1960/03/01 by R. E. Kalman · 35 citations
Computer Science · Physics and Astronomy · #Scientific Research and Discoveries #Statistical Mechanics and Entropy #Target Tracking and Data Fusion in Sensor Networks
paper · doi:10.1115/1.3662552
crossref issued 1960/03/01 · crossref published 1960/03/01 · crossref published-online 1960/03/01 · crossref published-print 1960/03/01 · openalex publication_date 1960/03/01 · crossref created 2011/11/08 · crossref deposited 2019/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04 · crossref indexed 2026/08/05
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.