基于先验知识的递归卡尔曼滤波的代理人联合状态和输入估计

现代自主系统的目的是为了应对许多具有挑战性的场景，在这些场景中，代理将面临意外事件和复杂的任务。控制指令和未知输入的干扰噪声的存在会对机器人的性能产生负面影响。以前的联合输入和状态估计研究在没有任何先验信息的情况下分别研究连续和离散情况。本文将连续空间和离散空间的估计结合到一个基于期望-最大（EM）算法的统一理论中。通过引入事件的先验知识作为约束条件，提出了不等式优化问题，以确定增益矩阵或动态权重，实现具有较低方差和更精确决策的最佳输入估计。最后，实验的统计结果表明，我们的算法在连续空间中比KF的方差提高了81%，比RKF提高了47%；在离散空间中，我们的输入估计器的正确决策概率有了显著提高，识别能力也通过实验进行了分析。

原文题目：Joint State and Input Estimation of Agent Based on Recursive Kalman Filter Given Prior Knowledge

原文：Modern autonomous systems are purposed for many challenging scenarios, where agents will face unexpected events and complicated tasks. The presence of disturbance noise with control command and unknown inputs can negatively impact robot performance. Previous research of joint input and state estimation separately study the continuous and discrete cases without any prior information. This paper combines the continuous space and discrete space estimation into a unified theory based on the Expectation-Maximum (EM) algorithm. By introducing prior knowledge of events as the constraint, inequality optimization problems are formulated to determine a gain matrix or dynamic weights to realize an optimal input estimation with lower variance and more accurate decision-making. Finally, statistical results from experiments show that our algorithm owns 81\% improvement of the variance than KF and 47\% improvement than RKF in continuous space; a remarkable improvement of right decision-making probability of our input estimator in discrete space, identification ability is also analyzed by experiments.