Discrete-time Solutions to the Continuous-time Differential Lyapunov Equation With Applications to Kalman Filtering, Report no. LiTH-ISY-R-3055

Prediction and ltering of continuous-time stochastic processes require a solver of a continuous-time di erential Lyapunov equation (cdle). Even though this can be recast into an ordinary di erential equation (ode), where standard solvers can be applied, the dominating approach in Kalman lter applications is to discretize the system and then apply the discrete-time di erence Lyapunov equation (ddle). To avoid problems with stability and poor accuracy, oversampling is often used. This contribution analyzes over-sampling strategies, and proposes a low-complexity analytical solution that does not involve oversampling. The results are illustrated on Kalman ltering problems in both linear and nonlinear systems.