Rico's Nerd Cluster

「离开世界之前 一切都是过程」

Introduction Kurtosis is a statistic that tells us how strongly a distribution is influenced by unusually large values. For sensor residuals, that is useful because two datasets can have the same ...

Posted by Rico's Nerd Cluster on November 8, 2026

Electronics - General Electronics Notes

Encoders, Motors, Capacitors, IMU, Testing, Telecommunication

Electronics EEPROM EEPROM (Electrically Erasable Programmable Read-Only Memory) is a type of non-volatile memory used in microcontrollers to store small amounts of data that must be preserved whe...

Posted by Rico's Nerd Cluster on June 3, 2017

Electronics - Embedded Systems Notes

HAL

HAL vs SAL Hardware Abstraction Layer (HAL) is software that abstracts hardware-specific details from the application or higher-level software. It provides a unified API for accessing hardware fun...

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

Electronics - Communication Protocols

Encoding / Decoding, Error Checking (CRC), Base64, EtherCAT

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 - Sherman-Morrison-Woodbury Equation

How Kalman Filter Reduces Computation For Inverse

The Sherman-Morrison-Woodbury Equation is: \[\boxed{ AB(D+CAB)^{-1} = \left(A^{-1}+BD^{-1}C\right)^{-1}BD^{-1} }\] Assume all displayed inverses exist. Direct proof Define \[X=AB(D+CAB)^{...

Posted by Rico's Nerd Cluster on March 5, 2017

Math - Differential Entropy

Differential Entropy Differential entropy is the entropy version for a continuous random variable. For a discrete variable: 1 2 3 4 H(x) = -sum(p(x) * log(p(x))) // continuous version h(X) = -∫ ...

Posted by Rico's Nerd Cluster on March 5, 2017

Math - Integration Approximations

Trapezoidal Rule

Trapezoidal Rule If the robot drives forward while turning left, using yaw_mid, moves the displacement along the middle of the arc rather than entirely along the old heading. Integrate pose using...

Posted by Rico's Nerd Cluster on March 2, 2017

Math - Trace, Determinant, Frobenius Norm

Trace Properties and Proofs, Von-Neumann's Trace Inequality

Determinant \[\det(AB) = \det(A)\,\det(B)\] For an orthogonal matrix \(Q\) (i.e., \(Q^\top Q = I\)), we have \(\det(Q) = \pm 1\): \[\begin{aligned} Q^\top Q &= I \\ \Rightarrow\; \d...

Posted by Rico's Nerd Cluster on February 28, 2017

Math - Linear Fitting

Plane Fitting, Line Fitting, Isotropic Matrix, Condition Number of Covariance Matrix

Given a group of points x_i = [x, y, z], how do we find a plane and a line that best fit them? Plane Fitting Points on a plane satisfy: \[\begin{gather*} \begin{aligned} & n^Tx + d = 0 \end{...

Posted by Rico's Nerd Cluster on February 25, 2017

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Robotics @ Northwestern University

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