Linear dynamic filtering with noisy input and output 1 Ivan Markovsky and Bart
نویسندگان
چکیده
Estimation problems for linear time-invariant systems with noisy input and output are considered. The smoothing problem is a least norm problem. An efficient algorithm using a Riccati-type recursion is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem. 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 February 25, 2004 Abstract State estimation problems for linear time-invariant systems with noisy inputs and outputs are considered. An efficient recursive algorithm for the smoothing problem is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem.State estimation problems for linear time-invariant systems with noisy inputs and outputs are considered. An efficient recursive algorithm for the smoothing problem is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem.
منابع مشابه
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 ill...
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