Nonlinear Kalman Filter

1. Extended Kalman Filter

EKF uses Taylor series to linearize the system equation.

Prediction step:

Correction Step:

2&3. Central Difference Kalman Filter(CDKF) and Unscented Kalman Filter (UKF)

Given mean and covariance, create 2 more input points that are located gamma standard deviation away from the mean.

with tuning parameters shown in table below:

Preparation:

Prediction:

Correction:

Final Result (Comparing EKF, CDKF, and UKF)

Reference

[1] Eric A. Wan, Rudolph van der Merwe. The Unscented Kalman Filter for Nonlinear Estimation. Oregon Graduate Institute of Science & Technology, Feb 2000