非线性无偏最优估计器及高精度跟踪算法研究

In the investigation of maneuvering target tracking that based on the state-space-described Kalman-like nonlinear filters, due to some negative issues, such as the linear regression presented by the criterion of linear minimum variance unbias estimation (BLUE), and the nonlinearity of the sensor-obtained observations, as well as the high flexibility of maneuvering mode, certain improvement of the nonlinear estimator wih high accuracy is frequently explored and the involved topic is regarded as an important chellenge by the tracking comnunity.. Firstly, to start from the point of the linear assumption in the BLUE, in this planed project we will explore the criterion of nonlinear & unbiased optimality estimation with a general viewpoint, then accordingly a general theoretical framework of high accuracy nonlinear & optimal estimation will be formulated, moreover, we are also obliged to investigate the distinguished strategies to deal the high dimensional/nonlinear/non-Gaussian problems, so as to efficiently enlarge the application scope of the new estimator.. Secondly, equiped with the proposed nonlinear & optimal estimation theory, we will focus on the optimal utilization of both the position observation and the Doppler observation in a jointed manner, meanwhile, to suggest a well-designed filtering algorithm with high accuracy correspondence to the jointed optimality scheme.. Finally, with an enlarged research viewpoint, for the purpose of estimation accuracy and reliability evaluation, which includes the proposed optimality estimator in this project, and the other developed suboptimal nonlinear traking methods fulfiled in practice, we are obliged to set up a new theoretical framework about the online computation of the Crammer-Rao low boundary (CRLB), and to analysis the theoretical bound in a large parameters range presented by different estimators, so as to benefit their performance evaluation and practical application.

在利用最小方差线性无偏估计（BLUE）准则下的Kalman类非线性滤波器，进行运动目标跟踪研究中，由于传感器量测的非线性，以及目标运动模式的高机动性，高精度非线性滤波器一直是机动跟踪领域重点研究之问题。首先，从BLUE准则的线性假设着手，本课题将建立非线性无偏最优估计准则，并在此准则下给出高精度非线性最优滤波的通用理论框架，进而给出针对高维/非高斯情况的处理技术。其次，将探索非线性最优滤波框架下，实现传感器位置/Doppler量测联合优化利用机制，并给出针对该联合利用问题的高精度专有滤波算法；最后，为了进一步对已有的不同非线性滤波算法在典型参数范围内进行精度和可靠性评价，有必要给出在线计算Crammer-Rao下界的理论框架，并探索不同滤波算法的Crammer-Rao理论下界，以指导算法性能分析和实际应用。

高精度非线性滤波一直是机动目标跟踪/大数据同化领域的重要研究内容。在机动跟踪/数据同化实践中，存在传感器量测非线性，以及目标运动模式的不确定性和高机动性，传统方法即最小方差线性无偏估计（BLUE）准则下的Kalman类非线性滤波在理论和实践上都明显不足。因此，本课题主要开展一下工作：（1）着眼于BLUE准则的线性假设，建立非线性无偏最优估计准则，并给出高精度非线性最优滤波的通用理论框架。（2）探索非线性最优滤波框架下，实现传感器多量测联合优化滤波机制以及高精度实现算法；（3）对非线性滤波算法在典型参数范围内进行精度和可靠性评价并以之指导算法性能分析和实际应用。.本课题取得的重要结果：（1）建立了非线性无偏最优估计准则下非线性最优滤波器（UEVF），并在此框架下建立了优化格式和迭代格式二种不同策略，并进行精度和可靠性分析评价。（2）针对高机动多目标精确跟踪问题，结合所提出的非线性无偏最优滤波方法，建立了基于粒子概率假设密度(PF-PHD)滤波的多传感器联合检测、跟踪和分类算法；针对非线性/非高斯系统下高机动多目标精确跟踪问题，提出了基于高斯混合概率假设密度（GM-PHD）滤波的高精度加权并行滤波方法；针对高效计算的多目标跟踪问题，提出基于量测-估计关联的扩展高斯混合概率假设密度(EGM-PHD)方法，并进行精度和可靠性分析评价。结合变分滤波的误差学习/估计方法，对大数据同化及统计估计的精度和计算效率取得结果。（3）针对复杂背景噪声及高杂波下多目标/扩展目标精确跟踪问题，结合所提出UEVF框架，提出基于扩展目标概率假设密度滤波器（ET-PHD）的多目标联合检测、跟踪与分类方法。针对复杂噪声背景下多目标精确跟踪问题，结合具有一般性的新生目标强度假设，提出基于关联的自适应新生目标强度的概率假设密度滤波。各自进行大数据量的精度和可靠性分析评价。.大量理论和实验分析表明，所提非线性无偏优化滤波框架及其应用扩展方法，对于高精度机动跟踪、高精度数据同化等带有强非线性的问题具有重要理论和应用意义。