Why is the concept of a state covariance matrix necessary in estimation?

1. What is state covariance matrix?
2. What does the covariance matrix represent?
3. What does covariance mean in the Kalman filter?
4. Why is Kalman filter used?

What is state covariance matrix?

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 does covariance mean in the Kalman filter?

The covariance matrix used in the Kalman Filter represents the error of a multidimensional gaussian distributed data set.

Why is Kalman filter used?

Kalman filters are used to optimally estimate the variables of interests when they can't be measured directly, but an indirect measurement is available. They are also used to find the best estimate of states by combining measurements from various sensors in the presence of noise.