A Computational Multivariate-based Technique for Inertial Sensor Calibration

Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration

“…In this section, we present the theoretical framework of this work more formally and study the different proposed solutions for the considered setting. More specifically, in the following sections, we describe and study the solutions, including those put forward in [9] and [10], which are a direct extension of the GMWM. The latter is currently employed, among others, for sensor calibration on a single stochastic error signal issued from an inertial sensor calibration session (see, e.g., [8], [11]).…”

“…Given that we cannot directly observe the criterion in (2) that would allow us to find the value of θ 0 , we need to consider estimators for this quantity. For this reason, this work studies different solutions, among which those put forward in [9] and [10] whose finite sample performance was investigated through preliminary simulations and applied studies. These solutions are intuitive estimators for the quantity of interest θ 0 but, as shown further on, have different properties and actually turn out to be the same under specific or more general circumstances.…”

“…Although the latter approach remains a valid one, it may not be optimal since the different replicates can contain important information to appropriately model these signals for navigation purposes. In fact, the problem of considering the information from all replicates was first put forward in [9] and subsequently in [10] where it is underlined how the replicates are important to carry out a comprehensive estimation procedure. More specifically, they find and define the setting of "near-stationarity" of the error measurement replicates where, instead of considering a stochastic model characterized by a fixed parameter vector, they postulate that the parameters of this model are also independent random variables that follow a certain stationary probabilistic distribution G. Among others, the reason for considering such a setting is based on observing the Wavelet Variance (WV) plots of the different IMU error replicates which appeared to approximately have the same shape but differed significantly over different scales.…”

“…In addition, given the dependence structure within each replicate, it is not possible to simply average the signals from each run. To address this problem, [9] and [10] put forward a solution that extends the definition of the GMWM in order to combine the information from each replicate in an adequate manner. This extension implicitly defines the parameter vector which is consequently used to best represent the overall parameter behaviour (considering that it is now a random variable) and to perform navigation updates.…”

“…However, they also consider another intuitive estimator which implies that the parameter value to target is possibly different (as explained later on in the paper). Given this preliminary research, this work intends to define three different solutions that can be considered for this problem (two of which are those put forward in [9]) and study their properties in order to clearly determine which method should be used for multi-signal calibration and under what circumstances. In addition, these properties allow to improve the understanding and performance of statistical inferential tools that can be used to assess the validity of the near-stationary hypothesis when dealing with multiple signal replicates.…”