An improved log-likelihood gradient for continuous-time stochastic systems with deterministic input

Using a covariance operator approach, we derive an explicit expression for the log-likelihood ratio gradient for system parameter estimation for continuous-time stochastic systems with deterministic inputs. The gradient formula includes the smoother estimates and derivatives of system matrices with no derivatives of estimates or covariance matrices. A deterministic input is also permitted, and the state noise covariance is not required to be nonsingular. Stable numerical techniques to calculate the gradient are also discussed