In this chapter, we use the Kalman filter to estimate the future state of a system. We present the theory, design, simulation, and implementation of the Kalman filter. We use as a case example the estimation of temperature using a Resistance Temperature Detector (RTD), which has not been reported before. After a brief literature review, the theoretical analysis of a Kalman filter is presented along with that of the RTD. The dynamics of the RTD system are analytically derived and identified using Matlab. Then, the design of a time-varying Kalman filter using Matlab is presented. The solution to the Riccati equation is used to estimate the future state. Then, we implement the design using C-code for a microprocessor ATMega328. We show under what conditions the system may be simplified. In our case, we reduced the order of the system to that of a system having a 1st order response, that of an RC system, giving us satisfactory results. Furthermore, we can find two first order systems whose response defines two boundaries inside which the evolution of a second order system remains.
Part of the book: Adaptive Filtering