  The importance of accurate soil moisture data for the development of modern
closed-loop irrigation systems cannot be overstated. Due to the diversity of
soil, it is difficult to obtain an accurate model for agro-hydrological system.
In this study, soil moisture estimation in 1D agro-hydrological systems with
model mismatch is the focus. To address the problem of model mismatch, a
nonlinear state-space model derived from the Richards equation is utilized,
along with additive unknown inputs. The determination of the number of sensors
required is achieved through sensitivity analysis and the orthogonalization
projection method. To estimate states and unknown inputs in real-time, a
recursive expectation maximization (EM) algorithm derived from the conventional
EM algorithm is employed. During the E-step, the extended Kalman filter (EKF)
is used to compute states and covariance in the recursive Q-function, while in
the M-step, unknown inputs are updated by locally maximizing the recursive
Q-function. The estimation performance is evaluated using comprehensive
simulations. Through this method, accurate soil moisture estimation can be
obtained, even in the presence of model mismatch.
