Another example is voltages. Many countries require in-home filtering of line voltages in order to power personal computers and peripherals. Without filtering, the power fluctuations would drastically shorten the useful lifespan of the devices. Kalman filtering has been applied in areas as diverse as aerospace, marine navigation, nuclear power plant instrumentation, demographic modeling, manufactring, and many others. This paper uses a tutorial, example-based approach to explain Kalman filtering.
Mathematics Consider the problem of estimating the variables of some system.
For instance, if our dynamic system consists of a spacecraft which is accelerating with random bursts of gas from its Reaction Control System thrusters, the vector x might consist of position p and velocity v . Now suppose we can measure the position p . Surely we can do better than just take each measurement at its face value, especially if we suspect that we have a lot of measurement noise. The Kalman filter is formulated as follows. Suppose we assume that the process noise w k is white gaussian noise with a covariance matrix Q .