A remark concerning discrete approximation to white noise and covariance calculation

Author

Bierman, G.

Author_Institution

Litton Systems Inc., Woodland Hills, CA, USA

Volume

Issue

fYear

1969

fDate

8/1/1969 12:00:00 AM

Firstpage

432

Lastpage

433

Abstract

If $\\dot{X} = AX + BU$ , where $U$ is "discretized" white noise ( $U$ is piece-wise constant and the constants are uncorrelated random variables), and it is assumed that $E{X(t)U\´(t)} = O$ , then the following covariance related jump equation results: $(d/dt)E{XX\´} = E{(d/dt)(XX\´)} + BQB\´$ . $Q$ is the covariance associated with $U$ . The relation of this phenomena to the idealized problem with $E{U(t) U\´(\\tau )} = Q\\delta (t - \\tau )$ is considered, and ramifications for digital simulation are discussed.

Keywords

Linear systems, time-varying; Time-varying systems, linear; Differential equations; Digital simulation; Kalman filters; Random variables; Stochastic processes; Vectors; White noise;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1969.1099218

Filename

1099218

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=800737