An extension of the Kalman Filter for a class of measurement models inspired by wide-baseline stereo

We consider the application of the Kalman Filter to systems with a certain type of measurement model. In addition to the state at the current time step, these measurements also depend on the state from one time step earlier. Although such measurement models are not encountered very often, they do appear in some practical control applications in robotic vision. In this paper, we derive a generalized Extended Kalman Filter from a modified form of the basic Bayes filter. The dependence of the measurement model on the previous state is made explicit through the law of total probability, which we include as an additional step in the standard prediction-correction cycle of the Bayes filter. We find that this dependence results in an increase in the measurement noise covariance. We present the mathematical formulation along with the proof of the filter equations. In the end, we demonstrate the filter through a simulation of Monocular SLAM with wide-baseline stereo measurements.