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The truck can be equipped with a GPS unit that provides an estimate of the position within a few metres.The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few metres of the real position.This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances.As an example application, consider the problem of determining the precise location of a truck.

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The Kalman filter has numerous applications in technology.This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration.This means that the Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new state.In the prediction phase, the truck's old position will be modified according to the physical laws of motion (the dynamic or "state transition" model).Not only will a new position estimate be calculated, but a new covariance will be calculated as well.

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