Extended Kalman Filter vs Unscented Kalman Filter for State Estimation

The Extended Kalman Filter (EKF) excels at computational efficiency because it linearizes the system dynamics and measurement models using a first-order Taylor series expansion. For example, in a standard visual-inertial odometry pipeline on a low-power embedded processor, an EKF can complete a full predict-update cycle in under 1 millisecond, making it the default choice for resource-constrained platforms where deterministic latency is critical.

The Unscented Kalman Filter (UKF) takes a fundamentally different approach by propagating a minimal set of carefully chosen sigma points through the true nonlinear functions. This strategy avoids the Jacobian derivation required by the EKF and captures the posterior mean and covariance accurately to the 3rd order (Taylor series) for any nonlinearity. The trade-off is a higher computational cost, typically 2-5x that of an EKF, as it requires multiple forward passes through the process and measurement models per iteration.

The key trade-off: If your priority is deterministic, low-latency execution on an embedded microcontroller with mildly nonlinear dynamics, choose the EKF. If you are estimating the state of a highly dynamic humanoid robot performing aggressive maneuvers where linearization errors cause filter divergence, the UKF's superior accuracy and robustness justify the additional computational load. Consider the UKF when the cost of a state estimation failure—such as a bipedal robot falling—far outweighs the cost of a slightly faster processor.

The Extended Kalman Filter (EKF) excels at computational efficiency and deterministic execution because it linearizes the system dynamics using a first-order Taylor series expansion. For example, on a standard ARM Cortex-A72 embedded processor, an EKF update for a 15-state IMU/GNSS fusion problem typically completes in under 50 microseconds. This makes it the default choice for high-rate (1 kHz) proprioceptive state estimation where the dynamics are relatively smooth, such as joint-level velocity filtering in a robotic arm. However, this linearization introduces significant errors when the dynamics are highly nonlinear, such as during the rapid attitude changes of a humanoid robot recovering from a push. In these cases, the Jacobian calculation can become ill-conditioned, leading to a divergence risk that requires careful tuning of process noise covariance.

The Unscented Kalman Filter (UKF) takes a fundamentally different approach by propagating a minimal set of carefully chosen sigma points through the true nonlinear dynamics, avoiding linearization entirely. This results in a third-order accuracy (Taylor series) for Gaussian inputs, compared to the EKF's first-order accuracy. In practice, for a humanoid's 24-DOF whole-body state estimation, a UKF can reduce the root mean square error (RMSE) of the base orientation estimate by 30-40% during aggressive locomotion maneuvers compared to an EKF. The trade-off is computational cost: the UKF requires propagating 2n+1 sigma points, making it roughly 3-5x more computationally expensive per iteration than an EKF for the same state dimension, which can push latency to over 200 microseconds on embedded hardware.

The key trade-off: If your priority is deterministic, low-latency execution on resource-constrained embedded hardware for systems with mild nonlinearities, choose the EKF. If you prioritize estimation accuracy and filter consistency for highly nonlinear dynamics—such as bipedal locomotion, aerial acrobatics, or high-speed legged maneuvers—and can afford the additional computational budget, choose the UKF. Consider a hybrid architecture where an EKF handles high-rate IMU propagation, and a lower-rate UKF corrects for visual or LiDAR updates to balance both constraints.