The encyclopedia · Engineering & Operations · Technical decision · 1960
The Kalman filter steered Apollo by trusting a model over noisy sensors
In 1960 Kalman's recursive filter blended a prediction with each noisy reading, so NASA could guide Apollo to the Moon.
NASA Ames Research Center · Research Institute for Advanced Studies
the move
All statistical estimates are undermined by faulty sensors, unexpected disturbances and imperfections in the model itself, so a single reading is never fully trustworthy. Guiding a spacecraft through a circumlunar orbit made this acute: tiny errors compound, and there was no reliable way to stay on course.
Kalman's 1960 algorithm solved it with a pair of dynamic equations, one that generates estimates of the unknown variables and one that estimates the accuracy of those uncertainty estimates. At each step it predicts where things should be, then corrects that prediction with the new sensor reading, weighting each by how confident it is.
The filter is recursive, so it only needs the previous estimate and the newest measurement rather than the whole history. NASA researchers staring at the Apollo guidance problem adopted it almost immediately, and it became the method for estimating the state of nearly any system you observe imperfectly.
why it works
- Weighting a model prediction and a measurement by their uncertainties produces a better estimate than either alone.
- The recursion stores only the previous estimate and its error, so it runs in constant memory on a computer.
- It turns a stream of noisy samples into a running best guess of an unobservable state.
what transfers
When no measurement is perfect, do not trust a single reading; keep a model of where things should be and merge each new observation in proportion to its certainty.
what came after
The Kalman filter became a mainstay of flight-control software, used to guide Apollo and the Orion capsule, to calibrate cargo dockings on the ISS, to forecast the weather, to pinpoint cellphone locations and to tune drones and submarines, and it earned Kalman the National Medal of Science in 2008.
references
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