随机连续线性系统基于Legendre多项式逼近的参数估计  

PARAMETER ESTIMATION OF STOCHASTIC CONTINUOUS LINEAR SYSTEMS VIA LEGENDRE POLYNOMIALS APPROXIMATION

作　　者：赵明旺 

出　　处：《武汉钢铁学院学报》1994年第2期191-197,共7页

基　　金：冶金工业部教育司研究基金

摘　　要：本文研究随机连续线性系统基于Ｌｅｇｅｎｄｒｅ多项式过近的参数估计问题．文中先讨论了随机微分方程描述的随机连续系统的Ｌｅｇｅｎｄｒｅ多项式逼近，然后给出了最小二乘估计方法．在讨论了连续Ｗｉｅｎｅｒ过在的Ｌｅｇｅｎｄｒｅ多项式逼近值的相关性，并首次得到对Ｌｅｇｅｎｄｒｅ多项或应用于随机连续系统研究有重要意义的统计相关结果后，提出了能获得无偏一致估计的辅助变量法及三种选取辅助变量系统的方法．计算机仿真结果表明了本文方法的有效性．Parameter estimation problems for stochastic continuous linear systems via Legendrepolynomials approximation are researched in this paper. At first the Legendre polynomials approximation of stochastic continuous linear systems described by stochastic differential equationis discussed, and then the lint squares estimation algorithm is prasented. After discussing thecorrelativeness of the polynomials approximating values of continuous Wiener process whichcorrelative result is got first with important sense in application of the polynomials to stochasticcontinuous systems, the instrumental variabole method which can give an unbiased parameterestimation are proposed and three methods choosing instrumental varisble systems are suggested. Computer simulation shows that these algorithms are effective.

关 键 词：正交多项式 随机连续系统 参数估计 

分 类 号：TP271[自动化与计算机技术—检测技术与自动化装置]