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Linear Kalman Filter Deep Dive (and Target Tracking)

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Linear Kalman Filter Deep Dive (and Target Tracking)

This course is part of Applied Kalman Filtering Specialization

Instructor: Gregory Plett

Included with

Learn more

4 modules

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

4 modules

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

Skills you'll gain

Tools you'll learn

Matlab

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

26 assignments

Taught in English

91% of learners achieved a positive career outcome

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Build your subject-matter expertise

This course is part of the Applied Kalman Filtering Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

Learn new concepts from industry experts
Gain a foundational understanding of a subject or tool
Develop job-relevant skills with hands-on projects
Earn a shareable career certificate

There are 4 modules in this course

As a follow-on course to "Kalman Filter Boot Camp", this course derives the steps of the linear Kalman filter to give understanding regarding how to adjust the method to applications that violate the standard assumptions. Applies this understanding to enhancing the robustness of the filter and to extend to applications including prediction and smoothing. Shows how to implement a target-tracking application in Octave code using an interacting multiple-model Kalman filter.

Module details

Knowing how to derive the steps of the Kalman filter is important for understanding the assumptions that are made and to be able to re-derive the steps for different assumptions. This week, you will learn how to derive the steps and will gain insight into how the Kalman filter works.

What's included

7 videos12 readings6 assignments1 discussion prompt

7 videosTotal 116 minutes

2.1.1: Welcome to the course!8 minutes
2.1.2: Predict/correct mechanism of sequential probabilistic inference27 minutes
2.1.3: The Kalman-filter gain factor25 minutes
2.1.4: Summarizing the six steps of generic sequential probabilistic inference8 minutes
2.1.5: Deriving the three linear Kalman-filter prediction steps21 minutes
2.1.6: Deriving the three linear Kalman-filter correction steps24 minutes
2.1.7: Summary of "Deriving the linear Kalman filter" module plus next steps4 minutes

12 readingsTotal 120 minutes

Frequently Asked Questions10 minutes
Course Resources10 minutes
How to Use Discussion Forums10 minutes
Earn a Course Certificate10 minutes
Are you interested in earning an online MSEE degree?10 minutes
Notes for Lesson 2.1.110 minutes
Notes for Lesson 2.1.210 minutes
Notes for Lesson 2.1.310 minutes
Notes for Lesson 2.1.410 minutes
Notes for Lesson 2.1.510 minutes
Notes for Lesson 2.1.610 minutes
Notes for Lesson 2.1.710 minutes

6 assignmentsTotal 80 minutes

Graded assignment for week 130 minutes
Practice assignment for Lesson 2.1.210 minutes
Practice assignment for Lesson 2.1.310 minutes
Practice quiz for Lesson 2.1.410 minutes
Practice quiz for Lesson 2.1.510 minutes
Practice assignment for Lesson 2.1.610 minutes

1 discussion promptTotal 10 minutes

Introduce yourself10 minutes

Last week, you learned the assumptions made when deriving the Kalman filter. What if these assumptions are not met correctly? What if numeric roundoff error causes failure? This week, you will learn how to solve problems with the standard Kalman filter.

What's included

7 videos7 readings7 assignments3 ungraded labs

7 videosTotal 121 minutes

2.2.1: How do we improve the numeric robustness of a Kalman filter?15 minutes
2.2.2: How do we increase the precision of the linear Kalman filter?28 minutes
2.2.3: How do I initialize and tune a Kalman filter?21 minutes
2.2.4: What do we do when the noises are nonzero-mean?19 minutes
2.2.5: What do I do if the process and sensor noises are cross-correlated?19 minutes
2.2.6: What about when the process and sensor noises are not white?16 minutes
2.2.7: Summary of "Making the linear Kalman filter bulletproof" module plus next steps3 minutes

7 readingsTotal 70 minutes

Notes for Lesson 2.2.110 minutes
Notes for Lesson 2.2.210 minutes
Notes for Lesson 2.2.310 minutes
Notes for Lesson 2.2.410 minutes
Notes for Lesson 2.2.510 minutes
Notes for Lesson 2.2.610 minutes
Notes for Lesson 2.2.710 minutes

7 assignmentsTotal 90 minutes

Graded assignment for week 230 minutes
Practice assignment for Lesson 2.2.110 minutes
Practice assignment for Lesson 2.2.210 minutes
Practice assignment for Lesson 2.2.310 minutes
Practice assignment for Lesson 2.2.410 minutes
Practice assignment for Lesson 2.2.510 minutes
Practice assignment for Lesson 2.2.610 minutes

3 ungraded labsTotal 60 minutes

Lab to compare standard and square-root Kalman filters20 minutes
Lab to compare KF with and without bias correction20 minutes
Lab to compare KF with and without compensation for autocorrelated noises20 minutes

The standard linear Kalman filter works well for state estimation, but can be extended to implement prediction and smoothing as well. Further, we can speed up the steps or even eliminate steps in some circumstances. This week, you will learn some extensions and refinements to linear Kalman filters.

What's included

7 videos7 readings7 assignments3 ungraded labs

7 videosTotal 130 minutes

2.3.1: Automatically detecting bad measurements with a Kalman filter21 minutes
2.3.2: Processing measurements sequentially for multi-output systems21 minutes
2.3.3: Using the Kalman filter for prediction19 minutes
2.3.4: Using the Kalman filter for smoothing18 minutes
2.3.5: Steady-state Kalman filters19 minutes
2.3.6: Continuous-time Kalman filters30 minutes
2.3.7: Summary of "Extensions and refinements to linear Kalman filters" module plus next steps2 minutes

7 readingsTotal 70 minutes

Notes for Lesson 2.3.110 minutes
Notes for Lesson 2.3.210 minutes
Notes for Lesson 2.3.310 minutes
Notes for Lesson 2.3.410 minutes
Notes for Lesson 2.3.510 minutes
Notes for Lesson 2.3.610 minutes
Notes for Lesson 2.3.710 minutes

7 assignmentsTotal 90 minutes

Graded assignment for week 330 minutes
Practice assignment for Lesson 2.3.110 minutes
Practice assignment for Lesson 2.3.210 minutes
Practice assignment for Lesson 2.3.310 minutes
Practice assignment for Lesson 2.3.410 minutes
Practice assignment for Lesson 2.3.510 minutes
Practice assignment for Lesson 2.3.610 minutes

3 ungraded labsTotal 60 minutes

A Kalman predictor20 minutes
A Kalman smoother20 minutes
Steady-state Kalman filter20 minutes

A popular application of Kalman filters is to track (usually non-cooperating) targets. This week, you will learn how to implement standard and specialized Kalman filters suited for target tracking.

What's included

6 videos6 readings6 assignments2 ungraded labs

6 videosTotal 107 minutes

2.4.1: Some unique features of the target-tracking application24 minutes
2.4.2: Tracking with polar measurements and a Cartesian state16 minutes
2.4.3: The interacting-multiple-model Kalman filter26 minutes
2.4.4: Implementing the IMM Kalman filter in Octave21 minutes
2.4.5: Steady-state alpha-beta-gamma target-tracking filters18 minutes
2.4.6 :Summary of "Target-tracking application using a linear Kalman filter" module plus next steps3 minutes