Covariance Matrix Computation of the State Variable of a Stationary Gaussian Process

1998 ◽  
pp. 249-254
Author(s):  
Hirotugu Akaike
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
The State ◽  
Stationary Gaussian Process ◽  
Matrix Computation ◽  
State Variable

Modelling of repeatability phenomena using the stochastic ellipsoid approach

Robotica ◽  
2005 ◽  
Vol 24 (4) ◽  
pp. 477-490 ◽  
Author(s):  
Jean-François Brethé ◽  
Eric Vasselin ◽  
Dimitri Lefebvre ◽  
Brayima Dakyo
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Angular Position ◽  
Jump Process ◽  
Second Order ◽  
Stationary Gaussian Process ◽  
Industrial Manipulator ◽  
The Mean

A stochastic ellipsoid modelling of repeatability is proposed for industrial manipulator robots. The covariance matrix of angular position is determined introducing the jump process, which reveals to be a first and second order stationary Gaussian process.From this accurate covariance matrix, the stochastic ellipsoid theory gives the density of position in the workspace around the mean position. Hence the pose repeatability index can be computed in different locations. Computed and experimental repeatability are compared. Experimental repeatability variability is studied. A new “intrinsic repeatability index” is proposed. In conclusion, the modelling reflects well the location and load influence on the repeatability.

On Estimation of the Conditional Probability of Correct Classification

1978 ◽  
Vol 27 (1-4) ◽  
pp. 49-58
Author(s):  
Shibdas Bandyopadhyay
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Conditional Probability ◽  
Classification Problem ◽  
Stationary Gaussian Process ◽  
Correct Classification ◽  
Conditional Distributions ◽  
Population Distributions ◽  
Population Classification ◽  
Standard Classification

Four different estimators of the conditional probability of correct classification are considered for the two population classification problem with known covariance matrix where the population distributions follow a stationary Gaussian process. The estimators and their conditional distributions are observed to be identical to the corresponding results for the two population equal sample standard classification problem.

The excursions of a stationary Gaussian process outside a large two-dimensional region

2001 ◽  
Vol 33 (1) ◽  
pp. 141-159
Author(s):  
Robert Illsley
Keyword(s):  
Gaussian Process ◽  
Density Function ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Gaussian Processes ◽  
Asymptotic Distributions ◽  
Piecewise Smooth ◽  
Stationary Gaussian Process ◽  
Two Dimensional ◽  
Marginal Density

Let X(t) be a continuous two-dimensional stationary Gaussian process with mean zero, having a marginal density function p[x] and covariance matrix R(t). Let Δ = {∂L; L > 0} be a family of piecewise smooth boundaries of similar two-dimensional star-shaped regions ΓL. We show that, under two conditions on R(t), the asymptotic distribution of the duration of an excursion of X(t) outside ΓL, for large L, depends on the position of the maximum of p[x] on ∂L and on whether R′(0) is zero or not, should the maximum occur at a vertex. We obtain the asymptotic distributions of the duration of an excursion for each of the three cases that arise. We also generalise some results of Breitung (1994) on the asymptotic crossing rates of vector Gaussian processes.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

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