Linear Kalman Filter Deep Dive (and Target Tracking)

Linear Kalman Filter Deep Dive (and Target Tracking)

This course is part of Applied Kalman Filtering Specialization

Instructor: Gregory Plett

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Assessments

26 assignments

Taught in English

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This course is part of the Applied Kalman Filtering Specialization

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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 videosTotal 116 minutes

2.1.1: Welcome to the course!8 minutesPreview module
2.1.2: Predict/correct mechanism of sequential probabilistic inference26 minutes
2.1.3: The Kalman-filter gain factor24 minutes
2.1.4: Summarizing the six steps of generic sequential probabilistic inference7 minutes
2.1.5: Deriving the three linear Kalman-filter prediction steps21 minutes
2.1.6: Deriving the three linear Kalman-filter correction steps23 minutes
2.1.7: Summary of "Deriving the linear Kalman filter" module plus next steps3 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

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
Graded assignment for week 130 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 120 minutes

2.2.1: How do we improve the numeric robustness of a Kalman filter?15 minutesPreview module
2.2.2: How do we increase the precision of the linear Kalman filter?27 minutes
2.2.3: How do I initialize and tune a Kalman filter?20 minutes
2.2.4: What do we do when the noises are nonzero-mean?18 minutes
2.2.5: What do I do if the process and sensor noises are cross-correlated?18 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 steps2 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

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
Graded assignment for week 230 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 filter20 minutesPreview module
2.3.2: Processing measurements sequentially for multi-output systems20 minutes
2.3.3: Using the Kalman filter for prediction18 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

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
Graded assignment for week 330 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 minutesPreview module
2.4.2: Tracking with polar measurements and a Cartesian state15 minutes
2.4.3: The interacting-multiple-model Kalman filter25 minutes
2.4.4: Implementing the IMM Kalman filter in Octave21 minutes
2.4.5: Steady-state alpha-beta-gamma target-tracking filters17 minutes
2.4.6 :Summary of "Target-tracking application using a linear Kalman filter" module plus next steps2 minutes