A New Approach to Linear Filtering and Prediction Problems

Authors: Rudolf E. Kalman

Published: 1960 (Journal Paper)

Source: Journal of Basic Engineering

Algorithm: Kalman filter

DOI: 10.1115/1.3662552

Summary

Introduces the Kalman filter, a recursive algorithm for optimal linear state estimation from noisy measurements. Derives the filter equations via a state-space formulation and shows that the estimation problem is dual to the LQR control problem—arguably the most influential paper in modern control theory and signal processing.

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 coefficients 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.

Links

Primary

Paper liberzon.csl.illinois.edu

Standard

DOI 10.1115/1.3662552

Alternate

asmedigitalcollection.asme.org asmedigitalcollection.asme.org

Tags

• Kalman filter

• State estimation

• Linear filtering

• Optimal estimation

• Stochastic control

• Recursive estimation