Estimation for incomplete information stochastic systems from discrete observations

This paper is concerned with the estimation problem for incomplete information stochastic systems from discrete observations. The suboptimal estimation of the state is obtained by constructing the extended Kalman filtering equation. The approximate likelihood function is given by using a Riemann sum and an Ito sum to approximate the integrals in the continuous-time likelihood function. The consistency of the maximum likelihood estimator and the asymptotic normality of the error of estimation are proved by applying the martingale moment inequality, Holder's inequality, the Chebyshev inequality, the Burkholder-Davis-Gundy inequality and the uniform ergodic theorem. An example is provided to verify the effectiveness of the estimation methods.