  In this article, we introduce the joint maximum a posteriori state path and
parameter estimator (JME) for continuous-time systems described by stochastic
differential equations (SDEs). This estimator can be applied to nonlinear
systems with discrete-time (sampled) measurements with a wide range of
measurement distributions. We also show that the minimum-energy state path and
parameter estimator (MEE) obtains the joint maximum a posteriori noise path,
initial conditions, and parameters. These estimators are demonstrated in
simulated experiments, in which they are compared to the prediction error
method (PEM) using the unscented Kalman filter and smoother. The experiments
show that the MEE is biased for the damping parameters of the drift function.
Furthermore, for robust estimation in the presence of outliers, the JME attains
lower state estimation errors than the PEM.
