Kalman filter error covariance matrix

1. What is error covariance matrix in Kalman filter?
2. What is the error covariance matrix?
3. How do you initialise the covariance matrix of a Kalman filter?
4. What is background error covariance?

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 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.

How do you initialise the covariance matrix of a Kalman filter?

Since the model of the Kalman filter does not start with any old measure, the initial state vector x0 - is chosen to be zero. The initial covariance matrix Po is chosen equal to a diagonal matrix with a value equal to 10. The value of the variance of the noise R is chosen to be equal to a constant = 0.05.

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.