Identification of Non-Gaussian Stochastic System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Sung-man Park ◽  
O-shin Kwon ◽  
Jin-sung Kim ◽  
Jong-bok Lee ◽  
Hoon Heo
Keyword(s):  
Random Process ◽  
Random Noise ◽  
Stochastic Simulations ◽  
Kolmogorov Equation ◽  
Gaussian Random Process ◽  
System Parameters ◽  
Analysis Technique ◽  
Gaussian Analysis ◽  
Gaussian System ◽  
Non Gaussian

This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.

scholarly journals Duration Distribution and Up-crossings Rate of Generalized Hyperbolic Processes

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Moh’d T. Alodat ◽  
Khalid M. Aludaat
Keyword(s):  
Gaussian Process ◽  
Random Process ◽  
Alternative Model ◽  
Sea Surface ◽  
Surface Elevation ◽  
Gaussian Random Process ◽  
Duration Distribution ◽  
Non Gaussian

A Gaussian process is usually used to model the sea surface elevation in the oceanography. As the depth of the water decreases or the sea severity increases, the sea surface elevation departs from symmetry and Gaussianity. In this paper, a stationary non-Gaussian random process called the generalized hyperbolic process is used as an alternative model. The process generates a family of processes. We derive the rate of up-crossings for this process and the distribution of the height of the process. We also derive the duration distribution of an excursion for the generalized hyperbolic process.

Numerical Generation of Compound Random Processes with an Arbitrary Autocorrelation Function

2018 ◽  
Vol 17 (01) ◽  
pp. 1850001 ◽  
Author(s):  
Dima Bykhovsky ◽  
Tom Trigano
Keyword(s):  
Random Process ◽  
Autocorrelation Function ◽  
Analytical Study ◽  
Random Processes ◽  
The Other ◽  
Gaussian Random Process ◽  
Numerical Examples ◽  
Compound Process ◽  
Numerical Generation ◽  
Non Gaussian

The generation of non-Gaussian random processes with a given autocorrelation function (ACF) is addressed. The generation is based on a compound process with two components. Both components are solutions of appropriate stochastic differential equations (SDEs). One of the components is a Gaussian process and the other one is non-Gaussian with an exponential ACF. The analytical study shows that a compound combination of these processes may be used for the generation of a non-Gaussian random process with a required ACF. The results are verified by two numerical examples.

scholarly journals Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

2021 ◽  
Author(s):  
Robin E Upham ◽  
Michael L Brown ◽  
Lee Whittaker
Keyword(s):  
Power Spectrum ◽  
Random Noise ◽  
Power Spectra ◽  
Stage Iv ◽  
Wishart Distribution ◽  
Weak Lensing ◽  
Dependence Structure ◽  
Gaussian Fields ◽  
Non Gaussian ◽  
Parameter Constraints

Abstract We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from Stage IV weak lensing surveys.

Dynamic Target Tracking Based on Particle Filter in Actual Environment

2013 ◽  
Vol 683 ◽  
pp. 824-827
Author(s):  
Tian Ding Chen ◽  
Chao Lu ◽  
Jian Hu
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Target Tracking ◽  
Monitoring System ◽  
Filter Method ◽  
Complex Scene ◽  
Actual Environment ◽  
Dynamic Target ◽  
Gaussian System ◽  
Non Gaussian

With the development of science and technology, target tracking was applied to many aspects of people's life, such as missile navigation, tanks localization, the plot monitoring system, robot field operation. Particle filter method dealing with the nonlinear and non-Gaussian system was widely used due to the complexity of the actual environment. This paper uses the resampling technology to reduce the particle degradation appeared in our test. Meanwhile, it compared particle filter with Kalman filter to observe their accuracy .The experiment results show that particle filter is more suitable for complex scene, so particle filter is more practical and feasible on target tracking.

scholarly journals Incremental Non-Gaussian Analysis on Multivariate EEG Signal Data

2012 ◽  
Vol E95.D (12) ◽  
pp. 3010-3016 ◽  
Author(s):  
Kam Swee NG ◽  
Hyung-Jeong YANG ◽  
Soo-Hyung KIM ◽  
Sun-Hee KIM
Keyword(s):  
Eeg Signal ◽  
Gaussian Analysis ◽  
Non Gaussian

scholarly journals Non-Gaussian Analysis of Diffusion Weighted Imaging in Head and Neck at 3T: A Pilot Study in Patients with Nasopharyngeal Carcinoma

PLoS ONE ◽  
2014 ◽  
Vol 9 (1) ◽  
pp. e87024 ◽  
Author(s):  
Jing Yuan ◽  
David Ka Wai Yeung ◽  
Greta S. P. Mok ◽  
Kunwar S. Bhatia ◽  
Yi-Xiang J. Wang ◽  
...  
Keyword(s):  
Pilot Study ◽  
Nasopharyngeal Carcinoma ◽  
Head And Neck ◽  
Diffusion Weighted Imaging ◽  
Diffusion Weighted ◽  
Gaussian Analysis ◽  
Non Gaussian
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