#science

Kalman Filter Notation

2025-03-08

This article is a WIP - I'll add more notations as I find themKalman filtering notation is terrible. Every author uses a different, confusing, notation. I am not able to standardise it, but at least I can provide some of the key references and explain what notation they use.This article assumes some familiarity with th

#kalman-filtering #mathematics #signal-processing #science

How to Differentiate Solutions

2025-03-01

\[y = 3x\] \[\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{3(x + \Delta x) - 3x}{\Delta x}\] \[\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{3x + 3\Delta x - 3x}{\Delta x}\] \[\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{3 \Delta x}{\Delta x}\] \[\frac{dy}{dx} = 3\]\[y = 2x^2 + 5x\] \[\frac{dy}{dx} =

#mathematics #science

How to Differentiate

2025-03-01

Differentiation is an essential skill for anyone who wants to get into physics, mathematics, computer science, engineering or any technical field.Why do we want to differentiate? What purpose can it serve? The reason for differentiation is that we want to know the gradient, or steepness, of a function at any given poin

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Kalman Filter: Filtering a Sin Wave

2025-02-23

\[ \newcommand{\Lagr}{\mathscr{L}} \]The sin wave tracking problem presents us with a unique opportunity. There are many possible solutions to this problem, some linear and some non-linear. This allows us to see the effect of different kinds of Kalman filters in actionFirst, let's just quickly write a simple method whi

#kalman-filtering #mathematics #signal-processing #science

Kalman Filter: Tracking a Cannon Ball

2025-02-15

So far, we have been using linear Kalman filters to track reasonably simple problems. However, more complex problems require more complex Kalman filters. One of the primary limitations of the Kalman filter is that it is not capable of handling non-linear situations very well. In this example, we will be tracking a cann

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Kalman Filter: Falling with Control Term

2025-02-08

In previous blogs, we looked at objects falling under gravity. In those blogs we asked the Kalman filter to try and estimate the position, velocity and acceleration from the readings. However, we know in advance what gravity is doing. So, why don't we instead tell the Kalman filter that the object is accelerating? That

#kalman-filtering #mathematics #signal-processing #science

Kalman Filter: How to Solve the Riccati Equations

2025-01-25

I've already published two blogs on practical applications of the Kalman filter. In both of those blogs, I use the somewhat throw away line "simply solve the Riccati equations". If you are not familiar with the Riccati equations then this line could be very confusing indeed. So I hope to clear up any confusio

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Kalman Filtering Object with Constant Velocity

2025-01-04

In a previous blog entry we looked at tracking a falling object. That was focused on the practical implementation. This time we will cover tracking an object moving at constant velocity but focus more on the actual derivation of the filter. Let's start with the differential state-space equations.\[ \begin{bmatrix} \dot

#programming #science #mathematics #kalman-filtering #signal-processing

Kalman Filtering Falling Objects

2025-01-04

In this blog we will track a falling object using a Kalman filter. Our goal will be to create a simulation of a falling object, and filter that with the Kalman filter. We'll plot the residuals and see how well we can reconstruct the original signal from the noisey signal. We'll code this in Rust, which is a great choic

#programming #science #mathematics #kalman-filtering #signal-processing

The Death of Scientism

2024-03-05

Zoé Ziani was working on her PhD thesis in the field of behavioural psychology. She was looking at a particular paper "CGK 2014" (an abbreviation for The Contaminating Effects of Building Instrumental Ties: How Networking Can Make Us Feel Dirty). This paper is about how individuals can feel "pysically d

#science #philosophy