This paper addresses the challenge of representing and reasoning about spatial relationships in robotics, where such relationships are inherently uncertain. The authors propose a stochastic map, a representation that captures the best estimates of spatial relationships and their uncertainties. The stochastic map is designed to handle multiple frames of reference and uncertain relative information, making it suitable for dynamic environments and flexible reasoning. The paper introduces methods for building, reading from, and incrementally updating the stochastic map as new spatial information is obtained. These methods are based on state estimation and filtering theory, providing a robust framework for estimating uncertain spatial relationships. The authors also discuss the interpretation of the stochastic map, including how to calculate probabilities based on the estimated mean and covariance. The paper includes an example of a mobile robot navigating an environment, demonstrating how the stochastic map can be used to estimate the robot's location and the organization of its surroundings. The methods presented are efficient and can be implemented using recursive algorithms, making them practical for real-world applications.This paper addresses the challenge of representing and reasoning about spatial relationships in robotics, where such relationships are inherently uncertain. The authors propose a stochastic map, a representation that captures the best estimates of spatial relationships and their uncertainties. The stochastic map is designed to handle multiple frames of reference and uncertain relative information, making it suitable for dynamic environments and flexible reasoning. The paper introduces methods for building, reading from, and incrementally updating the stochastic map as new spatial information is obtained. These methods are based on state estimation and filtering theory, providing a robust framework for estimating uncertain spatial relationships. The authors also discuss the interpretation of the stochastic map, including how to calculate probabilities based on the estimated mean and covariance. The paper includes an example of a mobile robot navigating an environment, demonstrating how the stochastic map can be used to estimate the robot's location and the organization of its surroundings. The methods presented are efficient and can be implemented using recursive algorithms, making them practical for real-world applications.