Kalman filtering in extended noise environments

• Published in: IEEE transactions on automatic control Vol. 50; no. 9; pp. 1396 - 1402
• Main Authors: Diversi, R., Guidorzi, R., Soverini, U.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-09-2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Digital filters; Errors-in-variables filtering; Exact sciences and technology; Filtering algorithms; Information filtering; Information filters; Kalman filtering; Kalman filters; Noise generators; optimal filtering; recursive filtering; State estimation; Stochastic resonance; Working environment noise; Additive noise; Input error; Monte Carlo method; Output error; Minimal variance; Optimal filtering; Kalman filter; Kalman filtering; Input estimation; Optimal estimation; Errors-in-variables filtering; Recursive filtering
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2005.854627

This note introduces an extended environment for Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal (minimal variance) estimation of noise-corrupted input and output sequences. This environment includes as subcases both errors-in-variables filtering (optimal estimate of inputs and outputs from noisy observations) and traditional Kalman filtering (optimal estimate of state and output in presence of state and output noise). A Monte Carlo simulation shows that the performance of this extended filtering technique leads to the expected minimal variance estimates.