线性连续回归模型基于Chebyshev多项式逼近的Markov参数估计

MARKOV PARAMETER ESTIMATION FOR LINEAR CONTINUOUS REGRESSIVE MODELS VIA CHEBYSHEV POLYNOMIALS APPROXIMATION

文中先提出了基于Ｃｈｅｂｙｓｈｅｖ多项式逼近，有连续Ｗｉｅｎｅｒ过程扰动的线性连续回归模型最小二乘参数估计算法，然后讨论了Ｗｉｅｎｅｒ过程的Ｃｈｅｂｙｓｂｅｖ多项式逼近值的相关性，在此基础上，提出了能获得参数估计误差方差为最小的Ｍａｒｋｏｖ参数估计（最小方基估计）算法。文中还将所提出的估计方法推广至控制领域中所讨论的随机连续动态系统的参数估计中，计算机仿真结果显示了本文方法的有效性。

Firstly,the least-squares parameter estimation method for linear continuous regressive models disturbed with Wiener process via Chebyshev polynomial approximation is proposed,then the correlativeness of the polynomial approximating values of Wiener process is discussed.Based on the correlative results of the approximating values of Wiener process,Markov parameter estimation algorithm which can give an unbiased consistent estimated values with the minimum covariance of the parameter estimated error is proposed.These estimation methods proposed in this ppper are discussed,also,to apply on the parameter estimation problem of stochastic dynamical continuous systems in control field. Finally,the computer simulation results show the effectiveness of these parameter methods.