Numerical simulation of continuous-time stochastic dynamical systems with noisy measurements and their discrete-time equivalents

Computer-aided control system design software packages offer several numerical methods to simulate continuous-time (CT) deterministic dynamical systems. However, simulating stochastic dynamical systems (SDSs) has not received as much attention. This paper presents a self-contained treatment of how to simulate linear time-invariant CT SDSs with noisy measurements. The system model considered is quite general and avoids many simplifying assumptions generally made in the literature. An analytical solution to a state-space representation of the CT SDS is presented, and numerical approximations to such solution are derived. Moreover, the connection between the CT SDS and a discrete-time (DT) statistically equivalent system is established. Numerical methods for computing the various DT system and noise statistics matrices are discussed. An example is presented to illustrate the application of the various methods discussed in this paper.