State estimation error covariance matrix

1. What is the error covariance matrix?
2. What is error covariance matrix in Kalman filter?
3. What does covariance matrix tell us?
4. What is background error covariance?

What is the error covariance matrix?

The error covariance matrix (ECM) is a dataset that specifies the correlations in the observation errors between all possible pairs of vertical levels. It is given as a two-dimensional array, of size NxN , where N is the number of vertical levels in the sounding data products.

What is error covariance matrix in Kalman filter?

The Kalman Filter (KF) is a recursive scheme that propagates a current estimate of a state and the error covariance matrix of that state forward in time. The filter optimally blends the new information introduced by the measurements with old information embodied in the prior state with a Kalman gain matrix.

What does covariance matrix tell us?

It is a symmetric matrix that shows covariances of each pair of variables. These values in the covariance matrix show the distribution magnitude and direction of multivariate data in multidimensional space. By controlling these values we can have information about how data spread among two dimensions.

What is background error covariance?

Background error covariance matrices (B): Describes errors in the background state (forecast from previous analysis). Depends on the analysis errors of the previous assimilation, and on forecast model error.