Showing papers by "Martin Morf published in 1974"
TL;DR: In this paper, the Chandrasekhar-type Riccati-type difference equation is replaced by another set of difference equations, which are then used for recursive estimation in constant continuous-time linear systems.
Abstract: Certain recently developed fast algorithms for recursive estimation in constant continuous-time linear systems are extended to discrete-time systems. The main feature is the replacement of the Riccati-type difference equation that is generally used for such problems by another set of difference equations that we call of Chandrasekhar-type. The total number of operations in the new algorithm is in general less than with the Riccati-equation based Kalman filter, with significant reductions being obtained in several important special cases. The algorithms are derived via a factorization of increments of the Riccati equation variable, a method that can be extended to nonsymmetric Riccati equations as well.
215 citations
TL;DR: The important case of autoregressive processes is studied and it is shown how the Chandrasekhar-type equations can be used to obtain and generalize the well known Levinson-Wiggins-Robinson (LWR) recursion for estimation of stationary autore progressive processes.
Abstract: Several results exposing the interrelations between state-space and frequency-domain descriptions of multivariable linear systems are presented. Three canonical forms for constant parameter autoregressive-moving average (ARMA) models for input-output relations are described and shown to corrrespond to three particular canonical forms for the state variable realization of the model. Invariant parameters for the partial realization problem are characterized. For stochastic processes, it is shown how to construct an ARMA model, driven by white noise, whose output has a specified covariance. A two-step procedure is given, based on minimal realization and Cholesky-factorization algorithms. Though the goal is an ARMA model, it proves useful to introduce an artificial state model and to employ the recently developed Chandrasekhar-type equations for state estimation. The important case of autoregressive processes is studied and it is shown how the Chandrasekhar-type equations can be used to obtain and generalize the well known Levinson-Wiggins-Robinson (LWR) recursion for estimation of stationary autoregressive processes.
99 citations