实际应用中信号和噪声的统计知识经常是未知的,为探究未知噪声环境中加权随机汇池网络模型的信号参数估计性能,本文研究了加权随机汇池网络中信号估计的递归最小二乘自适应递推算法,分析了该模型下算法的收敛性、均方误差、学习曲线等统计特征。在非平稳输入信号下,引入遗忘因子,探究了算法有效跟踪信号变化的能力。实验结果验证了关于算法收敛性与均方误差性能的理论分析,同时还证实了自适应过程中的超阈值随机共振现象。本文研究结果对于加权随机汇池网络的实际应用具有理论指导义。
In practice, the probability distribution model of the background noise is often unknown. Under this circumstance, a recursive least square adaptive algorithm is developed to estimate the random signal via the weighted stochastic pooling network. The analytical formula of the recursive least square adaptive algorithm is derived, and the convergence of the algorithm, the mean square error of the network outputs and the learning curve are analyzed. For non-stationary input signals, the proposed algorithm with the forgetting factor can effectively track the change of the signal. These theoretical results are demonstrated by the numerical experiments, and the phenomenon of suprathreshold stochastic resonance is also observed. The obtained results lay the fundamental framework for the application of the weighted stochastic pooling network in signal estimation.
[1]Zozor S, Amblard P O, Duchêne C. On pooling networks and fluctuation in suboptimal detection framework[J]. Fluctuation and Noise Letters, 2007, 7(1):39-60.
[2]Stocks N G. Suprathreshold stochastic resonance in multilevel threshold systems[J]. Physical Review Letters, 2000, 84(11): 2310-2313.
[3]Stocks N G. Information transmission in parallel threshold arrays: Suprathreshold stochastic resonance[J]. Physical Review E, 2001, 63(4): 11-14.
[4]Benzi R, Sutera A, Vulpiani A. The mechanism of stochastic resonance [J]. Journal of Physical A, 1981, 14(11): 453-457.
[5]Gammaitoni L, Hänggi P, Jung P, et al. Stochastic resonance [J]. Reviews of Modern Physics, 2008, 70(1): 45-105.
[6]McDonnell M D, Amblard P O, Stocks N G. Stochastic pooling networks[J]. Journal of Statistical Mechanics Theory & Experiment, 2009, (1):01012.
[7]Xu L, Vladusich T, Duan F, et al. Decoding suprathreshold stochastic resonance with optimal weights[J]. Physics Letters A, 2015, 379(38): 2277-2283.
[8]Xu L, Duan F, Abbott D, et al. Optimal weighted suprathreshold stochastic resonance with multigroup saturating sensors[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 457:348-355.
[9]Xu L, Duan F, Gao X, et al. Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance[J]. Royal Society Open Science, 2017, 4(9): 1-12.
[10] 景文腾,韩博,耿金花,等. 最优加权随机汇池网络估计性能研究[J].复杂系统与复杂性科学,2018, 15(3):89-93.
Jing Wenteng,Han Bo,Geng Jinhua, et al. Study of estimation performance of optimally weighted stochastic pooling networks[J].Complex System and Complexity Science, 2018, 15(3): 89-93.
[11] 韩博,景文腾,耿金花,等.最优加权随机汇池网络的自适应算法研究[J].复杂系统与复杂性科学, 2018, 15(4): 85-89.
Han Bo,Jing Wenteng,Geng Jinhua, et al. Study of adaptive algorithms for optimally weighted stochastic pooling networks [J].Complex System and Complexity Science, 2018, 15(4):85-89.
[12] 曹宏举,郭巧丽. 最小二乘法的多角度分析及其应用[J].高等数学研究,2019,22(01):49-51.
Cao Hongju, Guo Qiaoli. Multi aspects analysis and application of least square method[J]. Studys in College Mathmatics, 2019, 22(1):49-51.
[13] Ding F, Wang X,Chen Q, et al. Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition[J]. Circuits, Systems, and Signal Processing, 2016, 35(9):3323-3338.
[14] Mao X, Li Q, Xie H,et al. Least squares generative adversarial networks[C]. IEEE International Conference on Computer Vision. Italy: IEEE, 2017: 2813-2821.
[15] Zhu B, Wei Y. Carbon price forecasting with a novel hybrid ARIMA and least squares support vector machines methodology[J]. Omega-international Journal of Management Science, 2013, 41(3):517-524.
[16] Manolakis D G, Lngle V K, Kogon S M. Statistical and Adaptive Signal Processing[M]. America:McGraw Hill, 2000.
[17] Haykin S. Adaptive filter theory, Fifth Edition [M].America:Pearson, 2013.
[18] Diniz P S R. Adaptive Ftering: Algorithms and Practical Implementation[M]. 4th ed. Germany:Springer, 2012.
