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⇱ Linear Kalman Filter Deep Dive (and Target Tracking) | Coursera

Linear Kalman Filter Deep Dive (and Target Tracking)

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Linear Kalman Filter Deep Dive (and Target Tracking)

Included with

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
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

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.
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  • 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.

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 videos•Total 116 minutes
  • 2.1.1: Welcome to the course!•8 minutes
  • 2.1.2: Predict/correct mechanism of sequential probabilistic inference•27 minutes
  • 2.1.3: The Kalman-filter gain factor•25 minutes
  • 2.1.4: Summarizing the six steps of generic sequential probabilistic inference•8 minutes
  • 2.1.5: Deriving the three linear Kalman-filter prediction steps•21 minutes
  • 2.1.6: Deriving the three linear Kalman-filter correction steps•24 minutes
  • 2.1.7: Summary of "Deriving the linear Kalman filter" module plus next steps•4 minutes
12 readings•Total 120 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 2.1.1•10 minutes
  • Notes for Lesson 2.1.2•10 minutes
  • Notes for Lesson 2.1.3•10 minutes
  • Notes for Lesson 2.1.4•10 minutes
  • Notes for Lesson 2.1.5•10 minutes
  • Notes for Lesson 2.1.6•10 minutes
  • Notes for Lesson 2.1.7•10 minutes
6 assignments•Total 80 minutes
  • Practice assignment for Lesson 2.1.2•10 minutes
  • Practice assignment for Lesson 2.1.3•10 minutes
  • Practice quiz for Lesson 2.1.4•10 minutes
  • Practice quiz for Lesson 2.1.5•10 minutes
  • Practice assignment for Lesson 2.1.6•10 minutes
  • Graded assignment for week 1•30 minutes
1 discussion prompt•Total 10 minutes
  • Introduce yourself•10 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 videos•Total 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 steps•3 minutes
7 readings•Total 70 minutes
  • Notes for Lesson 2.2.1•10 minutes
  • Notes for Lesson 2.2.2•10 minutes
  • Notes for Lesson 2.2.3•10 minutes
  • Notes for Lesson 2.2.4•10 minutes
  • Notes for Lesson 2.2.5•10 minutes
  • Notes for Lesson 2.2.6•10 minutes
  • Notes for Lesson 2.2.7•10 minutes
7 assignments•Total 90 minutes
  • Practice assignment for Lesson 2.2.1•10 minutes
  • Practice assignment for Lesson 2.2.2•10 minutes
  • Practice assignment for Lesson 2.2.3•10 minutes
  • Practice assignment for Lesson 2.2.4•10 minutes
  • Practice assignment for Lesson 2.2.5•10 minutes
  • Practice assignment for Lesson 2.2.6•10 minutes
  • Graded assignment for week 2•30 minutes
3 ungraded labs•Total 60 minutes
  • Lab to compare standard and square-root Kalman filters•20 minutes
  • Lab to compare KF with and without bias correction•20 minutes
  • Lab to compare KF with and without compensation for autocorrelated noises•20 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 videos•Total 130 minutes
  • 2.3.1: Automatically detecting bad measurements with a Kalman filter•21 minutes
  • 2.3.2: Processing measurements sequentially for multi-output systems•21 minutes
  • 2.3.3: Using the Kalman filter for prediction•19 minutes
  • 2.3.4: Using the Kalman filter for smoothing•18 minutes
  • 2.3.5: Steady-state Kalman filters•19 minutes
  • 2.3.6: Continuous-time Kalman filters•30 minutes
  • 2.3.7: Summary of "Extensions and refinements to linear Kalman filters" module plus next steps•2 minutes
7 readings•Total 70 minutes
  • Notes for Lesson 2.3.1•10 minutes
  • Notes for Lesson 2.3.2•10 minutes
  • Notes for Lesson 2.3.3•10 minutes
  • Notes for Lesson 2.3.4•10 minutes
  • Notes for Lesson 2.3.5•10 minutes
  • Notes for Lesson 2.3.6•10 minutes
  • Notes for Lesson 2.3.7•10 minutes
7 assignments•Total 90 minutes
  • Practice assignment for Lesson 2.3.1•10 minutes
  • Practice assignment for Lesson 2.3.2•10 minutes
  • Practice assignment for Lesson 2.3.3•10 minutes
  • Practice assignment for Lesson 2.3.4•10 minutes
  • Practice assignment for Lesson 2.3.5•10 minutes
  • Practice assignment for Lesson 2.3.6•10 minutes
  • Graded assignment for week 3•30 minutes
3 ungraded labs•Total 60 minutes
  • A Kalman predictor•20 minutes
  • A Kalman smoother•20 minutes
  • Steady-state Kalman filter•20 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 videos•Total 107 minutes
  • 2.4.1: Some unique features of the target-tracking application•24 minutes
  • 2.4.2: Tracking with polar measurements and a Cartesian state•16 minutes
  • 2.4.3: The interacting-multiple-model Kalman filter•26 minutes
  • 2.4.4: Implementing the IMM Kalman filter in Octave•21 minutes
  • 2.4.5: Steady-state alpha-beta-gamma target-tracking filters•18 minutes
  • 2.4.6 :Summary of "Target-tracking application using a linear Kalman filter" module plus next steps•3 minutes
6 readings•Total 60 minutes
  • Notes for Lesson 2.4.1•10 minutes
  • Notes for Lesson 2.4.2•10 minutes
  • Notes for Lesson 2.4.3•10 minutes
  • Notes for Lesson 2.4.4•10 minutes
  • Notes for Lesson 2.4.5•10 minutes
  • Notes for Lesson 2.4.6•10 minutes
6 assignments•Total 80 minutes
  • Practice assignment for Lesson 2.4.1•10 minutes
  • Practice assignment for Lesson 2.4.2•10 minutes
  • Practice assignment for Lesson 2.4.3•10 minutes
  • Practice assignment for Lesson 2.4.4•10 minutes
  • Practice assignment for Lesson 2.4.5•10 minutes
  • Graded assignment for week 4•30 minutes
2 ungraded labs•Total 40 minutes
  • Converting polar to Cartesian•20 minutes
  • The IMM•20 minutes

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Instructor

University of Colorado System
9 Courses•85,362 learners

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