Sequential square root filtering and smoothing of discrete linear systems

• Authors: Gerald J. Bierman
• Venue: Automatica (Journal of IFAC)
• Year: 1974

Square-root information estimation algorithms are immensely important estimation analysis tools that are not sufficiently well understood nor adequately exploited. In an endeavor to rectify this state of affairs an expository derivation of the square-root information filter/smoother is given. It is based on the recursive least-squares method and is easier to grasp, interpret and generalize than are the dynamic programming arguments previously used. Backward smoothing algorithms, both square-root and covariance recursions, are derived as direct and consequences of the method. A comparison of smoothing algorithms indicates that those presented in this paper are the most efficient. Partitioning the results to separate bias parameters provides further computational economies and reduction of storage requirements. The principal objective of this paper is to inspire greater utilization of square-root estimation algorithms. Arguments supporting this thesis are the new least-squares filter/smoother derivations, enhanced numerical accuracy, reduced computation, and lower storage requirements.