%0 Journal Article %1 Kalman_1960 %A Kalman, Rudolph Emil %D 1960 %I ASME %J Journal of Basic Engineering %K dsp filter paper research %N 1 %P 35 %R 10.1115/1.3662552 %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 = {2018-09-10T18:21:16.000+0200}, author = {Kalman, Rudolph Emil}, biburl = {https://www.bibsonomy.org/bibtex/297df10d092de1a7e3d1f23ee77a2ed96/analyst}, description = {A New Approach to Linear Filtering and Prediction Problems | Journal of Fluids Engineering | ASME DC}, doi = {10.1115/1.3662552}, interhash = {46000cea585242435901ab4a9f5738b5}, intrahash = {97df10d092de1a7e3d1f23ee77a2ed96}, journal = {Journal of Basic Engineering}, keywords = {dsp filter paper research}, number = 1, pages = 35, publisher = {ASME}, timestamp = {2018-09-10T18:21:16.000+0200}, title = {A New Approach to Linear Filtering and Prediction Problems}, url = {http://dx.doi.org/10.1115/1.3662552}, volume = 82, year = 1960 }