error covariance matrixの例文

• With H the observation matrix and R the observation error covariance matrix, which contains the posterior probability distribution, with Kriging mean:
• In the Unscented Kalman Filter ( UKF ), the square root of the state error covariance matrix is required for the unscented transform which is the statistical linearization method used.
• The UKF requires the calculation of a matrix square root of the state error covariance matrix, which is used to determine the spread of the sigma points for the unscented transform.
• The following alternative formula is advantageous when the number of data points m is large ( such as when assimilating gridded or pixel data ) and the data error covariance matrix R is diagonal ( which is the case when the data errors are uncorrelated ), or cheap to decompose ( such as banded due to limited covariance distance ).
• In FGLS, we proceed in two stages : ( 1 ) the model is estimated by OLS or another consistent ( but inefficient ) estimator, and the residuals are used to build a consistent estimator of the errors covariance matrix ( to do so, we often need to examine the model adding additional constraints, for example if the errors follow a time series process, we generally need some theoretical assumptions on this process to ensure that a consistent estimator is available ); and ( 2 ) using the consistent estimator of the covariance matrix of the errors, we implement GLS ideas.