A New Approach to Linear Filtering and Prediction ProblemsSource: Journal of Fluids Engineering:;1960:;volume( 082 ):;issue: 001::page 35Author:R. E. Kalman
DOI: 10.1115/1.3662552Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the co-efficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix.
keyword(s): Filtration , Equations , Filters , Stochastic processes , Errors , Noise (Sound) AND Dynamic systems ,
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contributor author | R. E. Kalman | |
date accessioned | 2017-05-08T23:54:41Z | |
date available | 2017-05-08T23:54:41Z | |
date copyright | March, 1960 | |
date issued | 1960 | |
identifier issn | 0098-2202 | |
identifier other | JFEGA4-27220#35_1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl/handle/yetl/119389 | |
description abstract | The classical filtering and prediction problem is re-examined using the Bode-Shannon representation of random processes and the “state-transition” method of analysis of dynamic systems. New results are: (1) The formulation and methods of solution of the problem apply without modification to stationary and nonstationary statistics and to growing-memory and infinite-memory filters. (2) A nonlinear difference (or differential) equation is derived for the covariance matrix of the optimal estimation error. From the solution of this equation the co-efficients of the difference (or differential) equation of the optimal linear filter are obtained without further calculations. (3) The filtering problem is shown to be the dual of the noise-free regulator problem. The new method developed here is applied to two well-known problems, confirming and extending earlier results. The discussion is largely self-contained and proceeds from first principles; basic concepts of the theory of random processes are reviewed in the Appendix. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | A New Approach to Linear Filtering and Prediction Problems | |
type | Journal Paper | |
journal volume | 82 | |
journal issue | 1 | |
journal title | Journal of Fluids Engineering | |
identifier doi | 10.1115/1.3662552 | |
journal fristpage | 35 | |
journal lastpage | 45 | |
identifier eissn | 1528-901X | |
keywords | Filtration | |
keywords | Equations | |
keywords | Filters | |
keywords | Stochastic processes | |
keywords | Errors | |
keywords | Noise (Sound) AND Dynamic systems | |
tree | Journal of Fluids Engineering:;1960:;volume( 082 ):;issue: 001 | |
contenttype | Fulltext |