一組快速解根型方位估計子之效能評估

Abstract

本論文探討以Root-MUSIC法為基礎之訊號源方位估計法之效能比較。對線 形等間距分佈 (linear equally spaced)感測器陣列而言，可用特徵分 解(eigen-decomposition)與多項式解零根的方法求得方位估計值，而其 中所需的特徵值分解可利用波束空間轉換(beamspace transformation)來 減少運算量；高階多項式經由雜訊特徵矩陣 (noise eigenvector matrix)做帶狀轉換(banded transformation)後可以降至較低階數之多項 式，形成多個低階多項式同時解零根之形式。吾人提出兩種方法:疊代( iterative)法及共同零根法來求出低階多項式的近似零根，進而求出方位 估計值。最後吾人以電腦模擬驗證多項式降階方法的可行性，並在不同環 境條件下作不同方位估計法的效能評估。 In this thesis, methods of reducing computational complexity in root-form eigen-based direction-of-arrival (DOA) estimation are investigated. For linear equally spaced (LES) array, root-form eigen-based estimation methods require an eigenvalue decomposition (EVD) and a high-order polynomial rooting. The complexity of EVD can be reduced by beamspace transformation and the high-order polynomials can be reduced to lower ones by banded transformation which is obtained from the factorization of noise eigenvector matrix. We show that these lower-order polynomials rooting can be executed in parallel. Two approaches, the iterative method and the common null method along with the decomposition of effective spatial passband, are proposed for the solving of lower-order polynomials. We compare the performance of these reduced-order DOA estimation methods in different scenarios by a complete set of the computer simulations.