What Is a Kalman Filter? How Robots Combine Noisy Sensor Measurements.

What Is a Kalman Filter?

A Kalman filter is a mathematical algorithm that estimates the changing state of a system by combining predictions with imperfect measurements.

It is widely used in robotics, navigation, aerospace, and other applications where sensors produce noisy or uncertain information.

For example, a mobile robot may combine measurements from wheel encoders and other suitable sensors to estimate its position and velocity.

Rather than trusting one measurement completely, a Kalman filter accounts for uncertainty when updating its estimate.

Key Takeaways

• Kalman filters combine mathematical predictions with measurements to estimate a system's state.
• They track uncertainty as well as estimated values.
• The classical Kalman filter is designed for linear models under particular statistical assumptions; nonlinear robotics applications often use extensions.

How Does a Kalman Filter Work?

Imagine a robot traveling along a warehouse aisle.

Its wheels indicate that it has moved forward one meter.

However, the wheels may slip slightly, making that estimate imperfect.

Another sensor provides additional movement information, but its measurements also contain noise.

A Kalman filter maintains an estimate of the robot's state and uncertainty.

It repeatedly performs two operations.

Prediction: Use the previous state and a system model to estimate what should happen next.

Update: Compare a new measurement with the prediction and adjust the estimate according to their uncertainties.

For example, if a sensor is known to be relatively noisy, the filter may place less weight on its measurement.

If a measurement is considered reliable, it may have a greater influence on the result.

What Is the Kalman Gain?

The Kalman gain determines how strongly the estimate should be adjusted in response to a new measurement.

It depends on the uncertainty in the prediction and the measurement.

For a simplified example, imagine a robot's predicted position is relatively uncertain while a new reference measurement is highly precise.

The filter may make a relatively large correction toward the measurement.

If the measurement is unreliable, the correction may be smaller.

The gain is calculated mathematically rather than being an arbitrary fixed weighting in the general Kalman filtering process.

Kalman Filter vs. Extended Kalman Filter

The standard Kalman filter assumes linear state and measurement models.

Many robotic systems involve nonlinear relationships.

An extended Kalman filter, or EKF, uses local linear approximations to apply Kalman-style estimation to suitable nonlinear models.

For example, the movement of a wheeled robot depends on its heading, which introduces nonlinear relationships.

EKFs are therefore commonly used in mobile robot localization.

Other alternatives include unscented Kalman filters and particle filters.

Why Is a Kalman Filter Useful in Robotics?

Robots rarely have a perfect measurement of their position or movement.

Sensors introduce noise, delays, biases, and other uncertainties.

A filtering system can combine complementary sources of information to produce more useful estimates.

However, incorrect models or uncertainty settings can produce poor results.

The filter cannot recover information that its sensors and assumptions do not provide.

Frequently Asked Questions

Does a Kalman filter require artificial intelligence?

No. It is a mathematical state-estimation algorithm, not necessarily a machine learning model.

Can a Kalman filter eliminate sensor drift?

It can reduce or correct some errors when suitable reference measurements are available, but it cannot guarantee drift-free operation.

The Bottom Line

Kalman filters help robots estimate their state using imperfect information. Their combination of prediction, measurement, and uncertainty makes them fundamental tools for navigation and sensor fusion.