Extreme Bounds Analysis in the Kalman Filter

In this article, using the representation that the Kalman filter recursions in state-space models can be expressed as a matrix-weighted average of prior and sample estimates, we supplement the usual filtering algorithm by an extreme bounds analysis.Specifically, as the covariance matrix of the state error is varied in the class of symmetric and positive-definite matrices, the filtering estimates are shown to be in an ellipsoid.