方位估測(DOA)是指從陣列感應器所接收到的含雜訊量測值中去估算多個入射訊號方位。對於實際方位估測上的應用，傳統的次空間法存在著一些固有問題。近來，Kim 和Wen提出虛擬共變異數矩陣技術，用來改善次空間法在實際方位估測上的應用。但他們仍然是由於高的計算複雜度而違反即時性需求。
在這份論文，我們提出兩種不同的方法來滿足傳統次空間法在實際方位估測上的應用需求，而它們能適用於只有單一快照擷取情況下的均勻線性陣列感應器（ULA）。我們的第一種方法是提出了一個新的快速方位估測演算法，它是使用正交投影和由基於正向-反向數據矩陣所求出的雜訊虛擬特徵向量技術。我們的第二種方法是提出另一個新的快速方位估測演算法，它是使用縮減訊號次空間和由基於正向數據矩陣所求出的雜訊虛擬特徵向量技術。不需要特徵值分解的計算以及藉由縮減訊號次空間技術，對比起Kim 和Wen的快速方位估測演算法，我們所提出的方法可以減少它們的計算複雜性(Kim和Wen的計算複雜性是 ，而我們的方法是 ，在這 代表感應器數目)，同時能保持更好或相似的高解析度能力。
模擬結果顯示，對於訊雜比= 5分貝，三個來自[2.3,9.7,17.8]的不相關訊號和 =23，我們的第一種方法和Wen的方法的解析度機率是約為 0.8，而Kim的方法是小於 0.6，對於訊雜比= 5分貝，兩個來自[5,10.5]的相關訊號以及一個來自[16]的不相關訊號和 =22，我們的第二種方法的解析度機率是接近0.2，而Kim的方法是接近0。

The problem of the direction-of-arrival (DOA) is to estimate the directions of multiple incident signals from noisy measurements received at a sensor array. For practical DOA estimation applications, the conventional subspace-based method has some inherent problems. Recently, Kim and Wen proposed pseudocovariance matrix techniques to improve the performance of subspace-based algorithms in the practical DOA estimation applications. But they still are against real-time requirement due to high computation complexity.
In this dissertation, we proposed two different approaches with application to the uniform linear sensor array (ULA) in a single snapshot case to satisfy the demands of practical applications for conventional subspace algorithms. The first part of our approaches presents a novel fast DOA algorithm, using an orthogonal projection and noise pseudo-eigenvector technique with forward-backward data model. The second part of our approaches presents another novel fast DOA algorithm, using the technologies of the shrinking signal subspace and the noise pseudo-eigenvector with forward data model. Without eigendecomposition computation and employing shrinking signal subspace technique, our proposed approaches can reduce computational complexity(the computational complexity of Kim’s and Wen’s methods is while ours is , where denotes the number of sensors) while maintaining better or similar resolution capability when contrasted to Kim’s and Wen’s fast DOA estimation algorithms.
Simulation results showed that for SNR=5 dB, three uncorrelated signals from [2.3,9.7,17.8] and =23, the resolution probability of the first approach and Wen’s method were about 0.8 while Kim’s method is less than 0.6, and for SNR=5 dB, two coherent signals from [5,10.5] and one uncorrelated signal from [16] and =22, the resolution probability of the second approach was close to 0.2 while Kim’s method was close to 0.

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