Update State estimate with observation zn+1:
Update the error Covariance:
Forecast steps:
Project the State ahead:
Project the
error Covariance ahead:
Extended Kalman Filter
(EKF) :
The EKF is a statistical
assimilation technique that updates the soil moisture profile based on the relative magnitudes of the covariances of the
observations and the model profile estimates. The main advantage of EKF is that the entire profile may be updated because of the correlation between the surface soil moisture and the
soil moisture of deeper soil. The algorithm tracks the conditional mean of a statistically optimal
estimate of a state vector X through a series of forecast
and update steps.
Observations Z
X
Update steps:
Compute the Kalman gain:
