Connection between continuous and discrete Riccati equations with applications to Kalman filtering

The aim of the paper is to explore the relationship between the continuous-time Ricatti equation and the corresponding discrete-time equation with fast sampling. The interconnection is established by formulating the discrete case using delta operators. The application of these results to the Kalman filtering problem highlights the importance of analogue prefiltering in the sampling process. A secondary benefit arising from the use of the delta operator is that improved numerical behaviour is obtained for solution algorithms, compared with that obtainable with the usual shift operator.