Kalman Filter is an algorithm for estimating state while considering different error source such as sensor measurement, state prediction, and other kinds of noise and uncertainty. The algorithm constiute of two stages, the measurement update and the state prediction. These two stages form a iterating cycle and continuously calculate the optimal estimation of the state.
Kalman Filter treats all source of uncertainty as a gaussian distribution.
The goal prediction of a rover.
Gaussian distribution consist of two parameters, mean (μ) and its variance (σ²).
$p(x1 < x < x2) = \int_{x1}^{x2}f(x)dx$
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The area under the distribution curve represents the probability of x being in the range.
Two gaussian distribution blend into one with incline to more certain one.
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After the fusion of the prior belief and the measurement, a optimal estimation has formed. Combined this estimation with the new command, we got the new state prediction. The state prediction then becomes the new prior belief.