR), a novel maximum-likelihood-based Doppler centroid estimation algorithm is developed. During the estimation process, the Doppler centroid is estimated by using the maximum-likelihood approach to combine the range-frequency-variant Doppler characteristics in each channel, such as the cross-functions between neighbouring channels in the range-frequency domain. In addition, the channel mismatch in phase and along azimuth baseline position measurement error can also be estimated. Finally, the experimental results of some real squint mode MC-HRWS SAR data are utilised to validate the theoretical investigations and the proposed approach.

An approach to evaluate and monitor RISAT-1 SAR from level-0 raw data

Data quality evaluation of synthetic aperture radar (SAR) products is essential with respect to mission performance and reliability of the data products for users. The generation of any value-added SAR product starts with a level-0 raw data product, so it is vital firstly to analyse and monitor the raw data. In other words, any inconsistency or error occur because of data, the SAR processor requires to ‘quality evaluate’ the raw data first to ensure that the higher level of data products meets the user specifications. Many parameters can be evaluated from the raw data per se before SAR processing. Here, an independent approach is formulated to evaluate the long-term stability and performance of the SAR system from raw data. Quality parameters such as echo data statistics in terms of bias in the mean of Inphase (I) and Quadrature in phase (Q), power imbalance, phase imbalance, antenna pattern in elevation for the qualified swath, Doppler centroid estimation, and chirp phase and amplitude stability were evaluated and monitored for various scenes of an orbit and characterized in detail for different beams covering the near to far range. In the Radar Imaging Satellite (RISAT-1), the SAR beam is formed by a number of transmit/receive modules (TRMs) (total number of active TRMs depends on the look angle), and the consolidated effect of TRMs can be observed from the raw data instead of individual TRMs, which enables examination of the overall behaviour of beams, from near to far range in different orbits, for temporal stability. In this article, for the first time, a novel approach is taken to observe and evaluate the antenna pattern for the 3 dB qualified swath from range-uncompressed raw data and to relatively monitor the different beams from level-0 raw data for the qualified swath, for both extended homogeneous and non-homogeneous targets. Furthermore, the approach is justified in that it is not necessary to perform range compression, and also one can use scenes with heterogeneous targets to estimate and monitor the beamwidth parameter of the antenna pattern. This article focuses on the results obtained from RISAT-1 level-0 raw data from various beams covered in strip-map mode. The methodology to evaluate the RISAT-1 SAR system from raw data is discussed. Analysis is carried out with respect to different beams (60 beam data of different orbits either side, covering near to far nadir swath coverage) of fine resolution strip-map-1 (FRS-1) mode in circularly transmitted and linearly received polarization, with a defined swath of 25 km with 3 m × 2 m (azimuth × range) resolution. The results of evaluation and monitoring analysis show consistency in the identified parameters observed over time for different beams, and they are within specifications.