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 studied the continuous and discrete cases without any prior information. This paper combines the continuous and discrete input cases 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.

翻译：现代自主系统被用于许多具有挑战性的场景，代理将面临意外事件和复杂任务。控制命令和未知输入值带来的干扰噪声可能会对机器人性能产生负面影响。先前关于输入和状态联合估计的研究分别研究了连续和离散情况，没有任何先验信息。本文基于期望最大（EM）算法将连续和离散输入情况结合为一个统一的理论。通过引入事件的先验知识作为约束条件，将不等式优化问题形式化为确定增益矩阵或动态权重以实现更低方差和更准确的决策的最优输入估计。最后，实验的统计结果表明，我们的算法在连续空间中比KF提高了81％的方差，比RKF提高了47％的方差；在离散空间中，我们的输入估计器的正确决策性能有显着提高，还通过实验分析了识别能力。