Calibration of inertial sensors in the case of varying temperature

In our study we consider the inertial navigation system (INS) calibration problem. The sensor error model includes a set of conventional parameters and the sensor error variations over temperature. In previous research, we have shown that the sensor error temperature variations can be estimated in an experiment with changing temperature. An important part of practical implementation of the proposed approach is the estimation of the temperature time derivative inside the INS using temperature sensors measurements. For a number of reasons, doing this directly from temperature sensor measurements is not trivial. We propose a pattern for approximation function and analyze the connection between this function and a model of the thermal process inside the INS, which is described by the heat equation.