Square root information filtering using the covariance spectral decomposition

Abstract

A square-root state-estimation algorithm is introduced which operates in the information mode in both the time and the measurement update stages. The algorithm, called the V-Lambda filter, is based on the spectral decomposition of the covariance matrix into a V Lambda V/sup T/ form, where V is the matrix whose columns are the eigenvectors of the covariance matrix and Lambda is the diagonal matrix of its eigenvalues. The algorithm updates a normalized state estimate along with the information matrix square-root factors, thus doing away with the gain computation. Singular value decomposition is used as a sole computational tool in both the eigenvectors-eigenvalues and the normalized state-estimate updates, rendering a complete estimation scheme with exceptional numerical stability and precision. A typical numerical example is used to demonstrate the performance of the V-Lambda filter as compared to that of the corresponding conventional Kalman algorithm.<>