Enkhmurun Bayasgalan
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Collection of random notes on science
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Enkhmurun Bayasgalan
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Matrix Theory
Matrix Theory
References
Norms
Norms
Vector Norms
Matrix Norms
Matrix Factorization
Matrix Factorization
Singular Value Decomposition
QR Decomposition
Cholesky Decomposition
Matrix Calculus
Matrix Calculus
Identities
Matrix Calculus
Software Implementation
Software Implementation
Storage
Multiplication
Kinematics
Kinematics
Rotations and Cross-Relations
Rotations and Cross-Relations
Angular Velocity
Rotation Matrix
Euler Angles
Axis-Angle
Quaternions
Lie Group and Lie Algebra
Lie Group and Lie Algebra
Matrix Groups and Lie Theory
Special Orthogonal and Special Euclidean Groups
Derivativeand Perturbation Definitions
Jacobians
Perturbations
Difference, Interpolation, and Perturbation
Jacobians
Jacobians
Perturbed Rotations via Euler Angles
Perturbed Rotations via Rotation Vector
Perturbed Poses via Rotation Vector
Optimization on Smooth Manifolds
Optimization on Smooth Manifolds
Interpolation
Difference of Rotations
Cartesian Position
Velocity
Acceleration
Camera Motion
Camera Motion
Camera Pose
References
Estimation Theory
Estimation Theory
References
Probability Theory
Probability Theory
Terminologies
Mean and Mode
Variability Measures
Univariate Sample Example
Multivariate Sample Properties
Observations as Time Series
Probability
Bayes' Rule
Random Variables
Transformations of Random Variables
Multiple Random Variables
Distributions
Distributions
Discrete Uniform Distribution
Uniform Distribution
Bernoulli and Binomial Distributions
Poisson Distribution
Geometric Distribution
Multinomial Distribution
Exponential Distribution
Gamma Distribution
Logistic Distribution
Normal Distribution
Chi-square Distribution
Beta Distribution
Weibull Distribution
Optimization
Optimization
Sets
Sets
Norms, Distance, and Unit Ball
Open and Closed Sets
Geometry
Convex Sets
Nonconvex Sets
Functions
Functions
Functions, Gradient, Jacobian, Hessian
Convex Functions
Nonconvex Functions
Optimization Problem Formulation
Duality Theory
Unconstrained Optimization
Unconstrained Optimization
Optimality Conditions
Gradient Desent
Newton's Method
Quasi-Newton Method
Gauss-Netwon Method
Golden Section
Quadratic Fit
Nelder-Mead Method
Linear Programming
Linear Programming
Modelling Using Linear Programs
Algrebraic Aspects
Simplex Method
Linear Stochastic Program
Nonlinear Program
Robust Optimization
Column and Constraint Generation
Dantzig-Wolfe Decomposition
Nonlinear Programming
Nonlinear Programming
Least Squares
Perturbation Methods
Integer Programming
Integer Programming
Discrete Optimization Models
Modelling Nonconvex Functions
Modelling Nonconvex Sets
Modelling Logical Relations
Statistical Estimators
Statistical Estimators
Moment-Matching Estimator
Maximum Likelihood Estimator
Bayesian Inference
Bayesian Inference
Bayesian Inference
Bayesian Network
Maximum a Posteriori Estimator
Least Squares Estimator
Least Squares Estimator
Least Squares
Linear Least Squares
Linear Weighed Least Squares
Linear Recursive Least Squares
Nonlinear Least Squares
Least Squares with Dynamics
Kalman Filter
Kalman Filter
Discrete-Time Kalman Filter
Extended Kalman Filter
Extended Kalman Filter
Continuous-Time EKF
Factor Graphs
Factor Graphs
Definition
Representations
Using Factor Graph
Using Factor Graph
Simple Averaging
Weighted Averaging
Weighted Non-Linear Least Squares
Dynamical Systems
Navigation
Navigation
References
Coordinate Frames
Geodesy
Geodesy
Primer on Geodesy
ECEF To Curvilinear Position
Orthometric Height
Rotation of Earth
Gravity Models
Frame Transformations
IMU and Gravity Models
IMU and Gravity Models
IMU Measurements
IMU Error Models
Inertial Navigation Equations
Inertial Navigation
Inertial Navigation
IMU
Architecture
Navigation Equations in ECI Frame
Navigation Equations in ECEF Frame
Navigation Equations in Local Tangent-Plane Frame
Radio Positioning
Radio Positioning
Position by Ranging
Position by Ranging
Ranging
Positioning from Passive Ranging
Angular Position
Time Standards
GPS
GPS
Time
GPS Signals
GPS Receiver
Computer Vision
Computer Vision
Termanologies
Image Processing
Image Processing
Correlation Filter
Image Features
Image Features
ORB
Two-View Geometry
Two-View Geometry
Epipolar Geometry
Essential and Fundamental Matrix
Homography
Image Compression
Image Compression
Compression via Low-Rank Matrix Approximation
Software
Software
Concurrency
Concurrency
OpenMP
OpenMP
Basic Usage
Examples
Examples
Calculating PI
Papers
Papers
Software
Notation and Nomenclature
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