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首页> 外文期刊>Automatic Control, IEEE Transactions on >Time and Spectral Domain Relative Entropy: A New Approach to Multivariate Spectral Estimation
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Time and Spectral Domain Relative Entropy: A New Approach to Multivariate Spectral Estimation

机译：时域和谱域相对熵：多元谱估计的新方法

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摘要

The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates. This naturally leads to a new spectral estimation technique where a multivariate version of the Itakura–Saito distance is employed. It may be viewed as an extension of the approach, called THREE, introduced by Byrnes, Georgiou, and Lindquist in 2000 which, in turn, followed in the footsteps of the Burg–Jaynes Maximum Entropy Method. Spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate. The corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework. Indeed, it is equal to the one featured by THREE in the scalar case. The solution is computed via a globally convergent matricial Newton-type algorithm. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.
机译：针对联合平稳高斯过程引入了频谱相对熵率的概念。使用经典的信息理论结果，我们在时间和谱域相对熵率之间建立了显着的联系。这自然导致了一种新的频谱估计技术，其中使用了Itakura–Saito距离的多元版本。可以将其看作是方法的扩展，该方法由Byrnes，Georgiou和Lindquist于2000年提出，后来又沿Burg–Jaynes最大熵方法的脚步进行。此处，频谱估计以约束频谱近似问题的形式重铸，其中距离等于过程的相对熵率。相应的解决方案带来了复杂性上限，与目前在多通道框架中可用的上限相比有所提高。实际上，它等于标量情况下“三”的特征。该解决方案是通过全局收敛矩阵牛顿型算法计算的。仿真表明，该新技术在处理多元光谱估计任务方面是有效的，特别是在数据记录较短的情况下。

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