Rico贾若童的博客

Electronics - Communication Protocols

Encoding / Decoding, Error Checking (CRC)

Error Checking CRC GF(2) Math GF(2) is pronounced as “Galois Field 2”. Often used in cryptography, it’s a binary field that contains only 0 and 1 for error correction. Some properties of GF(2):...

Posted by Rico's Nerd Cluster on June 1, 2017

Electronics - EMF and Eddy Current

Electromotive Force (EMF，电动势) In short, EMF is: 1 changing magnetic field -> induced voltage It’s characterized by the Faraday’s law: \[\begin{gather*} \begin{aligned} & \epsilon = -N \...

Posted by Rico's Nerd Cluster on June 1, 2017

Math - SO(3) Perturbations

Left Perturbation, Right Perturbation, BCH Formula

Left and Right Perturbations Imagine we have a world frame, a car frame, and a pedestrian. Now the car has rotated from the car1 pose to the car2 pose. We assume the pedestrain has not moved: In ...

Posted by Rico's Nerd Cluster on February 22, 2017

Math - Lie Group

Group Definition, Lie Group and Lie Algebras, Skew Matrices, Manifold

Group Definition Group (Group) is an algebraic structure consisting of a set and an operation. Denote the set as A, and the operation as ⋅. Then, the group can be written as G=(A,⋅). Closure (...

Posted by Rico's Nerd Cluster on February 22, 2017

Math - Multivariate Normal Distribution

PDF, Linear Transformation

PDF “Variate” is basically a synonym to “random variable”. If we have a vector of random variables and we want to find their joint distributution, then we call this “multivariate” distribution. I...

Posted by Rico's Nerd Cluster on February 13, 2017

Math - MAP(Maximum A-Posteriori) and MLE (Maximum Likelihood Estimate)

Likelihood vs Probabilities

Likelihood VS Probabilities Probabilities describe the chances of discrete, mutually-exclusive possible states. These chances should sum up to 1. Likelihoods describe the chances or the plausibili...

Posted by Rico's Nerd Cluster on February 13, 2017

Math - t-SNE

Introduction van der Maaten, Geoff Hinton and Yoshua Bengio came up with “t-SNE” (pronounced as “tee-snee”) to reduce high dimensional data down to low dimensional data, so clusters between data i...

Posted by Rico's Nerd Cluster on February 7, 2017

Math - Null Space and Singular Value Decomposition (SVD)

How to find Null Space? How to implement that using Singular Value Decomposition (SVD)?

Introduction The three most basic & important matrix factorizations in pure & applied linear algebra are: QR Decomposition (Gram-Schmidt Orthogonalization) LU Decomposition (Gaussian...

Posted by Rico's Nerd Cluster on February 7, 2017

Math - Stats Basics Recap

Basic Statistics Concepts, Regression, Distributions, Covariance & Correlation

Basic Statistics Concepts Standard Deviation and Variance Variance of a distribution can be “biased” and “unbiased”. A biased variance is to always underestimate the real bias. $$ \begin{gather*}...

Posted by Rico's Nerd Cluster on February 4, 2017

Math - Interpoloation

Linear, Cubic, Bicubic Splines

Interpolation “Interpolation” is essentially “how to get through lines and predict the value of a point in between?”. The first step is to connect points. For that, we need a spline. A spline is a...

Posted by Rico's Nerd Cluster on January 26, 2017

Rico's Nerd Cluster