Rico's Nerd Cluster

「离开世界之前 一切都是过程」

Robotics - [ESKF Series 4] Full Error-State Kalman Filter (ESKF) in GNSS-Inertial Navigation System (GINS)

ESKF, GINS

If you haven’t checked out a motivational 2D robot example of ESKF, please check here. In this post, $\oplus$ is the “generic add”, which “adds” on a manifold. ESKF (On Manifold) in GINS (GPS-Int...

Robotics - [ESKF Series 3] Motivational Example Of Error-State Kalman Filter (ESKF)

ESKF

Motivating Example We use the same example as the one in the EKF post: imagine our world has two cones with known locations: c1, c2, and a diff drive with wheel encoders and a cone detector. T...

Robotics - [ESKF Series 1] IMU Model

Specific Force, IMU model

Introduction The IMU is a very common localization device. One can find it in most electronics nowadays: cars, smart watches, phones, even soccer balls. Knowing how IMU works could be a long proce...

Robotics Fundamentals - Extended Kalman Filter (EKF)

Kalman Filter Framework

Welcome To EKF - A Diff Drive Example EKF (Extended Kalman Filter) is widely applied in robotics to smooth sensor noises to get a better estimate of a car’s position. Now let’s take a look at a d...

Robotics Fundamentals - Kalman Filter

Kalman Filter Framework, Proofs With Minimizing Error Covariance

Kalman Filter FrameWork - Welcome to KF SLAM is a state estimation problem. A typical state estimation framework in discrete time is: \[\begin{gather*} \begin{cases} x_k = f(x_{k-1}, u_k) + ...

Robotics - An Overview Of Kalman Filter, Extended Kalman Filter, and Error State Kalman Filter

[1] What Does A Kalman Filter Do? If a system is a linear system, with Gaussian measurement and control noise, the Kalman Filter (KF) produces the minimum-covariance (i.e., the mean squared error)...

Robotics Fundamentals - Velocities

Velocities, Accelerations, Derivative of Rotations

Rotation-Only Velocity and Acceleration Assume we have a world frame, a car frame, and a point. The car is rotating around the world frame, no translation.The point itself is moving as well, $p_c’...

Robotics - Quaternion Kinematics

Definition of Quaternion, Relationship Between Quaternion and Rotation Matrix

Definition of Quaternion Quaternions can be represented as: \[\begin{gather*} q = [s, x, y, z] = s + xi + yj + zk = s + v v = (i, j, k) \end{gather*}\] i, j, k are 3 complex dimensions, where: ...

Robotics Fundamentals - [ESKF Series 2] GPS and Its Coordinate System

RTK GPS, UTM Coordinates

There are two types of GNSS: Traditional single-point GPS: 10m accuracy, usually found in phones RTK (Real-Time-Kinematics) GPS. centimeter accuracy. It talks to a base station. Each module g...

Robotics Fundamentals - Rotations

Representation of Rotations, Gimbal Lock

Representations of Rotation A rotation, can be respresented as $so(3)$ (Lie Algebra of Special Orthogonal Group), or $SO(3)$, (Special Orthogonal Group) and rotation vector. Representation 1 A ro...