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Modern autonomous systems are purposed for many challenging scenarios, whereagents will face unexpected events and complicated tasks. The presence ofdisturbance noise with control command and unknown inputs can negatively impactrobot performance. Previous research of joint input and state estimationseparately studied the continuous and discrete cases without any priorinformation. This paper combines the continuous and discrete input cases into aunified theory based on the Expectation-Maximum (EM) algorithm. By introducingprior knowledge of events as the constraint, inequality optimization problemsare formulated to determine a gain matrix or dynamic weights to realize anoptimal 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 continuousspace; a remarkable improvement of right decision-making probability of ourinput estimator in discrete space, identification ability is also analyzed byexperiments.

Joint State and Input Estimation of Agent Based on Recursive Kalman Filter Given Prior Knowledge