Kalman filter covariance matrix interpretation

1. What is covariance matrix in Kalman filter?
2. What does the covariance matrix represent?
3. What is an error covariance matrix?
4. What is covariance EKF?

What is covariance matrix in Kalman filter?

This uncertainty can be represented by a matrix known as the state covariance matrix, P. The state covariance matrix consists of the variances associated with each of the state estimates as well as the correlation between the errors in the state estimates.

What does the covariance matrix represent?

Because covariance can only be calculated between two variables, covariance matrices stand for representing covariance values of each pair of variables in multivariate data. Also, the covariance between the same variables equals variance, so, the diagonal shows the variance of each variable.

What is an 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 covariance EKF?

The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning pa- rameter in EKF, which is often simply postulated by the user.