State Estimation using Extend Kalman Filter (EKF) for robotics

EKF was designed to enable the Kalman filter to apply in non-linear motion systems such as robots. EKF generates more accurate estimates of the state than using just actual measurements alone. In this post, we will briefly walk through the Extended Kalman Filter, and we will get a feel of how sensor fusion works. In order to discuss EKF, we will consider a robotic car (self-driving vehicle in this case). We can model this car as illustrated in the figure below in a global coordinate frame with coordinates: Xglobal, Yglobal, and Zglobal (face upwards). The X_car and Y_car coordinates belong to the coordinate frame of the car which is moving with a linear velocity (V) and angular velocity (ω). The yaw angle (γ) measures how much the car is rotated around the global z-axis.

EKF is seen in almost every field of robotics for estimating states. The goal of EKF is to smooth out the noisy sensor measurements of the car for better state estimation. State here means where is the car located? and how much it is rotated? In order to estimate the state of the vehicle, EKF combines the noisy sensor measurements with the predicted sensor measurement to generate an optimal estimation. However, to understand how EKF functions we need to know about two mathematical building blocks of EKF:

• State-Space Model