DKDhruv Karnik

State estimation

CKF vs. EKF for Nonlinear State Estimation

A controlled comparison of Cubature and Extended Kalman Filters in indoor robot localization and coordinated-turn radar tracking.

Python · CKF · EKF · Radar tracking · Monte Carlo

Overview

The goal was to compare EKF and CKF under the same trajectories, process noise, and measurements, and to examine not only accuracy but also convergence, robustness, and computation time.

Indoor localization

The first experiment uses a unicycle motion model and noisy landmark-range measurements in a bounded 2D map with obstacles. After burn-in, both filters perform almost identically.

EKF post-burn-in RMSE0.01040 mCKF post-burn-in RMSE0.01037 m

In this relatively mild nonlinear case, CKF does not provide a meaningful accuracy advantage, while the single-trial runtime was about 7.12× EKF.

Coordinated-turn radar tracking

The second experiment introduces stronger nonlinearity through a coordinated-turn target model and radar observations. Here the filter behavior separates more clearly.

EKF post-burn-in RMSE4.163 mCKF post-burn-in RMSE3.948 m · 5.16% improvement

Monte Carlo robustness

Across 75 low-noise radar runs, CKF achieved 2.191 m average RMSE versus 3.840 m for EKF and outperformed EKF in 74 of 75 runs. The average CKF runtime was about 2.93× EKF in the radar study.

InterpretationCKF's extra computation is difficult to justify in the mild indoor case, but becomes valuable when measurement and motion nonlinearities are stronger.