A New Approach to Linear Filtering and Prediction Problems
R. Kalman. Journal of Basic Engineering, 82 (1):
35--45(March 1960)
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.
%0 Journal Article
%1 Kalman:1960
%A Kalman, R. E.
%D 1960
%I ASME
%J Journal of Basic Engineering
%K KalmanFilter observer
%N 1
%P 35--45
%T A New Approach to Linear Filtering and Prediction Problems
%U http://dx.doi.org/10.1115/1.3662552
%V 82
%X 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.
@article{Kalman:1960,
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.},
added-at = {2017-05-21T12:41:28.000+0200},
author = {Kalman, R. E.},
biburl = {https://www.bibsonomy.org/bibtex/29a80955abfd8a38d337021a591949e68/ristephens},
comment = {10.1115/1.3662552},
interhash = {46000cea585242435901ab4a9f5738b5},
intrahash = {9a80955abfd8a38d337021a591949e68},
issn = {00982202},
journal = {Journal of Basic Engineering},
keywords = {KalmanFilter observer},
month = mar,
number = 1,
pages = {35--45},
publisher = {ASME},
timestamp = {2017-05-21T12:41:28.000+0200},
title = {A New Approach to Linear Filtering and Prediction Problems},
url = {http://dx.doi.org/10.1115/1.3662552},
volume = 82,
year = 1960
}