Spatially constrained output injection for state estimation with banded closed-loop dynamics

This paper presents an extension of the Kalman filter that uses specific subset of the measurement to directly update only a specific subset of the state estimates rather than the entire state estimate. The ability to perform selective output injection allows us to structure the estimator gain so that the close-loop dynamics is banded. The one-step and the two-step forms of this filter are generally not equivalent. In future work, we plant to consider the problem of determining the exact conditions that guarantee the existence of a steady state covariance for linear time-invariant dynamics