Approximate joint diagonalization of a set of matrices provides a powerful framework for numerous statistical signal processing applications. For non-unitary joint diagonalization (NUJD) based on the least-squares (LS) criterion, outliers, also referred to as anomaly or discordant observations, have a negative influence on the performance, since squaring the residuals magnifies the effects of them. To solve this problem, we propose a novel cost function that incorporates the soft decision-directed scheme into the least-squares algorithm and develops an efficient algorithm. The influence of the outliers is mitigated by applying decision-directed weights which are associated with the residual error at each iterative step. Specifically, the mixing matrix is estimated by a modified stationary point method, in which the updating direction is determined based on the linear approximation to the gradient function. Simulation results demonstrate that the proposed algorithm outperforms conventional non-unitary diagonalization algorithms in terms of both convergence performance and robustness to outliers.
翻译:一组矩阵的近似联合对角化为众多统计信号处理应用程序提供了一个强大的框架。对于基于最小平方(LS)标准的非统一联合对角化(NUJD)标准而言,外端(也称为异常或不一致的观测)对性能有负面的影响,因为将剩余部分进行比对会放大其影响。为了解决这个问题,我们提议了一个新的成本功能,将软性决定式计划纳入最小平方算法,并开发一个高效的算法。外端的影响力通过在每个迭代步骤应用与残余错误相关的决定式对准权重而得到缓解。具体地说,混合矩阵是通过一个修改的定点法估计的,根据梯度函数的线性近度来确定更新方向。模拟结果表明,拟议的算法在趋同性能和对外部列的稳健性方面都比传统的非统一式对等算法。