TY - JOUR
T1 - A New Approach to Linear Filtering and Prediction Problems
PB - ASME
AU - Kalman, R. E.
Y1 - 1960/03/01
N1 - 10.1115/1.3662552
JO - Journal of Basic Engineering
SP - 35
EP - 45
VL - 82
IS - 1
N2 - 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.
SN - 0098-2202
M3 - doi: 10.1115/1.3662552
UR - http://dx.doi.org/10.1115/1.3662552
ER -