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针对一类双采样率随机时变系统,应用多项式变换技术和随机过程理论,在强持续激励条件下,研究了双率时变遗忘因子最小二乘法(dual-rate forgotten factor least squares,DR-FFLS)的参数估计收敛性,得到了参数估计误差上界的精确表达式。分析表明,随着数据长度k的增加,DR-FFLS算法的参数估计误差上界收敛到常数。同时分析了双率确定性时不变系统、随机时不变系统、确定性时变系统的参数估计误差上界。仿真实例验证了对于随机时变与不变双率系统,同样可得参数估计误差小于参数估计误差上界,并且随着k的增大,参数估计误差上界趋于常数。
Aiming at a class of double sampling rate random time-varying systems, the polynomial transformation technique and stochastic process theory are used to study the dual-rate forgotten factor least squares (DR-FFLS) ), We obtain the exact expression of the upper bound of error in parameter estimation. The analysis shows that with the increase of data length k, the upper bound of parameter estimation error of DR-FFLS algorithm converges to a constant. At the same time, the upper bounds of the error of parameter estimation for two-rate deterministic time-invariant system, stochastic time-invariant system and deterministic time-varying system are analyzed. The simulation results show that for the random time-varying and invariant dual-rate systems, the same estimated error of the parameter estimation is less than the upper bound of the parameter estimation error, and the upper bound of the parameter estimation error tends to be constant with the increase of k.