@article{10.1115/1.3662552,
    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.}},
    Author = {Kalman, R. E.},
    EPrint = {https://asmedigitalcollection.asme.org/fluidsengineering/article-pdf/82/1/35/5518977/35\\_1.pdf},
    File = {A New Approach to Linear Filtering and Prediction Problems - 35\_1 - a - n.pdf},
    ISSN = {0021-9223},
    Journal = {Journal of Basic Engineering},
    Keywords = {classic},
    Month = {03},
    Number = {1},
    Pages = {35-45},
    Title = {{A New Approach to Linear Filtering and Prediction Problems}},
    URL = {https://doi.org/10.1115/1.3662552},
    Volume = {82},
    Year = {1960},
    bdsk-url-1 = {https://doi.org/10.1115/1.3662552},
    date-added = {2020-10-17 11:58:20 +0200},
    date-modified = {2020-10-17 11:58:29 +0200},
    doi = {10.1115/1.3662552}
}

@article{10.1115/1.3662552, 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.}}, Author = {Kalman, R. E.}, EPrint = {https://asmedigitalcollection.asme.org/fluidsengineering/article-pdf/82/1/35/5518977/35\_1.pdf}, File = {A New Approach to Linear Filtering and Prediction Problems - 35_1 - a - n.pdf}, ISSN = {0021-9223}, Journal = {Journal of Basic Engineering}, Keywords = {classic}, Month = {03}, Number = {1}, Pages = {35-45}, Title = {{A New Approach to Linear Filtering and Prediction Problems}}, URL = {https://doi.org/10.1115/1.3662552}, Volume = {82}, Year = {1960}, bdsk-url-1 = {https://doi.org/10.1115/1.3662552}, date-added = {2020-10-17 11:58:20 +0200}, date-modified = {2020-10-17 11:58:29 +0200}, doi = {10.1115/1.3662552} }