What Is an Extended Kalman Filter? EKF Explained for Robotics.

What Is an Extended Kalman Filter?

An extended Kalman filter, or EKF, is a mathematical method used to estimate the state of a system when its motion or measurements involve nonlinear relationships.

In robotics, an EKF commonly combines information from sensors to estimate a robot's position, orientation, or movement.

For example, a mobile robot may receive information from wheel encoders, an inertial measurement unit, and a positioning system.

Each source has limitations. An EKF can combine their measurements to produce an estimate that accounts for uncertainty.

Key Takeaways

• An EKF estimates a system's state by combining predictions with incoming measurements.
• It extends the standard Kalman filter to certain nonlinear systems by approximating their behavior locally.
• EKFs are widely used for localization and sensor fusion, but their performance depends on appropriate models and uncertainty estimates.

How Does an Extended Kalman Filter Work?

Imagine a warehouse robot traveling along a corridor.

Its wheel encoders indicate that it has moved two meters.

However, the wheels may have slipped slightly, making that measurement imperfect.

An inertial sensor provides additional information about the robot's motion, but its readings also contain noise.

An EKF maintains an estimate of the robot's state and how uncertain that estimate is.

The algorithm repeatedly performs two main operations.

Prediction: Estimate the robot's next state using a motion model and previous information.

Correction: Compare new sensor measurements with the predicted state and adjust the estimate.

The correction takes account of the uncertainty associated with the model and measurements.

Why Is It Called an Extended Kalman Filter?

The conventional Kalman filter is designed for linear system models under particular statistical assumptions.

Many physical systems are nonlinear.

For example, the relationship between a mobile robot's heading and its movement through a room involves trigonometric calculations.

An EKF handles these nonlinear relationships by using local linear approximations, commonly calculated using Jacobian matrices.

This allows a Kalman-style estimation process to be applied to a wider range of systems.

EKF vs. Sensor Fusion

Sensor fusion is the broader process of combining information from multiple sensors.

An EKF is one method for performing sensor fusion.

Other approaches include complementary filters, unscented Kalman filters, and particle filters.

The best method depends on the application, computational constraints, and characteristics of the system.

ROS provides the robot_localization package, which includes EKF-based state estimation.

What Are the Limitations of an EKF?

An EKF depends on the quality of its underlying models.

If its assumptions are inaccurate or sensor uncertainties are poorly configured, the estimate can become unreliable.

Because the filter approximates nonlinear relationships, strongly nonlinear behavior can also create difficulties.

Frequently Asked Questions

Does an EKF eliminate GPS or odometry errors?

No. It combines imperfect information to improve estimates, but it cannot guarantee error-free localization.

Can an EKF operate without GPS?

Yes. It can combine wheel odometry, inertial sensors, and other suitable information.

The Bottom Line

Extended Kalman filters help robots estimate their movement and position by combining uncertain measurements with mathematical predictions. They are a widely used foundation of modern robotic localization.