Continuous- Time Kaiman Filter
The continuous Kaiman filter is used when the measurements are continuous functions of time. Discrete measurements arise when a system is sampled, perhaps as part of a digital control scheme. Because of today's advanced microprocessor technology and the fact that microprocessors can provide greater accuracy and computing power than analog computers, digital control is being used more frequently instead of the classical analog control methods. This means that for modern control, applications, the discrete Kaiman filter is usually used. There are several ways to derive the continuous-time Kalman filter. One of the most satisfying is the derivation from the Wiener–Hopf equation. This chapter presents the derivation that is based on "unsampling" the discrete-time Kaiman, filter. This approach proves an understanding of the relation between the discrete and continuous filters. The chapter also provides insight into the behavior of the discrete Kaiman gain as the sampling period goes to zero.