Kalman Filter for Everyone
Course specifications
Duration: 10 hours
Number of sessions: 5 sessions (two hours per session)
Class time: Saturday, 12 to 2 pm (GMT); The final class time will be fixed after coordination with students.
How to participate in the class: Classes are held in "zoom" environment. The link to participate in the class will be sent after the final registration.
Course tuition: The course fee is 300$ (1800 RMB). There is no charge for pre-registration. The course tuition is charged upon final registration.
Programming language: MATLAB programming language is used in this course.
Instructor: Dr. Mahdi Shadabfar
Programming language: MATLAB programming language is used in this course.
Instructor: Dr. Mahdi Shadabfar
If you have any queries regarding this course, please visit our "Contact Us" page.
Course description
The Kalman filter is a computational tool utilized in numerous fields of science and engineering today and is needed by a large number of students and researchers. The majority of sources in this field have addressed the issues with mathematical proofs and control engineering literature, making it difficult to comprehend for most audiences. However, understanding how the Kalman filter works and how to apply it in practice is not a complicated issue and can be taught with a clear expression without requiring computational complexity. The purpose of this course, as the title implies, is to present the concepts of the Kalman filter to the general audience, regardless of their academic specialization. All the material presented in this course is explained with thorough explanations and various examples, in such a way that the theory of the subject is clarified and its application is practiced on various examples.
In this course, in addition to the conventional Kalman Filter, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are also described, and their performance is discussed. This course is beneficial for anyone interested in learning about and implementing the Kalman filter. After completing this course, students can readily pursue the subject of the Kalman filter in any speciality within their preferred major.
In this course, in addition to the conventional Kalman Filter, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are also described, and their performance is discussed. This course is beneficial for anyone interested in learning about and implementing the Kalman filter. After completing this course, students can readily pursue the subject of the Kalman filter in any speciality within their preferred major.
Course content
1. Session 1: Recursive Filter
1.1. Average filter
1.1.1. Recursive expression for average
1.1.2. Average filter function
1.1.3. Example: Voltage measurement
1.1.4. Summary
1.2. Moving average filter
1.2.1. Stock price and moving average
1.2.2. Recursive expression of moving average
1.2.3. Moving average filter function
1.2.4. Example: Sonar
1.2.5. Summary
1.3. Low-pass filter
1.3.1. Limitation of moving average
1.3.2. 1st order low-pass filter
1.3.3. Low-pass filter function
1.3.4. Example: Sonar
1.3.5. Summary
1.4. Summary of Session 1
2. Session 2: Theory of Kalman Filter
2.1. Introduction to Kalman filter
2.1.1. Introduction
2.1.2. Kalman filter algorithm
2.2. Estimation process
2.2.1. Introduction
2.2.2. Computation of an estimate
2.2.3. Varying weight
2.2.4. Error covariance
2.2.5. Summary
2.3. Prediction process
2.3.1. Computation of a prediction
2.3.2. Difference between prediction and estimation
2.3.3. Reinterpretation of the expression for computing an estimate
2.4. System model
2.4.1. Introduction
2.4.2. System model
2.4.3. Covariance of the noise
2.5. Summary of Session 2
3. Session 3: Examples
3.1. Extremely simple example
3.1.1. System model
3.1.2. Kalman filter function
3.1.3. Test program
3.1.4. Error covariance and Kalman gain
3.1.5. Summary
3.2. Estimating velocity from position
3.2.1. System model
3.2.2. Kalman filter function
3.2.3. Result of the estimation
3.2.4. Estimating position with velocity
3.2.5. Measuring velocity with sonar
3.2.6. Efficient Kalman filter function
3.2.7. Power of system model
3.3. Estimating velocity from position
3.3.1. System model
3.3.2. Kalman filter function
3.3.3. Result of the estimation
3.3.4. Estimating position with velocity
3.3.5. Measuring velocity with sonar
3.3.6. Efficient Kalman filter function
3.3.7. Power of system model
3.4. Tracking an object in an image
3.4.1. System model
3.4.2. Kalman filter function
3.4.3. Test program
3.4.4. Test program 2
3.5. Attitude reference system
3.5.1. Introduction
3.5.2. Attitude determination with gyros
3.5.3. Attitude determination with accelerometers
3.5.4. Attitude determination through sensor fusion
3.5.4.1. System model
3.5.4.2. Kalman filter for sensor fusion
3.1.1. System model
3.1.2. Kalman filter function
3.1.3. Test program
3.1.4. Error covariance and Kalman gain
3.1.5. Summary
3.2. Estimating velocity from position
3.2.1. System model
3.2.2. Kalman filter function
3.2.3. Result of the estimation
3.2.4. Estimating position with velocity
3.2.5. Measuring velocity with sonar
3.2.6. Efficient Kalman filter function
3.2.7. Power of system model
3.3. Estimating velocity from position
3.3.1. System model
3.3.2. Kalman filter function
3.3.3. Result of the estimation
3.3.4. Estimating position with velocity
3.3.5. Measuring velocity with sonar
3.3.6. Efficient Kalman filter function
3.3.7. Power of system model
3.4. Tracking an object in an image
3.4.1. System model
3.4.2. Kalman filter function
3.4.3. Test program
3.4.4. Test program 2
3.5. Attitude reference system
3.5.1. Introduction
3.5.2. Attitude determination with gyros
3.5.3. Attitude determination with accelerometers
3.5.4. Attitude determination through sensor fusion
3.5.4.1. System model
3.5.4.2. Kalman filter for sensor fusion
4. Nonlinear Kalman filter
4.1. Extended Kalman filter
4.1.1. Introduction
4.1.2. Linearized Kalman filter
4.1.3. Extended Kalman filter
4.1.3.1. Nonlinear system model
4.1.3.2. Extended Kalman filter algorithm
4.1.4. Example 1: Radar tracking
4.1.4.1. System model
4.1.4.2. Extended Kalman filter function
4.1.4.3. Test program
4.1.5 Example 2: Attitude reference system
4.1.5.1. System model
4.1.5.2. Extended Kalman filter function
4.1.5.3. Test program
4.1.6. Summary
4.2. Unscented Kalman filter
4.2.1. Introduction
4.2.2. Unscented transformation
4.2.2.1. Introduction
4.2.2.2. Unscented transformation algorithm
4.2.2.3. Unscented transformation function
4.2.3. Unscented Kalman filter
4.2.3.1. Nonlinear system model
4.2.3.2. Comparision with an extended Kalman filter
4.2.3.3. Unscented Kalman filter algorithm
4.2.4. Example 1: Radar tracking
4.2.4.1. System model
4.2.4.2. Unscented Kalman filter function
4.2.4.3. Test program
4.2.5. Example 2: Attitude reference system
4.2.5.1. System model
4.2.5.2. Unscented Kalman filter function
4.2.5.3. Test program
4.2.6. Summary
4.1.1. Introduction
4.1.2. Linearized Kalman filter
4.1.3. Extended Kalman filter
4.1.3.1. Nonlinear system model
4.1.3.2. Extended Kalman filter algorithm
4.1.4. Example 1: Radar tracking
4.1.4.1. System model
4.1.4.2. Extended Kalman filter function
4.1.4.3. Test program
4.1.5 Example 2: Attitude reference system
4.1.5.1. System model
4.1.5.2. Extended Kalman filter function
4.1.5.3. Test program
4.1.6. Summary
4.2. Unscented Kalman filter
4.2.1. Introduction
4.2.2. Unscented transformation
4.2.2.1. Introduction
4.2.2.2. Unscented transformation algorithm
4.2.2.3. Unscented transformation function
4.2.3. Unscented Kalman filter
4.2.3.1. Nonlinear system model
4.2.3.2. Comparision with an extended Kalman filter
4.2.3.3. Unscented Kalman filter algorithm
4.2.4. Example 1: Radar tracking
4.2.4.1. System model
4.2.4.2. Unscented Kalman filter function
4.2.4.3. Test program
4.2.5. Example 2: Attitude reference system
4.2.5.1. System model
4.2.5.2. Unscented Kalman filter function
4.2.5.3. Test program
4.2.6. Summary
5. Frequency analysis and filter
5.1. High-pass filter
5.1.1. Introduction
5.1.2. Laplace transformation and filter
5.1.3. High-pass filter
5.1.4. High-pass filter function
5.1.5. Example: Sonar
5.1.6. Conclusion
5.2. Complementary filter
5.2.1. Introduction
5.2.2. Concept of complementary filter
5.2.3. Example: Attitude reference system
5.2.3.1. Complementary filter
5.2.3.2. Complementary filter function
5.2.3.3. Test program
5.2.4. Another example of a complementary filter
5.1.1. Introduction
5.1.2. Laplace transformation and filter
5.1.3. High-pass filter
5.1.4. High-pass filter function
5.1.5. Example: Sonar
5.1.6. Conclusion
5.2. Complementary filter
5.2.1. Introduction
5.2.2. Concept of complementary filter
5.2.3. Example: Attitude reference system
5.2.3.1. Complementary filter
5.2.3.2. Complementary filter function
5.2.3.3. Test program
5.2.4. Another example of a complementary filter
Pre-registration deadline
Enrolling in this course will enable you to become an expert in the field of Kalman filtering, equipping you with the essential skills to conduct research in this area. Pre-registration is currently available, and you can access the pre-registration link at the bottom of this page.
Pre-registration
Pre-registration for this course is now open. To enroll, please register your details using the following link. Once the class has met the required number of participants, you will receive an email notification to pay the tuition fee and complete your registration. The date, time, and link for attending the lessons, along with other important details, will be communicated to you via email.
Pre-registration
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