The invention is related to methods and apparatus that use a visual sensor and dead reckoning sensors to process Simultaneous Localization and Mapping (SLAM). These techniques can be used in robot navigation. Advantageously, such visual techniques can be used to autonomously generate and update a map. Unlike with laser rangefinders, the visual techniques are economically practical in a wide range of applications and can be used in relatively dynamic environments such as environments in which people move. One embodiment further advantageously uses multiple particles to maintain multiple hypotheses with respect to localization and mapping. Further advantageously, one embodiment maintains the particles in a relatively computationally-efficient manner, thereby permitting the SLAM processes to be performed in software using relatively inexpensive microprocessor-based computer systems.