1. COMM 1004: Detection & Estimation Lecture 5 Maximum Likelihood Estimation (MLE)

2. Maximum Likelihood Estimation (MLE)

4. Example 1:
Let 𝑋(𝑛); 𝑛=0, 1,…,𝑁−1 be a sequence of independent, identically distributed Gaussian random variables having unknown mean 𝜃 and a known variance 𝜎 2 . Estimate the mean 𝜃 using ML algorithm.

5. Check if this estimator is unbiased??

6. Properties of Maximum Likelihood Estimation

7. Example: Find the MLE for the DC level A, given:

10. Applications: Phase Estimation of sinusoidal signal

11. The log likelihood function can be written as:

14. MLE: Extension to Vector Parameter

15. Example: MLE of Vector Parameter

16. MLE for General Linear Models

18. Range Estimation Problem
Signal duration

19. Tsampling
T N
Ts M

20. N-1

21. Does not depend on the observation_
Irrelevant Term
Does not depend on the observation

23. Monte Carlo Simulations (Useful in your project)
Reading material
Monte Carlo Simulations (Useful in your project)

26. Asymptotic Properties of Estimators