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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.

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Gravimeters fabricated with MEMS suffer from temperature-dependent drifts in their long-term stability. We analyze the thermal contributions to the signal, and we propose three mechanisms to mitigate their effects. The first one uses materials that fulfill the condition αE=−2α, where thermal expansion is canceled by the temperature variation of Young’s modulus. The second one uses the thermal expansion to introduce a compression that compensates variation in the force of the spring. In the third one, expansion compensates the displacement of the proof mass in the sensor, rather than the force. The three mechanisms are robust since they only depend on the temperature of the sensor itself.