An Automatic Cloud Tracking System Based on the Cross-Covariance Method

1980 ◽  
Author(s):  
David H. Lee ◽  
Roland E. Nagle
Keyword(s):  
Tracking System ◽  
Cross Covariance ◽  
The Cross ◽  
Cloud Tracking

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

scholarly journals Second-order properties and central limit theory for the vertex process of iteration infinitely divisible and iteration stable random tessellations in the plane

2010 ◽  
Vol 42 (4) ◽  
pp. 913-935 ◽  
Author(s):  
Tomasz Schreiber ◽  
Christoph Thäle
Keyword(s):  
Correlation Function ◽  
Point Process ◽  
Central Limit ◽  
Pair Correlation ◽  
Density Parameter ◽  
Infinitely Divisible ◽  
Limit Theory ◽  
Vertex Point ◽  
Cross Covariance ◽  
The Cross

The point process of vertices of an iteration infinitely divisible or, more specifically, of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation function, as well as the cross-covariance measure and the cross-correlation function of the vertex point process and the random length measure in the general nonstationary regime. We also give special formulae in the stationary and isotropic setting. Exact formulae are given for vertex count variances in compact and convex sampling windows, and asymptotic relations are derived. Our results are then compared with those for a Poisson line tessellation having the same length density parameter. Moreover, a functional central limit theorem for the joint process of suitably rescaled total edge counts and edge lengths is established with the process (ξ, tξ), t > 0, arising in the limit, where ξ is a centered Gaussian variable with explicitly known variance.

scholarly journals The New Second and Higher Order Spectral Technique for Damage Monitoring of Structures and Machinery

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Len Gelman
Keyword(s):  
Higher Order ◽  
Spectral Technique ◽  
Cross Covariance ◽  
Spectral Components ◽  
Damage Monitoring ◽  
The Cross ◽  
Higher Order Spectra

The new second and higher order spectral technique, the cross-covariance of complex spectral components, is proposed for monitoring damage of structure and machinery Normalization of the proposed technique is also developed. It is shown by simulation that the proposed technique provides effectiveness gain for detecting of damage compared to the higher order spectra.

scholarly journals Estimating sediment thickness by using horizontal distance to outcrop as secondary information

2017 ◽  
Author(s):  
Nils-Otto Kitterød
Keyword(s):  
Cross Validation ◽  
Estimation Error ◽  
Small Scale ◽  
Horizontal Distance ◽  
Estimation Variance ◽  
Sediment Thickness ◽  
Preferential Sampling ◽  
Cross Covariance ◽  
The Cross ◽  
Secondary Information

Abstract. Sediment thickness (D) was estimated utilizing a publically available well database from Norway, GRANADA. General challenges associated with such databases typically involve clustering and bias of the data material due to preferential sampling. However, if information about horizontal distance to the nearest outcrop (L) is included, does the spatial estimation of D improve? This idea was tested comparing two cross-validation results: ordinary kriging (OK) where L was disregarded; and co-kriging (CK) where cross-covariance between D and L was included. The analysis resulted in only minor differences between OK and CK in terms of absolute estimation error, however CK produced more precise results than OK. All observations were declustered and transformed to standard normal probability density functions before estimation and back transformed for the cross-validation analysis. The semivariogram analysis gave correlation lengths for D and L of approx. 10 km and 6 km. These correlations reduce the estimation variance in the cross-validation analysis because more than 50 % of the data material had two or more observations within a radius of 5 km. The small-scale variance of D, however, was about 50 % of the total variance, which gave an accuracy of less than 60 % for most of the cross-validation cases. Despite of the noisy character in the data material, the analysis demonstrates that L can be used as a secondary information to reduce the estimation variance of D.

Use of Phase Streamlines for Covariance Localization in Ensemble Kalman Filter for Three-Phase History Matching

2012 ◽  
Vol 15 (03) ◽  
pp. 273-289 ◽  
Author(s):  
Shingo Watanabe ◽  
Akhil Datta-Gupta
Keyword(s):  
Kalman Filter ◽  
Gas Phase ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Model Parameters ◽  
Ensemble Size ◽  
Three Phase ◽  
Cross Covariance ◽  
The Cross ◽  
Water Cut

Summary The ensemble Kalman filter (EnKF) has gained increased popularity for history matching and continuous reservoir-model updating. It is a sequential Monte Carlo approach that works with an ensemble of reservoir models. Specifically, the method uses cross covariance between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross covariance and can cause loss of geologic realism from unrealistic model updates outside the region of the data influence and/or loss of variance leading to ensemble collapse. A common approach to remedy the situation is to limit the influence of the data through covariance localization. In this paper, we show that for three-phase-flow conditions, the region of covariance localization strongly depends on the underlying flow dynamics as well as on the particular data type that is being assimilated, for example, water cut or gas/oil ratio (GOR). This makes the traditional distance-based localizations suboptimal and, often, ineffective. Instead, we propose the use of water- and gas-phase streamlines as a means for covariance localization for water-cut- and GOR-data assimilation. The phase streamlines can be computed on the basis of individual-phase velocities which are readily available after flow simulation. Unlike the total velocity streamlines, phase streamlines can be discontinuous. We show that the discontinuities in water-phase and gas-phase streamlines naturally define the region of influence for water-cut and GOR data and provide a flow-relevant covariance localization during EnKF updating. We first demonstrate the validity of the proposed localization approach using a waterflood example in a quarter-five-spot pattern. Specifically, we compare the phase streamline trajectories with cross-covariance maps computed using an ensemble size of 2,000 for both water-cut and GOR data. The results show a close correspondence between the time evolution of phase streamlines and the cross-covariance maps of water-cut and GOR data. A benchmark uncertainty quantification (the PUNQ-S3) (Carter 2007) model application shows that our proposed localization outperforms the distance-based localization method. The updated models show improved forecasts while preserving geologic realism.

scholarly journals Robust Recursive Least-Squares Finite Impulse Response Predictor in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Stochastic Systems ◽  
Finite Impulse Response ◽  
The State ◽  
Recursive Least Squares ◽  
Prediction Algorithm ◽  
Estimation Accuracy ◽  
Cross Covariance ◽  
Observation Noise ◽  
The Cross ◽  
Robust Prediction

This paper newly proposes the robust RLS Wiener FIR prediction algorithm based on the innovation theory for the linear stochastic systems including with parameters. In the robust RLS Wiener predictor, the following information is used. (1) The system matrices for the signal and the degraded signal. (2) The observation matrices for the signal and the degraded signal. (3) The variance of the state for the degraded signal. (4) The cross-variance of the state for the signal with the state. (5) The variance of the observation noise. As a step to obtain the robust RLS Wiener FIR prediction algorithm, this paper presents the robust prediction algorithm of the signal using the covariance information etc. In the predictor, the following information is used. (1) The observation matrices for the signal and the degraded signal. (2) The variance of the state for the degraded signal. (3) The auto-covariance information of the state for the degraded signal. (4) The cross-covariance information of the state for the signal with that for the degraded signal. (5) The variance of the observation noise. The estimation accuracy of the proposed robust RLS Wiener FIR predictor is superior to the existing RLS Wiener FIR predictor.

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