檢測與估計

In various engineering works (as well as in many other works), we need to estimate the numerical value of some physical quantity or determine which condition among a number of alternatives is more likely. This course treats this subject. Needless to say, it will introduce some estimation and detection methods. But to put everything in perspective, we also need to consider some important foundational questions, such as: How to properly formulate estimation and detection problems? What are some proper objectives to aim for in estimation and detection? Are there any ultimate limits on how well we can do in attaining these objectives and, if so, what are they? How do the various estimation and detection methods perform and how does their performance compare to the ultimate limits? This course will also address these issues.

1. 線性代數(大學部層次)。 Linear Algebra (undergraduate-level). 2. 機率(大學部層次)。 Probability (undergraduate-level). 3. 運用複數的能力(如電路理論、訊號與系統等課程中之所需,未必需要修複變函數)。 Ability to work with complex numbers, such as that needed in Circuit Theory, Signals and Systems, etc., which you may be able to acquire without taking Complex Variables). 4. 訊號與系統(大學部層次)。 Signals and Systems (undergraduate-level). 5. 基本的隨機過程觀念(如大學部層次通訊原理、數位通訊原理等課程中所講到的觀念,但修過研究所層次的隨機過程課程更佳)。 Basics of Random Processes: The related discussion in the undergraduate courses Principles of Communication Systems and Principles of Digital Communication Systems usually suffices, but the graduate course Stochastic Processes is a plus.

Course website: https://mcube.nctu.edu.tw/~dwlin/courses/19detEst

1. 課程進行方式預定包括課堂講授、作業、及三次考試。 The course will be conducted as a regular lecture course. There will be homework assignments and three exams (tentative). 2. 評分方式於第一堂課及講義中公佈。 Details of the grading method will be described in the course notes and announced in the first lecture.

• The following is a somewhat ideal list of topics. Depending on the progress of the course, we may decide to dwell more on some topics and skip over some others. 1. Introduction 2. Minimum variance unbiased estimation (MVUE) – Desired estimator properties in classical estimation 3. Cramer-Rao lower bound (CRLB) – A useful upper bound on estimator performance 4. MVUE when CRLB cannot be attained 5. Best linear unbiased estimation (BLUE) – When MVUE may be asking for too much 6. Maximum likelihood estimation (MLE) – When it may not make good sense to minimize the variance 7. Least squares estimation (LSE) – A somewhat heuristic approach 8. Method of moments – Another somewhat heuristic approach 9. The Bayesian approach 10. Linear Bayesian estimation 11. Kalman filtering 12. Simple hypothesis testing – Statistical decision theory I 13. Detection of deterministic signals in noise 14. Detection of random signals in noise 15. Composite hypothesis testing – Statistical decision theory II

S. M. Kay, Fundamentals of Statistical Signal Processing. Vol. 1, Estimation Theory, and vol. 2, Detection Theory. Prentice Hall, 1993 (vol. 1) and 1998 (vol. 2).

地點

Announced in the first lecture.

時間

Announced in the first lecture.

聯絡方式

Announced in the first lecture.