Condensed Forms for Efficient Time-Invariant Kalman Filtering
Paul Van Dooren, Michel Verhaegen · SIAM Journal on Scientific and Statistical Computing · 1988
In this paper, new numerical implementations are developed for several “classical” types of Kalman filters. These implementations are based on the choice of an initial state transformation which “condenses” the original model and are therefore mainly meant for time-invariant systems. Since unitary transformations are used to generate these condensed forms, no loss of accuracy is thereby incurred. The use of these forms may lead to a complexity reduction of a factor of 7 in the subsequent recursions to compute the stationary solution of the discrete Riccati equation. It is shown that therefore these new implementations become competitive with the so-called “fast Chandrasekhar” implementation.