Square-Root Consider Filters with Hyperbolic Householder Reflections

Abstract

Maintaining positive-definiteness of a filter’s error covariance estimate is of paramount importance to any stable and reliable estimation scheme. Two widely used methods for protecting a filter from loss of positive-definiteness are that of consider filtering and square-root filtering. Despite their widespread use in estimation applications, a filtering methodology that combines the two techniques has yet to be presented in a unified, streamlined architecture. This paper develops a new approach to square-root filtering using hyperbolic Householder reflections. A specialization of the method is considered to permit computationally efficient applications, and a numerical example pertaining to a ballistic reentry is presented to validate the proposed approaches.