Non-Convex Projection Adaptive Hammerstein Filtering
-
摘要: 该文研究了Hammerstein系统参数辨识和非线性系统预测问题，提出一种基于非凸投影的自适应滤波算法。论文将问题归结为具有非凸可行域的约束优化问题，并建立了基于交替方向乘子法(ADMM)和递归最小二乘相结合的算法框架。在该算法框架下，非凸约束优化问题的全局最优解可通过岭回归和欧几里得(Euclid)投影循环计算得到。将提出的算法分别应用于Hammerstein系统的参数辨识、非线性未知系统预测以及非线性声学回声消除，并进行仿真实验，结果显示所提算法具有较好的收敛性和稳定性，能够得到较准确的辨识和预测效果。
-
关键词:
- 系统辨识 /
- 非线性预测 /
- 自适应滤波 /
- 参数估计 /
- Hammerstein系统
Abstract: This paper focuses on adaptive filtering techniques for parameter identification of Hammerstein systems and output prediction of nonlinear systems. By formulating the underlying filtering problem as a recursive bilinear least-squares optimization with the non-convex feasible region constraint, an algorithmic framework is developed based on recursive least-squares and Alternating Direction Method of Multipliers (ADMM). Under this framework, the solution to nonconvex constraint optimization problem can be obtained by implementing ridge regression and Euclidean projection. Simulation results in the context of system identification, nonlinear predication, and acoustic echo cancellation, reveal that the proposed algorithm has good convergence and stability, and can obtain more accurate identification and prediction results. -
算法1 提出的RncPLS算法 输入：d(n), x(n) 输出：${\hat {\boldsymbol{a}}}(n),{\hat {\boldsymbol{b}}}(n),{\boldsymbol{\theta}} (n) = {\bar {\boldsymbol{\theta}} _L}(n)$ 初始值：${ {\bar {\boldsymbol{\theta} } }_L}(0),\bar {\boldsymbol{R} }_L^{ - 1}(0),{ {\boldsymbol{\varphi} } }(0),{{\boldsymbol{\eta}} }(0)$ 算法迭代：在每个时刻n，由输入按照以下步骤得到估计值输出，迭代直至收敛。
1. ${ {\boldsymbol{k} } }(n) = \dfrac{ { {\bar {\boldsymbol{R} } }_L^{ - 1}(n - 1){\boldsymbol{ {h} } }(n)} }{ {\gamma + { {h}^{\rm{T} } }(n){\bar {\boldsymbol{R} } }_L^{ - 1}(n - 1){ {\boldsymbol{h} } }(n)} }$2. ${\bar {\boldsymbol{\theta}} _0}(n) = ({{\boldsymbol{I}}} - {{\boldsymbol{k}}}(n){ {{\boldsymbol{h}}}^{\rm{T}}}(n)){\bar {\boldsymbol{\theta}} _L}(n - 1) + {{\boldsymbol{k}}}(n)d(n)$，${\bar {\boldsymbol{R} } }_0^{ - 1}(n) = {\gamma ^{ - 1} }{\bar {\boldsymbol{R} } }_L^{ - 1}(n - 1) - {\gamma ^{ - 1} }{{\boldsymbol{k}}}(n){ { {\boldsymbol{h} } }^{\rm{T} } }(n){\bar {\boldsymbol{R} } }_L^{ - 1}(n - 1)$ 3. for l = 1, 2, ···, L 4. ${\tau _l}(n - 1) = \dfrac{ {\sqrt {\boldsymbol{\xi}} ({\chi _l}(n - 1) - \gamma {\chi _l}(n - 2))} }{ {1 - \gamma } }$，${ {{\boldsymbol{g}}}_l} = \dfrac{ {\sqrt {\boldsymbol{\xi}} {\bar {\boldsymbol{R}}}_{l - 1}^{ - 1}(n){ {{\boldsymbol{e}}}_l} } }{ {1 + {\boldsymbol{\xi}} {{\boldsymbol{e}}}_l^{\rm{T}}{\bar {\boldsymbol{R}}}_{l - 1}^{ - 1}(n){ {{\boldsymbol{e}}}_l} } }$ 5. ${\bar {\boldsymbol{\theta} } _l}(n) = ({\boldsymbol{I} } - \sqrt {\boldsymbol{\xi} } { {\boldsymbol{g} }_l}{\boldsymbol{e} }_l^{\rm{T} }){\bar {\boldsymbol{\theta} } _{l - 1} }(n) + {{\boldsymbol{g}}_l}{\tau _l}(n - 1)$，${\bar {\boldsymbol{R}}}_l^{ - 1}(n) = {\bar {\boldsymbol{R}}}_{l - 1}^{ - 1}(n) - \sqrt {\boldsymbol{\xi}} { {{\boldsymbol{g}}}_l}{{\boldsymbol{e}}}_l^{\rm{T}}{\bar {\boldsymbol{R}}}_{l - 1}^{ - 1}(n)$ 6. end for 7. $\omega (n) = {\boldsymbol{\theta} } (n) + {\boldsymbol{\eta}} (n - 1)$
8. ${\boldsymbol{\hat a} }(n) = {\boldsymbol{u} }(n){ {\boldsymbol{u} }^{\rm{T}}}(n){\omega _1}(n)$，${\hat {\boldsymbol{b} } }(n) = \dfrac{ { {\boldsymbol{\varTheta} } _2^{\rm{T} }(n){u}(n)} }{ {\omega _1^{\rm{T}}(n){u}(n)} }$9. $\varphi (n) = ({ {\boldsymbol{\varTheta} } ^{\rm{T} } }(n){\boldsymbol{u} }(n)) \otimes {\boldsymbol{u} }(n)$，${{\boldsymbol{\eta}} }(n) = {{\boldsymbol{\eta}} }(n - 1) + {{\boldsymbol{\theta}} }(n) - {\varphi }(n)$ 10. ${\boldsymbol{\chi} } (n) = {[{\chi _1}(n),{\chi _2}(n), \cdots ,{\chi _L}(n)]^{\rm{T}}}{\text{ = } }\varphi (n) - {\boldsymbol{\eta} } (n)$ 11. n = n+1，返回步骤1，直至达到收敛条件 
下载: 导出CSV
-
[1] GOKCEOGLU A, GHADAM A, and VALKAMA M. Steady-state performance analysis and step-size selection for LMS-adaptive wideband feedforward power amplifier linearizer[J]. IEEE Transactions on Signal Processing, 2012, 60(1): 82–99. doi: 10.1109/TSP.2011.2169254 [2] ALONGE F, D’IPPOLITO F, and CANGEMI T. Identification and robust control of DC/DC converter Hammerstein model[J]. IEEE Transactions on Power Electronics, 2008, 23(6): 2990–3003. doi: 10.1109/TPEL.2008.2005034 [3] SHI Kun, ZHOU G T, and VIBERG M. Compensation for nonlinearity in a Hammerstein system using the coherence function with application to nonlinear acoustic echo cancellation[J]. IEEE Transactions on Signal Processing, 2007, 55(12): 5853–5858. doi: 10.1109/TSP.2007.901657 [4] 赵益波, 严涛, 李春彪, 等. α-稳定分布噪声环境下的非线性回声消除研究[J]. 电子学报, 2020, 48(1): 59–65. doi: 10.3969/j.issn.0372-2112.2020.01.007ZHAO Yibo, YAN Tao, LI Chunbiao, et al. Research on nonlinear echo cancellation in the α-stable noise environment[J]. Acta Electronica Sinica, 2020, 48(1): 59–65. doi: 10.3969/j.issn.0372-2112.2020.01.007 [5] KOMATSU K, MIYAJI Y, and UEHARA H. Basis function selection of frequency-domain Hammerstein self-interference canceller for in-band full-duplex wireless communications[J]. IEEE Transactions on Wireless Communications, 2018, 17(6): 3768–3780. doi: 10.1109/TWC.2018.2816061 [6] 赵海全, 李磊. 一种抗冲击噪声的对数总体最小二乘自适应滤波算法[J]. 电子与信息学报, 2021, 43(2): 284–288. doi: 10.11999/JEIT200344ZHAO Haiquan and LI Lei. A Logarithmic Total least squares adaptive filtering algorithm for impulsive noise suppression[J]. Journal of Electronics &Information Technology, 2021, 43(2): 284–288. doi: 10.11999/JEIT200344 [7] MA Junxia, HUANG Biao, and DING Feng. Iterative identification of Hammerstein parameter varying systems with parameter uncertainties based on the variational Bayesian approach[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2020, 50(3): 1035–1045. doi: 10.1109/TSMC.2017.2756913 [8] WANG Dongqing, ZHANG Shuo, GAN Min, et al. A novel EM identification method for Hammerstein systems with missing output data[J]. IEEE Transactions on Industrial Informatics, 2020, 16(4): 2500–2508. doi: 10.1109/TII.2019.2931792 [9] HONG Xia, CHEN Sheng, HARRIS C J, et al. Single-carrier frequency domain equalization for Hammerstein communication systems using complex-valued neural networks[J]. IEEE Transactions on Signal Processing, 2014, 62(17): 4467–4478. doi: 10.1109/TSP.2014.2333555 [10] GREBLICKI W and PAWLAK M. The weighted nearest neighbor estimate for hammerstein system identification[J]. IEEE Transactions on Automatic Control, 2019, 64(4): 1550–1565. doi: 10.1109/TAC.2018.2866463 [11] GÓMEZ J C and BAEYENS E. Subspace-based identification algorithms for Hammerstein and wiener models[J]. European Journal of Control, 2005, 11(2): 127–136. doi: 10.3166/EJC.11.127-136 [12] LIU Ying and LI Chunguang. Distributed prediction via adaptive Hammerstein filter over networked systems[J]. IEEE Transactions on Signal and Information Processing over Networks, 2018, 4(3): 534–548. doi: 10.1109/TSIPN.2017.2780620 [13] JERAJ J and MATHEWS V J. Stochastic mean-square performance analysis of an adaptive Hammerstein filter[J]. IEEE Transactions on Signal Processing, 2006, 54(6): 2168–2177. doi: 10.1109/TSP.2006.873587 [14] 方维维, 刘梦然, 王云鹏, 等. 面向物联网隐私数据分析的分布式弹性网络回归学习算法[J]. 电子与信息学报, 2020, 42(10): 2403–2411. doi: 10.11999/JEIT190739FANG Weiwei, LIU Mengran, WANG Yunpeng, et al. A Distributed elastic net regression algorithm for private data analytics in internet of things[J]. Journal of Electronics &Information Technology, 2020, 42(10): 2403–2411. doi: 10.11999/JEIT190739 [15] LE Fengmin, MARKOVSKY I, FREEMAN C T, et al. Recursive identification of Hammerstein systems with application to electrically stimulated muscle[J]. Control Engineering Practice, 2012, 20(4): 386–396. doi: 10.1016/j.conengprac.2011.08.001 [16] DONG Shijian, LI Yu, ZHANG Wenan, et al. Robust extended recursive least squares identification algorithm for Hammerstein systems with dynamic disturbances[J]. Digital Signal Processing, 2020, 101: 102716. doi: 10.1016/j.dsp.2020.102716 [17] LEE K, BAEK Y, and PARK Y. Nonlinear acoustic echo cancellation using a nonlinear postprocessor with a linearly constrained affine projection algorithm[J]. IEEE Transactions on Circuits and Systems II:Express Briefs, 2015, 62(9): 881–885. doi: 10.1109/TCSII.2015.2435711 -
图(8) / 表(1)
计量
- 文章访问数: 585
- HTML全文浏览量: 202
- PDF下载量: 71
- 被引次数: 0
下载:
