scholarly journals Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Fangfang ◽  
Sun Shuli
Keyword(s):  
Computational Cost ◽  
Covariance Matrices ◽  
The State ◽  
Multirate Systems ◽  
Multiplicative Noises ◽  
Cross Covariance ◽  
Sampling Points ◽  
Optimal Fusion ◽  
The Cross ◽  
Local Filters

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

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 A partition-enhanced least-squares collocation approach (PE-LSC)

2021 ◽  
Vol 95 (8) ◽  
Author(s):  
P. Zingerle ◽  
R. Pail ◽  
M. Willberg ◽  
M. Scheinert
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Computation Time ◽  
Covariance Matrices ◽  
Kernel Functions ◽  
Intermediate Step ◽  
Target Area ◽  
Least Squares Collocation ◽  
Isotropic Coordinates ◽  
Cross Covariance

AbstractWe present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation needs only hours instead of weeks) in comparison with the classical unpartitioned LSC. Likewise, the memory requirement is reduced by a factor of about 360 (i.e., allocating memory in the order of GB instead of TB).

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.

scholarly journals Linear Optimal Fusion of Local Unbiased FIR Filters

2018 ◽  
Vol 210 ◽  
pp. 05004
Author(s):  
Xuefeng Fan ◽  
Shunyi Zhao ◽  
Yuriy S. Shmaiy
Keyword(s):  
State Space ◽  
Finite Impulse Response ◽  
State Space Model ◽  
Minimum Variance ◽  
Optimal Weights ◽  
Cross Covariance ◽  
Optimal Fusion ◽  
Local Filters ◽  
Noise Statistics ◽  
Time Invariant

This paper presents a multi-sensor decentralized fusion unbiased finite impulse response (UFIR) filter for discrete time-invariant state-space models. Fusion is provided in the minimum variance sense. By calculating the cross covariance between any of two local filters for the extended state-space model, linear optimal weights are derived to fuse local UFIR estimates. Simulation conduced for a two-state polynomial model shows that the proposed fusion UFIR filter has higher robustness than the fusion Kalman filter against errors in the noise statistics and temporary model uncertainties.

Accurate and Transferable Multitask Prediction of Chemical Properties with an Atoms-in-Molecule Neural Network

2018 ◽  
Author(s):  
Roman Zubatyuk ◽  
Justin S. Smith ◽  
Jerzy Leszczynski ◽  
Olexandr Isayev
Keyword(s):  
Neural Network ◽  
Molecular System ◽  
Computational Cost ◽  
Chemical Properties ◽  
The State ◽  
Molecular Properties ◽  
Training Data ◽  
Dft Methods ◽  
Benchmark Datasets ◽  
Quantum Phenomena

<p>Atomic and molecular properties could be evaluated from the fundamental Schrodinger’s equation and therefore represent different modalities of the same quantum phenomena. Here we present AIMNet, a modular and chemically inspired deep neural network potential. We used AIMNet with multitarget training to learn multiple modalities of the state of the atom in a molecular system. The resulting model shows on several benchmark datasets the state-of-the-art accuracy, comparable to the results of orders of magnitude more expensive DFT methods. It can simultaneously predict several atomic and molecular properties without an increase in computational cost. With AIMNet we show a new dimension of transferability: the ability to learn new targets utilizing multimodal information from previous training. The model can learn implicit solvation energy (like SMD) utilizing only a fraction of original training data, and archive MAD error of 1.1 kcal/mol compared to experimental solvation free energies in MNSol database.</p>

An Efficient Dual-Resolution Approach for Ensemble Data Assimilation and Tests with Simulated Doppler Radar Data

2008 ◽  
Vol 136 (3) ◽  
pp. 945-963 ◽  
Author(s):  
Jidong Gao ◽  
Ming Xue
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Radial Velocity ◽  
Computational Cost ◽  
Radar Data ◽  
Horizontal Resolution ◽  
Velocity Data ◽  
Background Error ◽  
Cross Covariance ◽  
Radial Velocity Data

Abstract A new efficient dual-resolution (DR) data assimilation algorithm is developed based on the ensemble Kalman filter (EnKF) method and tested using simulated radar radial velocity data for a supercell storm. Radar observations are assimilated on both high-resolution and lower-resolution grids using the EnKF algorithm with flow-dependent background error covariances estimated from the lower-resolution ensemble. It is shown that the flow-dependent and dynamically evolved background error covariances thus estimated are effective in producing quality analyses on the high-resolution grid. The DR method has the advantage of being able to significantly reduce the computational cost of the EnKF analysis. In the system, the lower-resolution ensemble provides the flow-dependent background error covariance, while the single-high-resolution forecast and analysis provides the benefit of higher resolution, which is important for resolving the internal structures of thunderstorms. The relative smoothness of the covariance obtained from the lower 4-km-resolution ensemble does not appear to significantly degrade the quality of analysis. This is because the cross covariance among different variables is of first-order importance for “retrieving” unobserved variables from the radar radial velocity data. For the DR analysis, an ensemble size of 40 appears to be a reasonable choice with the use of a 4-km horizontal resolution in the ensemble and a 1-km resolution in the high-resolution analysis. Several sensitivity tests show that the DR EnKF system is quite robust to different observation errors. A 4-km thinned data resolution is a compromise that is acceptable under the constraint of real-time applications. A data density of 8 km leads to a significant degradation in the analysis.

scholarly journals Survey of the state of conservation of the Mylodon listai (Xenarthra-Mylodontidae) skin fragment from the Pleistocene of Argentina kept at the Museum of La Plata (Argentina)

2016 ◽  
Vol 10 ◽  
pp. 44-53 ◽  
Author(s):  
Daniela Silvana Nitiu ◽  
Andrea Mallo ◽  
Mario Saparrat ◽  
Mauro Garcia Santa Cruz
Keyword(s):  
Relative Humidity ◽  
Environmental Parameters ◽  
The State ◽  
La Plata ◽  
Important Type ◽  
Fungal Load ◽  
Sampling Points

The aim of the present study was to assess the state of conservation of the fossilized skin fragment assigned to Mylodon listai preserved in a showcase of the Paleontology Hall of the Museum of La Plata. To this end, we conducted a volumetric aerobiological sampling both inside the showcase and in the hall to detect the presence of fungal load that could alter its preservation. We also determined the environmental parameters both inside and outside the showcase. The aerobiological sampling inside the showcase showed 3061.50 spores/m3 corresponding to 22 fungal types, while in the hall, 2283.20 spores/m3 corresponding to 14 fungal types where detected. Cladosporium was the most important type in all the sampling points. The temperatures recorded were lower than those recommended for the conservation of leather and the relative humidity values were acceptable in 70% of the record for this material

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