An Improved Posteriori Variance-Covariance Components Estimation Applied to Unconventional GPS and Multiple Low-Cost Imus Integration Strategy

Meliorating a priori stochastic model of Kalman filer (KF) is always challenging. To address this challenge, this paper simultaneously estimates and corrects the variance components for all of the process noise and measurement matrix (Q & R) by a posteriori variance-covariance components estimation (VCE) algorithm, which makes the most of the process noise residuals and measurement residuals and measurement redundancy contribution. Unsurprisingly, in the conventional error states-based integration mechanization, the stochastic model tuning is not easy for IMU because of the error measurements between the observables from inertial sensors and other aiding sensors. This research utilizes an unconventional multi-sensor integration strategy, in which a 3D kinematic trajectory model is deployed as the main part of system equation and the systematic errors of each IMU and the measurements of all sensors are individually modelled. Furthermore, the weights of measurements from each inertial sensor are defined on the basis of the posterior variances, so that we could properly distribute the function of each measurement in the fusion algorithm. A real dataset involving GPS and multiple IMUs is processed to validate the proposed posteriori VCE algorithm by applying the unconventional integration strategy.