A Designed AKF Algorithm Applied to Unconventional GPS and Multiple Low-cost IMUs Integration Strategy
Fei Yu, Minghong Zhu, Shu Xiao, College of Automation, Harbin Engineering University, Harbin, China; Jianguo Wang, York University, Canada
Conventionally, the Kalman filter on the basis of integration mechanization, such as GPS-aided inertial integrated navigation system, has been commonly built up using error states and error measurements. Its strong dependence on the a-priori error characteristics of inertial sensors may restrict the use of low-cost IMUs due to their low performance. In order to accurately reflect the evolution of the real state for a moving vehicle, this research applies an conventional KF that directly estimate navigational parameters instead of the error states to integrate GPS receivers and multiple low-cost IMUs, in which a kinematic trajectory model as the core of the KF system model is deployed and measurement updates for all sensor data inclusive of the ones from IMUs were directly performed. The unconventional strategy implements a true multi-sensor integrated system, no sensor functions as an aiding sensor. This design enables the direct use of the IMU’s raw outputs (specific force and angular rate) instead of applying them to the free inertial navigation calculation through the conventional integration mechanization. Therefore, no error measurements need to be constructed so that the posteriori variance components for all of the measurements and process noise vector can be estimated for improving the stochastic model of the Kalman filter. In practice, the a-priori variance matrix Q of the process noise vector and R of the measurement vector are unknown or approximated, which may produce unreliable results or cause the Kalman filter to diverge. With this in mind, this research proposed an adaptive Kalman filter(AKF) algorithm based on Helmert variance components estimation, to simultaneously estimate the variance matrix Q and R by taking advantage of the measurement residuals and the process noise residuals and the measurement redundancy contribution. If these different error resources could be studied separately, it could be very helpful to the performance evaluation. For this purpose, the system innovation vector is divided into three independent groups of residuals: the residuals of the measurement vector, the residuals of the process noise vector and the residuals of the predicted state vector exclusive of the effect of the process noise. Besides, the weights of measurements from each sensor are calculated by the posterior variances so that the function of each measurement can be reasonably distributed in the Kalman filter, achieving a better structure for the fusion algorithm. Moreover, the systematic errors and measurements of these multiple IMUs can be individually modeled instead of being a group of the commonly shared states for all of the IMUs because the assumption of “the common-mode errors of different sensors of the same design” is unreasonable. In this manuscript, all tests were under full physical simulation. The trajectory simulation of a land vehicle was designed as a temporary replacement of real body. The real-time raw outputs of three IMUs and GPS were simulated on practical basis. In order to approach the output from real sensor, several groups of random numbers were generated by a series of procedures, not generated using functional instructions that come with Matlab. The real-time raw outputs of multiple IMUs and GPS simulated were processed to demonstrate the performance by using the proposed unconventional integration strategy and the designed AKF algorithm based on variance components estimation. The results from experiments along with discussions are also presented.