Bayesian recursive filtering with partially observed inputs and missing measurements

In this paper, the problem of state estimation is considered for discrete-time stochastic linear systems subject to both partially observed inputs and multiple missing sensor measurements. First, the partially available information on the unknown inputs and the state equation are used to form the prior distribution of the state vector at each step. To obtain an analytically tractable likelihood function, the effect of missing measurements is broken down and the associated uncertainty is modeled as part of the measurement noise. A recursive optimal filter is obtained using Bayes' rule. Finally, a numerical example is provided to evaluate the effectiveness of the developed method.