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：现代自主系统旨在应对诸多具有挑战性的场景，其中智能体将面临意外事件和复杂任务。控制指令中存在的扰动噪声及未知输入会对机器人性能产生负面影响。此前关于联合输入与状态估计的研究分别针对连续和离散情况在无先验信息条件下进行探讨。本文基于期望最大化（EM）算法，将连续与离散输入情形统一纳入理论框架。通过引入事件先验知识作为约束条件，构建不等式优化问题以确定增益矩阵或动态权重，从而实现方差更低、决策更精准的最优输入估计。实验统计结果表明，在连续空间中，本算法相较于KF方差降低81%，较RKF降低47%；在离散空间中，输入估计器的正确决策概率显著提升，并通过实验分析了其辨识能力。