| 引用本文: | 王新梅,魏武,刘玮,刘峰,袁银龙.鲁棒卡尔曼滤波下的图像雅可比矩阵带时延补偿的估计[J].控制理论与应用,2015,32(8):1052~1057.[点击复制] |
| WANG Xin-mei,WEI Wu,LIU Wei,LIU Feng,YUAN Yin-long.Estimation of image Jacobian matrix with time-delay compensation based on robust Kalman filtering[J].Control Theory and Technology,2015,32(8):1052~1057.[点击复制] |
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| 鲁棒卡尔曼滤波下的图像雅可比矩阵带时延补偿的估计 |
| Estimation of image Jacobian matrix with time-delay compensation based on robust Kalman filtering |
| 摘要点击 2772 全文点击 1808 投稿时间：2014-10-29 修订日期：2015-09-01 |
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| DOI编号 10.7641/CTA.2015.41005 |
| 2015,32(8):1052-1057 |
| 中文关键词 鲁棒卡尔曼滤波 特征点图像时延补偿 图像雅可比矩阵时延补偿 |
| 英文关键词 robust Kalman filtering the feature point image with time-delay compensation image Jacobian matrix with time-delay compensation |
| 基金项目 国家自然科学基金项目(61472374, 61573148), 国家自然科学基金―天元基金项目(11426210), 中央高校基本科研业务费专项基金项目(CUGL 130223)资助. |
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| 中文摘要 |
| 传统的图像雅可比矩阵估计的方法没有考虑时延因素, 因此具有较大的估计误差. 为补偿时延带来的影响, 提出一种鲁棒卡尔曼滤波的方法, 实现时延情况下当前时刻特征点在图像空间中位置和速度的估计, 进而得到时延情况下较为准确的图像雅可比矩阵的估值. 具体说, 特征点在图像空间中当前时刻位置和速度是首先用卡尔曼滤波的方法估计的, 但观测噪声的描述却采用了马尔科夫链模型, 由此产生了过程噪声和观测噪声的互相关, 传统卡尔曼滤波受限. 为此, 我们引入滤波修正向量并重新定义过程方程及观测方程, 结合卡尔曼滤波中噪声的数学特性, 得到滤波修正向量消除互相关性, 从而构建出鲁棒卡尔曼滤波模型; 其次, 针对鲁棒卡尔曼滤波模型中存在的无法获得时延期间的观测向量的问题, 提出利用多项式拟合出这部分观测向量, 该多项式的选取综合考虑了特征点的位置、速度、加速度、加速度的变化率对于特征点轨迹的影响, 与实际情况相符; 最后, 由预测出的当前时刻特征点 在图像空间中的位置和速度, 实现时延情况下图像雅可比矩阵较为准确的估计. 仿真和实验结果验证了本文方法的可行性和优越性. |
| 英文摘要 |
| Time delay is not considered in the traditional methods for the estimation of image Jacobian matrix, which leads to large estimation error. To compensate for the impact of the time delay, a robust Kalman filtering method is presented through which the current position and velocity of the feature point in the image space under time delay are predicted, and then the accurate image Jacobian matrix under time delay can be obtained. Specifically, the current position and velocity of the feature point in the image space are predicted by Kalman filtering algorithm, but Markov chain model is used in the description of the measurement noise, then the cross-correlation between the process noise and measurement noise is produced, the application of traditional Kalman filtering algorithm is restricted. To deal with this problem, we introduce a filtering revision vector and redefine the process equation and measurement equation. By considering the mathematical properties of the noise in Kalman filtering algorithm, we can obtain the filtering revision vector and eliminate the crosscorrelation, thus developing a robust Kalman filtering model. Next, to obtain the measurement vectors which cannot be acquired in the robust Kalman filtering model owing to the existence of time delay, we propose a polynomial fitting method for its determination. The polynomial is properly selected by synthetically considering the real situation effects on the feature point trajectory from the position, the velocity, the acceleration and the change rate of acceleration of the feature point. Finally, from the predicted position and velocity of the feature point in the image space at the current time, we obtain the accurate image Jacobian matrix with time-delay compensation. Simulation and experimental results validate the feasibility and superiority of this method. |
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