Unitary PUMA Algorithm for Estimating the Frequency of a Complex Sinusoid
Unitary PUMA Algorithm for Estimating the Frequency of a Complex Sinusoid
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DOI：
10.1109/tsp.2015.2454471
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发表时间：
2015-07
影响因子：
5.4
通讯作者：
Cheng Qian;Lei Huang;H. So;N. Sidiropoulos;Junhao Xie
中科院分区：
文献类型：
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作者：
Cheng Qian;Lei Huang;H. So;N. Sidiropoulos;Junhao Xie
高斯白噪声中单个复正弦信号的一维(1-D)和二维(2-D)频率估计是一个有着广泛应用的经典信号处理问题。这里通过一种新的酉主-奇异向量利用模式分析(PUMA)方法重新讨论它，该方法是通过实值计算来实现的。二维酉PUMA首先被描述为一个迭代加权最小二乘优化问题。考虑到当用最小二乘法对二维酉PUMA进行初始化时，只需一次迭代就足够了，从而得到了计算上吸引人的闭式解。文中还给出了一种适用于一维情形的二维酉PUMA的变型。由于频率估计的实值计算和封闭形式的表达式，酉PUMA比一些最先进的方法在计算上更有效。此外，还从理论上推导了一维和二维酉PUMA估计量的渐近方差，并给出了数值结果，验证了所提方法的有效性。
One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-the-art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.