Traditional adaptive Kalman filtering algorithms based on innovation are often used to solve the problem of reduced or even divergent filtering estimation accuracy under abnormal measurement noise. However, these algorithms are usually characterized by difficulties in selecting window width and window weight, which cannot simultaneously take into account the filtering tracking sensitivity and filtering accuracy.In this paper, an adaptive Kalman filtering algorithm based on maximum likelihood estimation is proposed, which determines the window size and window weight size under the kth moment by designing a window adaptive selection function and a weight function to change the innovation covariance at the kth moment, which in turn changes the measurement noise covariance at the kth moment, so that the measurement noise covariance is no longer a fixed single value, but can better adapt to the changes in the environment, reflecting good adaptive characteristics. The simulation results based on GPS/SINS integrated navigation system demonstrate that the new filtering algorithm of this paper reflects higher filtering accuracy and stronger robustness under the carrier in multiple motion states and accompanied by time-varying measurement noise interference. Compared with the traditional adaptive Kalman filtering algorithm based on innovation, the accuracy of attitude angle estimation error under this method is improved by 119.97%; the accuracy of velocity estimation error is improved by 264.42%; the accuracy of position estimation error is improved by 156.69%.
The proper stochastic model of a global navigation satellite system (GNSS) makes a significant difference on the precise point positioning (PPP)/inertial navigation system (INS) tightly coupled solutions. The empirical Gaussian stochastic model is easily biased by massive gross errors, deteriorating the positioning precisions, especially in the severe GNSS blockage urban environment. In this paper, the distributional characteristics of the gross-error-contaminated observation noise are analyzed by the epoch-differenced (ED) geometry-free (GF) model. The Student’s t distribution is used to express the heavy tails of the gross-error-contaminated observation noise. Consequently, a novel sequential Student’s t-based robust Kalman filter (SSTRKF) is put forward to adjust the GNSS stochastic model in the urban environment. The proposed method pre-weights all the observations with the a priori residual-derived robust factors. The chi-square test is adopted to distinguish the unreasonable variances. The proposed sequential Student’s t-based Kalman filter is conducted for the PPP/INS solutions instead of the standard Kalman filter (KF) when the null hypothesis of the chi-square test is rejected. The results of the road experiments with urban environment simulations reveal that the SSTRKF improves the horizontal and vertical positioning precisions by 57.5% and 62.0% on average compared with the robust Kalman filter (RKF).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.