The global positioning system (GPS) as used on modern smartphones has a mean accuracy of about 5 meters radius under an open sky [van Diggelen and Enge, 2015; U.S. Government, 2022]. GPS becomes less accurate in cities, where buildings cause occlusion and reflection of GPS signals. Smartphones and self-driving cars use probabilistic localization, which improves accuracy by keeping track of the distribution over immediately preceding locations. Using hidden Markov models, current sensing information, with error estimates, is combined with the distribution of the previous position to give a distribution of the current position. You can tell if your phone does not combine previous estimates with sensing; it re-estimates your position at each time and the location estimation tends to jump around. For example, suppose you are walking along the side of a river, as you walk under a bridge the GPS reading becomes inaccurate, and can predict that you jump across the river. Keeping track of the distribution of where you just were and taking into account the accuracy of the signal can be used to give a much more accurate estimate of location. It is unlikely you jumped across the river. A similar methodology is used to guess activity in a smart watch, combining GPS, heart rate, and movement; the different activities each make predictions, which can be used as sensing information for a distribution of the activity of the wearer at each time.

For self-driving cars, accurate positioning is important as a single error can take the vehicle on the wrong route. The most reliable way to do this is to only travel on well-mapped routes. A mapping vehicle can pre-drive the routes with all of the sensors (e.g., GPS, lidar, radar, sonar, vision), so the self-driving car knows what sensor values to expect. The sensing needs to work under all weather conditions. It also needs to recognize events for which action is required, such as roadworks or someone running across the road. For a vehicle to travel on unmapped routes (e.g., on a detour because of an accident ahead), it needs to rely on more general capabilities. Techniques for positioning can also work indoors, using vision without GPS, as shown by Viswanathan et al. [2011] for an intelligent wheelchair.

Robots in a novel environment can simultaneously estimate location and construct a map (known as simultaneous localization and mapping (SLAM)). This is filtering with a richer representation of a state. The state now includes the map as well as the location, which makes the state space enormous. Thrun et al. [2005] overview the use of probability in robotics.