非高斯噪声环境下的鲁棒分布式多任务自适应算法研究

The multi-objective parameters estimation over wireless sensor networks, i.e., the multitask scenario, has been a wide attention issue in adaptive signal processing area. In practical environments, the non-Gaussian noise with impulses is also common such as α-noise. In this case, existing distributed adaptive algorithms originated from the Gaussian noise assumption would suffer from serious performance degradation or even divergence. Therefore, this project proposes to take advantage of criteria with insensitive property to impulsive noise, to develop some robust distributed multitask adaptive algorithms. Giving that the clusters of nodes in the network to which node belongs and there is one task per cluster, the supervised distributed multitask adaptive algorithms are studied, to estimate multiple parameter vectors of interest; subsequently, assuming that the nodes have no such a priori knowledge, the unsupervised distributed multitask algorithms are studied, to implement the nodes clustering and the estimation of multiple parameter vectors simultaneously. In terms of the learning manner of algorithms, the project firstly derives the robust least mean square (LMS) type by resorting to the instantaneous gradient descent rule; then, it derives the robust recursive least squares (RLS) type from the weighted least squares principle and further extends the dichotomous coordinate descent method to reduce significantly the computational complexity of RLS type. Based on the contaminated-Gaussian model for describing impulsive noise, the project analyzes the stability convergence condition, transient and steady-state behaviors of the proposed algorithms in the mean and mean square senses. In addition, the application of the proposed algorithms is studied for the frequency spectrum estimation of cognitive radio networks.

建立在无线传感器网络上的多目标参数估计即多任务场景，已成为自适应信号处理领域广受关注的主题。实际环境中，具有脉冲特性的非高斯噪声也是常见的，如α噪声。在这种情况下，针对高斯噪声环境的分布式自适应算法会遭受性能的严重退化、甚至发散。因此，本课题拟采用对脉冲噪声不敏感的策略，研究一些鲁棒分布式多任务自适应算法。首先已知网络节点的群划分信息，研究监督的分布式多任务算法，估计感兴趣的多个参数向量；然后针对无此先验信息情况，研究无监督的分布式多任务算法，同时实现节点群聚类和多个参数向量的估计。在算法学习方式上，首先基于瞬时梯度下降准则推导鲁棒LMS类型，然后基于加权最小二乘准则推导鲁棒RLS类型以及扩展二分坐标下降法降低RLS类型的计算复杂度。基于混合高斯噪声模型，研究所提算法在脉冲噪声环境下，均值和均方的稳定收敛条件、暂态和稳态行为。此外，针对认知无线电网络的频谱感知问题，拓展所提算法的应用。

近年来，建立在多节点信息融合基础上的自适应滤波器，分布式自适应滤波器理论获得了极大的关注，并具有广泛的工程应用前景。针对实际中常存在具有脉冲行为的非高斯噪声，本课题系统地研究鲁棒性好、收敛速度快和稳态误差小的分布式自适应滤波算法。其次，深入研究算法的理论性能，包括建立算法的均值和均方进化模型，给出算法的稳定收敛条件和收敛规律，以及揭示优于现有算法的理论机制。此外，针对基于递归最小二乘学习规则的鲁棒性算法，研究其计算复杂度低且无明显性能丢失的实现策略。最后，拓展了算法的应用，例如认知无线电的频谱感知、有源噪声控制和回声消除等，获得了较好的结果。目前，本课题已取得了阶段性的研究成果，在信号处理领域国际期刊上发表SCI论文24篇和会议论文9篇，申请中国发明专利3项，完成了预期目标。通过本课题的研究，拓展了鲁棒分布式自适应滤波理论和方法，探讨了分布式自适应滤波器的工程应用，这有助于推动分布式自适应滤波器的进一步发展。