摘要
本文讨论y_n=h_n*X_n为AR(q)模型,输入{X_n)为零均值独立同分布平稳序列,脉冲响应{h_n}为非最小相位的线性系统,如何由输出{y_n}的样本序列y_1,y_2,…,y_n估计系统的自回归系数a_0,a_1,…,a_q的反褶积问题,提出L_p(1<p<2)方法,即在约束条件sum from k=0 to q a_kh_(-k)=1之下,使sum from n=q+1 to N∣sum from b=0 to q a_by_(n-k)∣~p达极小,当有{h_(-k)}(0≤k≤q)的初始估计{h_(-k)^((0))}时,可由{h_(-k)^((0))}→{a_k^((1))}→{h_(-k)^((I))}→…进行迭代求解;在由{h_(-k)^((1))}求解{a_k^((1))}时,采用迭代加权最小二乘方法解L_p最优问题,文中给出的模拟计算例子表明了上述迭代方法的收敛性,且p愈接近1,迭代收敛域愈宽,而收敛速度愈慢,综合两者,作者认为宜选取1.2≤p≤1.5。
In this paper we discuss a category of linear system:yn=h1 * X, which is of AR(q) model,its input {X} is independent and identically distributed Stationary variables with zero expetation ,its pulse response {ks}Is at non -minimum phase. Now the dcconvolution problem is how to estimate auto-regressive coefficients a1,a2,…an of the system based on sample series y1,y2,…,yn. of output {Yn}. The author presents Lp(l<p<2) deconvolution method,thecriterion of which is min under the constrain . When initial estimates {K-k(o)} {0≤k≤q} of{K-k} are available this problem be solved iteratively via . At the step from {K-k(o)} to {abU+1} the Iteratively Reweighted Least Squares Algorithm is adopted to solve Lp optimal problem. Some simulated examples given in the paper show that the above iterative method is convergent,and the closer to 1 the p is,the wider the convergent range near {ak} will be,but making the converyence rate lower. The author thinks it suitable to choose 1.2≤p≤1.5.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
1990年第3期97-101,共5页
Control Theory & Applications
关键词
非最小相位
AR模型
线性系统
deconvolution
non-minimum phase
parameters estimate
