Optimal Estimation


CMPE Degree: This course is Not Applicable for the CMPE degree.

EE Degree: This course is Not Applicable for the EE degree.

Lab Hours: 0 supervised lab hours and 0 unsupervised lab hours.

Technical Interest Group(s) / Course Type(s): Systems and Controls

Course Coordinator:

Prerequisites: ECE 6550

Corequisites: None.

Catalog Description

Techniques for signal and state estimation in the presence of measurement
and process noise with the emphasis on Wiener and Kalman filtering.

Course Outcomes

Not Applicable

Student Outcomes

In the parentheses for each Student Outcome:
"P" for primary indicates the outcome is a major focus of the entire course.
“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.
“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( Not Applicable ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

Strategic Performance Indicators (SPIs)

Not Applicable

Course Objectives

Topical Outline

1. Introductory Material
a. Vector Spaces and Deterministic State Space Theory
b. Review: Probability, Stochastic Processes and Hilbert Spaces
c. Inverse Problem - Observer Theory
d. Bayesian Estimation
2. Least Squares Estimates and Linear Least Squares Estimates
a. Smoothing for Stationary Processes
b. Spectral Factorization and Wiener Filters
c. Discrete Time Recursive Estimation: Kalman Filter
d. Continuous Time Kalman Filters
e. Stationary Kalman Filters: Relations to Wiener Filters
f. The Riccati Equation
g. Information Forms
3. Complementary Topics:
a. Filtering with Time-correlated Measurement Noise: Johanson Filter
b. Crypto-Deterministic Filtering, Friedland Filter, Kalman Filter Divergence
c. Fast Algorithms and Square Root Forms
d. Scattering Theory and Relation to Filtering
e. Linearized and Extended Kalman Filter
4. Selected Advanced Topics