Reliable Overbounding for Stochastic IMU Error Models Using Interval Analysis

Robust error modeling of stochastic errors over time, such as in multisensory navigation, is crucial for integrity purposes. It can be addressed using the recently developed Power Spectral Density (PSD) overbounding method. Prior works have developed robust Inertial Measurement Unit (IMU) error models through PSD bounding, involving four parameters modeling white noise, First-order Gauss Markov random process (FOGMRP), and random walk components. This paper presents a novel method to address the challenge of ensuring PSD overbounding for stochastic IMU error models by providing reliable interval-valued parameter estimates. This is inherently meaningful, given the fact that numerous feasible combinations of the parameters are expected. Our approach leverages the interval analysis method, estimating the parameters efficiently and autonomously, reducing dependency on precise external information from manufacturers, which is necessary for existing methods. The output solutions are in the form of a set approximated by a number of four-dimensional interval boxes, allowing flexible selection by the users based on the application of interest. The methodology was validated through experiments using Safran STIM300 and MicroStrain 3DM-GQ4-45 IMUs under controlled, static conditions. Its reliability, demonstrated by the experimental results in terms of effectiveness and tightness of PSD bounding, will contribute to the advancement of resilient INS applications and desired sequential RAIM to ensure high integrity.