基于数据滤波的随机梯度辨识方法

Filtering-based stochastic gradient identification methods

针对有色噪声干扰下的随机系统,利用数据滤波技术,对输入输出数据进行滤波,将具有滑动平均噪声的原始系统转换为白噪声干扰下的系统,提出有限脉冲响应滑动平均系统的滤波增广随机梯度算法,并对该算法进行收敛性分析.此外,为了提高参数估计的精度和加快算法的收敛速度,使用多新息辨识理论提出滤波多新息增广随机梯度算法,并分析其收敛性.与增广随机梯度算法相比,所提出的滤波增广随机梯度算法和滤波多新息增广随机梯度算法可以得到更高精度的参数估计.最后,通过仿真实例表明了所提出算法的有效性.

This paper studies the parameter identification of stochastic systems with colored noises.Using the data filtering technology to filter the input and output data,which converts the original system with moving average noise to the system with white noise,we propose the filtering-based extended stochastic gradient algorithm and analyze its convergence.In addition,in order to improve the parameter estimation accuracy and accelerate the convergence rate,a filtering-based multi-innovation extended stochastic gradient algorithm is proposed by using the multi-innovation identification theory and its convergence is analyzed.Compared with the extended stochastic gradient algorithm,the proposed filtering-based extended stochastic gradient algorithm and the filtering-based multi-innovation extended stochastic gradient algorithm can obtain higher precision parameter estimates.Finally,the simulation results indicate that the proposed algorithms are effective.