Extensive validation of a real-time time derivative filter for quantized temperature measurements

The paper aims to validate a recently developed real-time estimation technique for the temperature time derivative inside a navigation-grade inertial system. According to our experience, sensors that are responsible for measuring the temperature of gyroscopes and accelerometers, often have a sufficiently wide quantization step to make the estimation of time derivative a challenge. When temperature inside an inertial unit changes quite slowly, it may result in constant measurements over several minutes whilst real temperature being non-constant. In this case, measurement errors do not have white noise properties, hence preventing traditional estimation algorithms from being optimal. We propose a parametric model for a short-term temperature approximation and specific estimation algorithm to determine the model parameters. It embodies a numerically stable finite-impulse-response modification of a conventional Kalman filter applied only on temperature sensor updates. This paper provides a brief description of the algorithm and an exhaustive analysis of its performance over a hundred of experiments with different temperature variation patterns.