使用正交投影近似子空間追蹤技術之快速適應性ESPRIT方法

Abstract

本論文提出一種新的使用正交投影近似子空間追蹤技術之快速適應性ESPRIT方法。ESPRIT是一項以子空間法為基礎的演算法，其主要的功用在於進行信號參數的估測，尤其是應用在利用由N對感應器所組成之陣列的輸出資料來進行r個信號源的方位估測(N必須大於r)。這套演算法在最初設計時，即是以批次式信號處理為基礎，因此需要繁雜的計算量來處理特徵值分解的問題。目前適應性ESPRIT演算法的實現，即是結合子空間追蹤技術以及傳統ESPRIT方法去降低運算複雜度。在本論文中，我們先針對古典的ESPRIT演算法以及適用於信號源方位估測的資料模型作一簡單的描述，然後介紹由Peter Strobach所提出的兩種適應性ESPRIT方法；Peter Strobach利用QR化簡、時序正交疊代、Given plane rotation的概念提出LORAF2、LORAF3兩種子空間追蹤技術，再進一步發展出兩套適應性ESPRIT演算法。我們在論文中提出一種使用正交投影近似子空間追蹤技術的快速適應性ESPRIT方法，本方法相當簡單且直觀，不需引入任何複雜的數值分析概念，且在每一次的更新處理中，只需要約11Nr + 10N + O(r^3) 的計算量，和Peter Strobach的兩種方法相比較，本技術的確有效降低了計算量和記憶量的需求成本。我們同時也藉由電腦模擬證實，本論文所提出的技術在信號源方位估測的應用上，的確擁有與Peter Strobach的方法相同的效能。

This thesis proposes a new and fast adaptive ESPRIT algorithm using orthonormal projection approximation subspace tracking (OPAST) technique. The estimation of signal parameters via rotational invariance techniques (ESPRIT) is an attractive subspace-based algorithm for estimating signal parameters, particularly the directions of arrival (DOA) of a set of r narrowband signal sources collected by an array composed of N sensor doublets, where N > r. The ESPRIT algorithm, originally designed in a batch signal processing, requires large amounts of computations to implement eigenvalue decomposition. Recently, the adaptive ESPRIT algorithm is realized normally by combining an adaptive subspace tracker with classical ESPRIT to reduce the arithmetic operation complexity. In this thesis, we describe the classical ESPRIT algorithm and the data model for DOA estimation first. Then, we present some simple introductions for two adaptive ESPRIT algorithms proposed by Peter Strobach. Peter Strobach uses the concepts of QR-reduction, sequential orthogonal iteration, and Givens plane rotation to develop two subspace trackers, called LORAF2 and LORAF3, then further proposes two adaptive ESPRIT algorithms. Further we propose a fast adaptive ESPRIT technique utilizing the OPAST method to implement works for real-time processing. This technique is very simple and intuitive in no need of many complex concepts in numerical analysis, and requires only about 11Nr + 10N + O(r^3) computational complexity every update. Compare with the adaptive ESPRIT algorithms proposed by Peter Strobach, our method indeed effectively saves the costs of computations and storage sizes. By computer simulations of DOA estimations, we also demonstrate that it has the good performance identical to the adaptive ESPRIT algorithms proposed by Peter Strobach.