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Nonlinear Kalman Filters (and Parameter Estimation)

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Nonlinear Kalman Filters (and Parameter Estimation)

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Intermediate level

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2 weeks to complete
at 10 hours a week
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Gain insight into a topic and learn the fundamentals.
Intermediate level

Recommended experience

2 weeks to complete
at 10 hours a week
Flexible schedule
Learn at your own pace

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Assessments

27 assignments

Taught in English

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This course is part of the Applied Kalman Filtering Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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There are 4 modules in this course

As a follow-on course to "Linear Kalman Filter Deep Dive", this course derives the steps of the extended Kalman filter and the sigma-point Kalman filter for estimating the state of nonlinear dynamic systems. You will learn how to implement these filters in Octave code and compare their results. You will be introduced to adaptive methods to tune Kalman-filter noise-uncertainty covariances online. You will learn how to estimate the parameters of a state-space model using nonlinear Kalman filters.

This week, you will learn how to implement the extended Kalman filter to estimate the state of a nonlinear system.

What's included

8 videos13 readings7 assignments1 discussion prompt1 ungraded lab

8 videos•Total 83 minutes
  • 3.1.1: Welcome to the course!•5 minutes
  • 3.1.2: Introducing nonlinear variations to Kalman filters•8 minutes
  • 3.1.3: Deriving the three extended-Kalman-filter prediction steps•13 minutes
  • 3.1.4: Deriving the three extended-Kalman-filter correction steps•8 minutes
  • 3.1.5: Introducing a nontrivial EKF example, finding derivatives•25 minutes
  • 3.1.6: Introducing Octave code to initialize and control EKF for state estimation•10 minutes
  • 3.1.7: Introducing Octave code to update EKF for state estimation•12 minutes
  • 3.1.8: Summary of "The extended Kalman filter" module plus next steps•2 minutes
13 readings•Total 130 minutes
  • Frequently Asked Questions•10 minutes
  • Course Resources•10 minutes
  • How to Use Discussion Forums•10 minutes
  • Earn a Course Certificate•10 minutes
  • Are you interested in earning an online MSEE degree?•10 minutes
  • Notes for Lesson 3.1.1•10 minutes
  • Notes for Lesson 3.1.2•10 minutes
  • Notes for Lesson 3.1.3•10 minutes
  • Notes for Lesson 3.1.4•10 minutes
  • Notes for Lesson 3.1.5•10 minutes
  • Notes for Lesson 3.1.6•10 minutes
  • Notes for Lesson 3.1.7•10 minutes
  • Notes for Lesson 3.1.8•10 minutes
7 assignments•Total 90 minutes
  • Graded assignment for week 1•30 minutes
  • Practice assignment for Lesson 3.1.2•10 minutes
  • Practice assignment for Lesson 3.1.3•10 minutes
  • Practice assignment for Lesson 3.1.4•10 minutes
  • Practice assignment for Lesson 3.1.5•10 minutes
  • Practice assignment for Lesson 3.1.6•10 minutes
  • Practice assignment for Lesson 3.1.7•10 minutes
1 discussion prompt•Total 10 minutes
  • Introduce yourself•10 minutes
1 ungraded lab•Total 30 minutes
  • Jupyter Lab to implement EKF code•30 minutes

This week, you will learn how to implement the sigma-point Kalman filter to estimate the state of a nonlinear system.

What's included

6 videos6 readings6 assignments1 ungraded lab

6 videos•Total 74 minutes
  • Lesson 3.2.1: Problems with EKF that are improved with sigma-point methods•10 minutes
  • 3.2.2: Approximating uncertain variables using sigma points•20 minutes
  • 3.2.3: Deriving the six sigma-point-Kalman-filter steps•14 minutes
  • 3.2.4: Introducing Octave code to initialize and control SPKF for state estimation•8 minutes
  • 3.2.5: Introducing Octave code to update SPKF for state estimation•20 minutes
  • 3.2.6: Summary of "The sigma-point (unscented) Kalman filter" module plus next steps•2 minutes
6 readings•Total 60 minutes
  • Notes for Lesson 3.2.1•10 minutes
  • Notes for Lesson 3.2.2•10 minutes
  • Notes for Lesson 3.2.3•10 minutes
  • Notes for Lesson 3.2.4•10 minutes
  • Notes for Lesson 3.2.5•10 minutes
  • Notes for Lesson 3.2.6•10 minutes
6 assignments•Total 80 minutes
  • Graded assignment for week 2•30 minutes
  • Practice assignment for Lesson 3.2.1•10 minutes
  • Practice assignment for Lesson 3.2.2•10 minutes
  • Practice assignment for Lesson 3.2.3•10 minutes
  • Practice assignment for Lesson 3.2.4•10 minutes
  • Practice quiz for Lesson 3.2.5•10 minutes
1 ungraded lab•Total 30 minutes
  • Jupyter Lab to implement SPKF code•30 minutes

This week, you will learn how to extend and refine nonlinear Kalman filters for special cases.

What's included

7 videos7 readings7 assignments3 ungraded labs

7 videos•Total 86 minutes
  • 3.3.1: Iterating the EKF for systems having significant measurement-equation nonlinearities•15 minutes
  • 3.3.2: Implementing the IEKF in Octave, plus an example•10 minutes
  • 3.3.3: Simplifying the SPKF when noises are additive•15 minutes
  • 3.3.4: Implementing the CKF in Octave•12 minutes
  • 3.3.5: Adaptively estimating noise covariance matrices: The AEKF•15 minutes
  • 3.3.6: Implementing the AEKF in Octave•16 minutes
  • 3.3.7: Summary of "Extensions and refinements to nonlinear Kalman filters" module plus next steps•3 minutes
7 readings•Total 70 minutes
  • Notes for Lesson 3.3.1•10 minutes
  • Notes for Lesson 3.3.2•10 minutes
  • Notes for Lesson 3.3.3•10 minutes
  • Notes for Lesson 3.3.4•10 minutes
  • Notes for Lesson 3.3.5•10 minutes
  • Notes for Lesson 3.3.6•10 minutes
  • Notes for Lesson 3.3.7•10 minutes
7 assignments•Total 90 minutes
  • Graded assignment for week 3•30 minutes
  • Practice assignment for Lesson 3.3.1•10 minutes
  • Practice assignment for Lesson 3.3.2•10 minutes
  • Practice assignment for Lesson 3.3.3•10 minutes
  • Practice assignment for Lesson 3.3.4•10 minutes
  • Practice assignment for Lesson 3.3.5•10 minutes
  • Practice assignment for Lesson 3.3.6•10 minutes
3 ungraded labs•Total 90 minutes
  • Jupyter notebook implementing IEKF•30 minutes
  • Jupyter notebook implementing CKF•30 minutes
  • Jupyter notebook implementing AEKF•30 minutes

This week, you will learn how to use nonlinear Kalman filters to estimate model parameter values.

What's included

7 videos7 readings7 assignments3 ungraded labs

7 videos•Total 94 minutes
  • 3.4.1: Deriving SPKF method for parameter estimation •21 minutes
  • 3.4.2: Implementing SPKF parameter estimation in Octave•16 minutes
  • 3.4.3: Deriving EKF method for parameter estimation •7 minutes
  • 3.4.4: Implementing EKF parameter estimation in Octave•13 minutes
  • 3.4.5: How to estimate states and parameters at the same time•17 minutes
  • 3.4.6: Implementing EKF joint state/parameter estimation in Octave•14 minutes
  • 3.4.7: Summary of "Parameter estimation and joint estimation" plus next steps•6 minutes
7 readings•Total 70 minutes
  • Notes for Lesson 3.4.1•10 minutes
  • Notes for Lesson 3.4.2•10 minutes
  • Notes for Lesson 3.4.3•10 minutes
  • Notes for Lesson 3.4.4•10 minutes
  • Notes for Lesson 3.4.5•10 minutes
  • Notes for Lesson 3.4.6•10 minutes
  • Notes for Lesson 3.4.7•10 minutes
7 assignments•Total 90 minutes
  • Graded assignment for week 4•30 minutes
  • Practice assignment for Lesson 3.4.1•10 minutes
  • Practice assignment for Lesson 3.4.2•10 minutes
  • Practice assignment for Lesson 3.4.3•10 minutes
  • Practice assignment for Lesson 3.4.4•10 minutes
  • Practice assignment for Lesson 3.4.5•10 minutes
  • Practice assignment for Lesson 3.4.6•10 minutes
3 ungraded labs•Total 90 minutes
  • Jupyter notebook for SPKF parameter estimation•30 minutes
  • Jupyter notebook for EKF parameter estimation•30 minutes
  • Jupyter notebook that implements joint EKF and joint SPKF•30 minutes

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University of Colorado System
9 Courses•85,362 learners

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