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# Data Fusion with Linear Kalman Filter

## Theory and Implementation

4.67 (84 reviews)

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## What you will learn

How to probabilistically express uncertainty using probability distributions

How to convert differential systems into a state space representation

How to simulate and describe state space dynamic systems

How to use Least Squares Estimation to solve estimation problems

How to use the Linear Kalman Filter to solve optimal estimation problems

How to derive the system matrices for the Kalman Filter in general for any problem

How to optimally tune the Linear Kalman Filter for best performance

How to implement the Linear Kalman Filter in Python

## Description

You need to learn know Data Fusion and Kalman Filtering!

The Kalman filter is one of the greatest discoveries in the history of estimation and data fusion theory, and perhaps one of the greatest engineering discoveries in the twentieth century. It has enabled mankind to do and build many things which could not be possible otherwise. It has immediate application in control of complex dynamic systems such as cars, aircraft, ships and spacecraft.

These concepts are used extensively in engineering and manufacturing but they are also used in many other areas such as chemistry, biology, finance, economics, and so on.

Why focus on Data Fusion and Kalman Filtering

• Data Fusion is an amazing tool that is used pretty much in every modern piece of technology that involves any kind of sensing, measurement or automation.

• The Kalman Filter is one of the most widely used methods for data fusion. By understanding this process you will more easily understand more complicated methods.

• Difficult for beginners to comprehend how the filter works and how to apply the concepts in practice.

• Evaluating and tuning the Kalman Filter for best performance can be a bit of a 'black art', we will give you tips and a structure so you know how to do this yourself.

• So you don’t waste time trying to solve or debug problems that would be easily avoided with this knowledge! Become a Subject Matter Expert!

What you will learn:

You will learn the theory from ground up, so you can completely understand how it works and the implications things have on the end result. You will also learn practical implementation of the techniques, so you know how to put the theory into practice.

We will cover:

• Basic Probability and Random Variables

• Dynamic Systems and State Space Representations

• Least Squares Estimation

• Linear Kalman Filtering

• Covers theory, implementation, use cases

• Theory explanation and analysis using Python and Simulations

By the end of this course you will know:

• How to probabilistically express uncertainty using probability distributions

• How to convert differential systems into a state space representation

• How to simulate and describe state space dynamic systems

• How to use Least Squares Estimation to solve estimation problems

• How to use the Linear Kalman Filter to solve optimal estimation problems

• How to derive the system matrices for the Kalman Filter in general for any problem

• How to optimally tune the Linear Kalman Filter for best performance

• How to implement the Linear Kalman Filter in Python

Who is this course for:

• University students or independent learners.

• Working Engineers and Scientists.

• Engineering professionals who wants to brush up on the math theory and skills related to Data Fusion and Kalman filtering.

• Software Developers who wish to understand the basic concepts behind data fusion to aid in implementation or support of developing data fusion code.

• Anyone already proficient with the math “in theory” and want to learn how to implement the theory in code.

So what are you waiting for??

Watch the course instruction video and free samples so that you can get an idea of what the course is like. If you think this course will help you then sign up, money back guarantee if this course is not right for you.

I hope to see you soon in the course!

Steve

## Screenshots    ## Content

Welcome

Welcome to the Course

Course Outline

Setting Up Python

Introduction

What is Data Fusion

How does Sensor Fusion Work

Probability

Basic Probability

Mutual Exclusivity

Conditional Probability

Bayes Theorem

Random Variables

Probability Density Functions

Expectation Operator

Distribution Statistical Properties

Uniform Probability Distribution

Gaussian Probability Distribution

Linear Transformation of Gaussian Distribution

Multiple Random Variables

Mutltvariate Statistics

Multivariate Gaussian Distribution

Linear Transformation of Uncertainities

Probability Notes and Summary

Dynamic Systems

Differential Equations

State Space Representation

Differential Equations and State Space

Continuous and Discrete Time

Mathematical Models of Dynamic Systems

Continuous to Discrete Model Conversions

Simulation of Models

Python Simulation Exercise

Dynamic System Notes and Summary

Least Squares Estimation

Estimation of a Constant

Estimation of a Constant Vector

Weighted Least Squares

Weighted Least Squares

Recursive Least Squares

Recursive Least Squares

Least Squares Estimation Summary

Linear Kalman Filter

What is the Kalman Filter

Types of Kalman Filters

How Does the Linear Kalman Filter Work

2D Tracker Example Problem Overview

2D Tracker Process Model

Kalman Filter Prediction Step

2D Tracker Prediction Step

2D Tracker Prediction Step Explaination

Kalman Filter Update Step

2D Tracker Update Step

2D Tracker Update Step Explaination

2D Tracker Initial Conditions

2D Tracker Initial Condition Explaination

Kalman Filter Tuning

2D Tracker Filter Tuning

Implementation Notes

Linear Kalman Filter Notes and Summary

Pendulum Example

Pendulum Estimation Problem

System and Measurement Dynamics

Kalman Filter Model Implementation

Kalman Filter Performance and Tuning

Summary

Conculsion

Kalman Filter Summary

## Reviews

H
Holman10 July 2021

This course explains the key concepts to understand the Kalman Filters design and main concepts. Well-developed examples and resources to test all exercises in Python. Basics in probability are very good explained.

D
Daniel6 July 2021

Excellent course!!! Simply excellent. Very well organized, there is enough information to be able to start applying the concepts. It is great that Python is used for examples and exercises. Because of this, we can see how a simulation (in Python, or any other language) is implemented (rather than using MATLAB’S Simulink, for example, in which case the simulation would have just magically happened and we would have learned nothing), how a least squares estimation is done, how a Kalman filter is implemented (again, NOT using MATLAB’s toolboxes, and just see that they work…. and we would learn nothing…). I suffered a bit doing the 3 example exercises, but that was because I did not know Python, and/or numpy; now, that I’ve done them, I know more ?. Thank you for this great course!

Q
Quentin14 February 2021

Above any lecture I ever had at university on this topic. This course directly goes to the essential: clean and efficient. I recommend it.

Y
Yashodhan14 February 2021

Awesome topic.. finally someone is speaking with right content on sensor fusion. A must do course for people working with sensors, ADAS, AI,Signal processing..Waiting for new courses from him on advance topics

J
Jonathan28 December 2020

The descriptions given for the mathmatics and formulas were a bit too short and abstract to follow the underlying meanings. However, I do like those Python implementation/examples given in the course, which is a really nice way to get my hands on the Kalman filter.

H
Hari28 December 2020

Pros : Well prepared course material, simulation tools and assignments, which really give a good insight into practical issues and their solutions. One of the best courses I have taken on Udemy. Cons : Would have liked to have the slides as a downloadable resource, since the downloadable documents don't reference the examples. I spent a fair amount of time taking screenshots and renaming them.

N
Nitish20 December 2020

You should have included more coding exercises for implementation of Kalman Filter 1D and 2D. Also have some quizzes to test the students knowledge

R
Rich21 November 2020

I would like to see more info for the mass damper example in chapter 29, specifically how you derived the F matrice for different time delta. You "say" how to do it but it yay just display the result

Udemy ID

## 8/15/2020

Course created date

## 1/7/2021

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