The measurement made in the environment can be used to improve the estimation of the state X (e.g., location) in this environment. Imagine that we are sleepwalking around the house in the middle of the night. When we wake up, we can figure out where we are by using our senses (sight, touch, etc.).

Mathematically, the initial knowledge about the environment can be described with probability distribution p(x) (prior). This distribution can be improved when a new measurement z (with belief p(z|x)) is available if the probability after the measurement is determined p(x|z). This can be achieved using the Bayesian rule $p(x|z)=bel(x)=\frac{p(z|x)p(x)}{p(z)}$. The probability p(z|x) represents the statistical model of the sensor, and ...

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