Real-Time Estimation of Temperature Time Derivative in Inertial Measurement Unit by Finite-Impulse-Response Exponential Regression on Updates

We present a filtering technique that allows estimating the time derivative of slowly changing temperature measured via quantized sensor output in real time. Due to quantization, the output may appear constant for several minutes in a row with the temperature actually changing over time. Another issue is that measurement errors do not represent any kind of white noise. Being typically the case in high-grade inertial navigation systems, these phenomena amid slow variations of temperature prevent any kind of straightforward assessment of its time derivative, which is required for compensating hysteresis-like thermal effects in inertial sensors. The method is based on a short-term temperature prediction represented by an exponentially decaying function, and on the finite-impulse-response Kalman filtering in its numerically stable square-root form, employed for estimating model parameters in real time. Instead of using all of the measurements, the estimation involves only those received when quantized sensor output is updated. We compare the technique against both an ordinary averaging numerical differentiator and a conventional Kalman filter, over a set of real samples recorded from the inertial unit.