실시간 도래각 추적을 위한 고속 부공간 기법에 관한 연구 = (A) Study on Fast Subspace Methods for Real-Time DOA (Direction-of-Arrival) Tracking

다국어 초록 (Multilingual Abstract)

This thesis presents a fast subspace tracking method, which is called GVFF (Gradient-based Variable Forgetting Factor) FAPI, based on FAPI (Fast Approximated Power Iteration) method and GVFF-RLS (Gradient-based Variable Forgetting Factor Recursive Least Squares). Since the conventional FAPI uses constant forgetting factor in estimating covariance matrix of source signals, it has difficulty in applying to non-stationary environments such as continuously changing DOA of source signals. To overcome the drawback of conventional FAPI method, the GVFF FAPI introduced the gradient-based variable forgetting factor derived from an improved means square error (MSE) analysis of RLS. In order to achieve the decreased subspace error in non-stationary environments, the GVFF-FAPI algorithm used an improved forgetting factor updating equation that can produce a fast decreasing forgetting factor when the gradient is positive and a slowly increasing forgetting factor when the gradient is negative.
Our numerical simulations show that GVFF-FAPI algorithm offers lower subspace error and root mean square error (RMSE) of tracked DOA of source signals than conventional RLS based DOA tracking methods.

목차 (Table of Contents)

• 목 차
• 제１장 서 론 4
• 제２장 배열 안테나 입사 신호의 도래각 추정 8
• 제 2.1 절 배열 안테나와 입사 신호 모델링 8
• 2.1.1. 등간격 선형 배열 안테나 8
• 2.1.2. 입사 신호 모델링 9
• 제 2.2 절 공간 공분산 행렬과 벡터 부공간 12
• 제 2.3 절 입사 신호의 도래각 추정 기법 15
• 2.3.1. Spectral 추정 기법 15
• 2.3.2. MVDR 추정기 15
• 2.3.3. 선형 예측 기법 16
• 2.3.4. MUSIC 알고리즘 17
• 2.3.5. Minimum-Norm 기법 18
• 2.3.6. DML 알고리즘 19
• 제３장 고속 부공간 추적 기법 21
• 제 3.1 절 PAST (Projection Approximation Subspace Tracking) 22
• 제 3.2 절 API (Approximated Power Iteration) 28
• 제 3.3 절 FAPI (Fast Approximated Power Iteration) 30
• 제 3.4 절 컴퓨터 모의 실험을 통한 성능 비교 35
• 제４장 적응 망각 인자 기반의 고속 부공간 추적 기법 40
• 제 4.1 절 Gradient-Based Variable Forgetting Factor RLS 41
• 제 4.2 절 Gradient-Based Variable Forgetting Factor FAPI 50
• 제 4.3 절 컴퓨터 모의 실험을 통한 성능 비교 53
• 제５장 결론 63
• 참고 문헌 64