提出了SGD(shape global deformation)算法并将其应用于回弹补偿分析中,进行补偿面的修改。其原理是以原始曲面为基础进行的曲面整体变形修改,这种方法能够保证变形前后的型面整体拓扑关系的一致性,保证曲面的质量、光顺程度,以便获得...提出了SGD(shape global deformation)算法并将其应用于回弹补偿分析中,进行补偿面的修改。其原理是以原始曲面为基础进行的曲面整体变形修改,这种方法能够保证变形前后的型面整体拓扑关系的一致性,保证曲面的质量、光顺程度,以便获得更精确的回弹补偿型面。经多个实例分析表明,该算法能够在很大程度上节省修改补偿型面的时间和精力,较大地提高曲面精度,回弹补偿更加准确。展开更多
Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when ...Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.展开更多
文摘提出了SGD(shape global deformation)算法并将其应用于回弹补偿分析中,进行补偿面的修改。其原理是以原始曲面为基础进行的曲面整体变形修改,这种方法能够保证变形前后的型面整体拓扑关系的一致性,保证曲面的质量、光顺程度,以便获得更精确的回弹补偿型面。经多个实例分析表明,该算法能够在很大程度上节省修改补偿型面的时间和精力,较大地提高曲面精度,回弹补偿更加准确。
基金supported in part by the National Key Research and Development Program of China(2023YFB3906403)the National Natural Science Foundation of China(62373118,62173105)the Natural Science Foundation of Heilongjiang Province of China(ZD2023F002)
文摘Over the past few decades, numerous adaptive Kalman filters(AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation(MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation.Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation,which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy,and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.
