Technology
What is a Kalman filter?
Your phone knows which way it is facing and a drone knows how fast it is moving, yet neither has a perfect sensor. What they have is a way of combining imperfect ones, published in 1960 and now at work in phones, drones, cars and spacecraft: the Kalman filter.
In short. A Kalman filter keeps a best estimate of something, such as position and speed, together with how unsure it is. At each step it predicts where things should be from a model of the motion, then corrects that prediction with the latest measurements, trusting each source in proportion to how reliable it is. R. E. Kalman published the method in 1960, and engineers at NASA’s Ames Research Center turned it into a practical tool for aerospace soon after.
Every sensor is wrong in its own way
- A gyroscope measures turning smoothly and quickly, but its estimate slowly drifts.
- An accelerometer knows which way is down, but it is jittery and confused by motion.
- Satellite positioning does not drift, but it updates slowly, jumps about and does not work indoors.
- A downward camera measures speed over the floor, if the floor has texture and the height is known: optical flow.
No single sensor is right, but together they can do much better than any one of them, if you know how far to trust each, moment by moment. That is the job of the filter.
Predict, then correct
- Predict. From the last estimate and a model of how things move, predict the new state: a drone moving at 1 m/s will be 10 cm further on a tenth of a second later. Because predictions drift, the uncertainty grows.
- Measure. Read the sensors.
- Correct. Blend the prediction and the measurement. The weight, called the Kalman gain, comes from their uncertainties: a precise measurement pulls the estimate strongly, a noisy one only a little. The uncertainty shrinks.
- Repeat, many times a second.
Kalman’s 1960 paper derived, among other results, an equation for how the uncertainty of the best estimate evolves, from which the filter itself follows without further calculation.
From a paper to spacecraft
A 1985 NASA report by McGee and Schmidt tells how researchers at Ames picked up Kalman’s work shortly after it appeared and reworked it into a practical tool for an aerospace application. The version they developed for systems that are not linear, now called the extended Kalman filter, is often still simply called the Kalman filter. Running it on the small computers carried by aircraft and spacecraft caused numerical trouble, which led to a “square-root” form of the filter and to its first test on a computer in flight.
Where it runs today
- Phones, combining the gyroscope, accelerometer and compass to know which way they face.
- Satellite navigation receivers, smoothing positions from noisy signals.
- Drones and robots, estimating position, speed and tilt from motion sensors, cameras and distance sensors.
- Cars, aircraft and spacecraft.
What it needs to work
- A good model of the motion. Predictions are only as good as the model behind them.
- Honest noise figures. A filter that trusts a sensor too much follows its noise; one that trusts it too little reacts late.
- Speed. For a fast machine, a late estimate is a wrong one. In our drone simulation, an estimate that arrives too late makes the drone wobble from side to side.
How Alkyon is designed
Alkyon, our concept for a flying home companion, is designed to estimate its position and speed from motion sensors, a downward optical flow sensor and depth sensors around it. In our simulation, that estimate has to arrive quickly, and its slow drift is one of our main open problems: what SLAM is explains how a map helps. It is a concept in development, for Europe only: how indoor drones navigate.
Sources, read 4 November 2026: R. E. Kalman, a new approach to linear filtering and prediction problems, Journal of Basic Engineering, 1960; McGee and Schmidt, discovery of the Kalman filter as a practical tool for aerospace and industry, NASA, 1985. General information.
Questions
What does a Kalman filter do, in simple terms?
It keeps a best estimate of something, such as a position and a speed, together with how unsure that estimate is. It predicts the next value from a model of the motion, then corrects the prediction with new measurements, trusting each in proportion to how reliable it is.
Where are Kalman filters used?
Wherever several imperfect sensors must be combined in real time: phones working out their orientation, satellite navigation receivers, drones and robots estimating their position and speed, cars, aircraft and spacecraft.