Linear dynamic filtering with noisy input and output 1

We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modified Kalman filter. The approach used is algebraic and the result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem. The result is illustrated with a simulation example. LINEAR DYNAMIC FILTERING WITH NOISY INPUT AND OUTPUT Ivan Markovsky ∗ and Bart De Moor ∗ ∗ ESAT, SCD-SISTA, K.U.Leuven, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium {Ivan.Markovsky,Bart.DeMoor}@esat.kuleuven.ac.be http://www.esat.kuleuven.ac.be/sista-cosic-docarch Tel: +32–16–32 17 09, Fax: +32–16–32 19 70 Abstract: We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modified Kalman filter. The approach used is algebraic and the result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem. The result is illustrated with a simulation example. We establish the equivalence between the optimal least-squares state estimator for a linear time-invariant dynamic system with noise corrupted input and output, and an appropriately modified Kalman filter. The approach used is algebraic and the result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem. The result is illustrated with a simulation example.