  We extend the linear mixed-effects state model to accommodate the correlated
individuals and investigate its parameter and state estimation based on
disturbance smoothing in this paper. For parameter estimation, EM and score
based algorithms are considered. Intermediate quantity of EM algorithm is
investigated firstly from which the explicit recursive formulas for the
maximizer of the intermediate quantity are derived out for two given models. As
for score based algorithms, explicit formulas for the score vector are achieved
from which it is shown that the maximum likelihood estimation is equivalent to
moment estimation. For state estimation we advocate it should be carried out
without assuming the random effects being known in advance especially when the
longitudinal observations are sparse. To this end an algorithm named mixture
Kalman filter with kernel smoothing (MKF-KS) is proposed. Numerical studies are
carried out to investigate the proposed algorithms which validate the efficacy
of the proposed inference approaches.
