Abstract
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 ( $\boldsymbol {Q}$ & $\boldsymbol {R}$ ) 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.
Highlights
Owing to the escalated use of vehicles on the road, several advanced vehicular technologies have been developed to assist the drivers to create a safe, comfortable and effortless driving environment [1]
The limitations of the Kalman filer (KF)-based inertial measurement unit (IMU)/Global Positioning System (GPS) integration approach are the necessity of stochastic modelling of sensor errors, which is difficult to be determined especially for low-accuracy accelerometers and gyroscopes, and the requirement for accurate priori information of the VC matrices of the noises associated with both low-cost IMU and GPS [11]
The first advantage how the low-cost IMU arrays are fused in this research is to enable the direct use of measurements for individual IMUs and separately model their systematic errors in Kalman filtering, in contrast to most existing approaches working under the supposition of ‘‘the common-mode errors of different sensors of the same design’’ [20]
Summary
Owing to the escalated use of vehicles on the road, several advanced vehicular technologies have been developed to assist the drivers to create a safe, comfortable and effortless driving environment [1]. The limitations of the KF-based IMU/GPS integration approach are the necessity of stochastic modelling of sensor errors, which is difficult to be determined especially for low-accuracy accelerometers and gyroscopes, and the requirement for accurate priori information of the VC (variance-covariance) matrices of the noises associated with both low-cost IMU and GPS [11]. The first advantage how the low-cost IMU arrays are fused in this research is to enable the direct use of measurements for individual IMUs and separately model their systematic errors in Kalman filtering, in contrast to most existing approaches working under the supposition of ‘‘the common-mode errors of different sensors of the same design’’ (the supposition means the IMUs of the same design share the same error model) [20]. The VCE algorithm proposed in this manuscript is computationally efficient and easy to implement, and even conducive to a better structure in the Kalman fusion filtering, improving the reliability and practicability of the multiple low-cost IMUs and GPS integrated navigation system.
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