Optimally Weighted Wavelet Variance-based Estimation for Inertial Sensor Stochastic Calibration

Different inertial sensor calibration techniques have been proposed to consider the sources of measurement error from inertial sensors. There has been a significant amount of literature which studies the stochastic errors calibration of such devices. The recent results of [1] have proved that among all possible methods the (Generalized Method of Wavelet Moments) (GMWM) presents various optimality and is computationally reliable. However, the GMWM estimators depend on weight matrix which considerably impact the quality of the estimated stochastic error models. In addition, such models are made of different components (typically high-frequency and low-frequency components) whose impacts on navigation vary depending on the context. For example, the high-frequency component of the error model may be more important when considering low-cost IMUs mounted on small size drones used for short-term missions. On the other hand, the situation may be reversed when considering navigational grade IMUs used, often autonomously, for long-term missions. With these differences, one may wish to select a GMWM estimator whose weight matrix has been tailored to estimate more reliably the elements of an error model believed to have the greatest impacts on navigation accuracy. In this article, we provide a formal answer to this question by proposing an optimally weighted GMWM estimator. Our results show that the proposed estimator is optimal for all parameters of the sensor error model we wish to estimate with the smallest possible uncertainty of the estimation. Therefore, regardless of the application, and independently of the context, the same optimally weighted estimator can be employed.