مرکز منطقه ای اطلاع رساني علوم و فناوري - A remark concerning discrete approximation to white noise and covariance calculation

DocumentCode :

800737

Title :

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.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=800737