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.
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A New Approach to Linear Filtering and Prediction Problems
R. E. Kalman
Research Institute for Advanced Study, Baltimore, Md.
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Kalman, R. E. (March 1, 1960). "A New Approach to Linear Filtering and Prediction Problems." ASME. J. Basic Eng. March 1960; 82(1): 35–45. https://doi.org/10.1115/1.3662552
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