Probabilistic ogm
To counter the issues with the naive OGM, the Probabilistic OGM was introduced. Instead of binary values, probabilistic OGMs use probabilities to represent the likelihood that a cell is occupied.
If \(P_{occ}\) is the probability that a cell is occupied, then:
\[P_{occ} = \frac{P(z_t | \text{occ}) P_{prev}}{P(z_t)}\]
where:
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\(P(z_t | \text{occ})\) is the probability of the sensor measurement \(z_t\) given that the cell is occupied.
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\(P_{prev}\) is the probability that the cell was occupied in the previous time step (prior).
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\(P(z_t)\) is the probability of the sensor measurement \(z_t\) at time \(t\).
This Bayesian update ensures that uncertainties in sensor measurements and temporary changes in the environment are handled more gracefully.
Demo
To try out the OGM algorithm, run this Google Colab notebook:
