In my last post in the extended Kalman filter derivation, I’ve talked about the linearization step. I have briefly talked about how the linearization step occurs so that the linear Kalman filter could be used to approximate the nonlinearity. I’ve…

## Extended Kalman Filter

In my last post, I’ve presented Kalman filter derivation in two different ways: 1) using expectation and 2) using probabilities. We know the linear Kalman filter is great when you have a conveniently ideal system which is linear and noises…

## Kalman Filter Derivation – HMM

In my last post, I’ve talked about Kalman Filter Derivation using expectation operator and mentioned that we can also derive Kalman filter using hidden Markov model (HMM) with Gaussian distributions. So in this post, I’ll cover that derivation. Kalman Filter…

## Kalman Filter Derivation

I highly recommend using a large screen to read this page. The LaTeX plug-in I’m using cuts off the converted math equation images when a small screen (e.g. phone) is used. I’ve had a post on Kalman Filter intro last…

## Kalman Filter – Intro

COVID-19 is hitting everywhere. I wish the best luck to all visitors and do hope you’re staying safe. Hope this ends soon. If you have worked on an estimation problem, whether it’s a probabilistic approach or not, the chances are…

## Law of Total Probability

In robotics literature, we observe endless number of equations written in probabilities. I’d like to point out few ones which I found typically useful to remember. You will find all these in any book with probability theory. or…

## Probability Distribution Functions

In my previous post, I briefly talked about probability density functions. I’d like to discuss more about this today. Probability ddistribution functions appear a lot of times in robotics literature; because all our measurements and knowledge are not perfect. You’ll…

## Bayes Rule: Example with probability density functions

In my previous post regarding Bayes Rule, I showed an example case of determining what kind of an apple is in a paper bag. In that example, all random variables are discrete — i.e. the type of apples (red Gala…

## Bayes Rule

Okay. For now, this is how this blog will work. With my imperfect knowledge of materials, honestly, writing an organized teaching material will be difficult; otherwise I’ll be writing a book ðŸ˜› Instead, I’ll be posting small bit by bit…