A new log-likelihood gradient formula for continuous time stochastic systems with uncertain matrix

We use a finitely additive white noise approach to derive an explicit expression for the gradient of the log-likelihood ratio for system parameter estimation in the case of a continuous time linear dynamic stochastic system and noisy observations. Our gradient formula, includes the smoother estimates of the state, and derivatives of the system matrices, but no derivatives of the estimates or error covariances. A scheme to calculate the log-likelihood gradient without solving any Ricatti equations is described