How accurate must my odometer reading be for SLAM ?
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That's what's great about SLAM: it doesn't matter. As long as your sensor noise is modeled appropriately and the odometer readings can be translated to position changes, the general algorithm holds.
In a practical sense, with very high uncertainty from odometery, it will update the position just fine, but will seem to ignore the odometer when any other information is available (e.g., laser and static landmarks). Without other information, your maps may look like junk, but it will faithfully produce an estimate with correspondingly high uncertainty.
How accurate must my odometer reading be for SLAM ?
There is no specific level for the accuracy. This is why the modern approaches for building SLAM are probabilistic approaches. This is due to the fact that noise in any sensor is inherited even with very accurate ones. The heavy load with very noisy sensors will be on your filters. You need very good filters to at least run SLAM in very simple maps (e.g. a bunch of points).