This paper presents a method for estimating uncertain spatial relationships in robotics. The approach involves representing spatial information as a stochastic map, which captures the best estimates of spatial relationships and their uncertainties. The map is built incrementally as new spatial information is obtained, and it allows for the propagation of uncertainty between different frames of reference. The stochastic map is based on probabilistic methods, which provide a more accurate and flexible approach to spatial reasoning compared to previous conservative methods like min-max bounds. The paper describes the representation of uncertain spatial relationships using mean and covariance matrices, and provides methods for combining and updating these estimates. The approach is applied to a mobile robot example, where the robot uses sensor information to update its map and improve its spatial estimates. The paper also discusses the use of Kalman filters for updating the map based on new sensor measurements, and highlights the importance of probabilistic reasoning in handling uncertainty in spatial relationships. The methods are developed within the context of state estimation and filtering theory, providing a solid foundation for further extensions and applications.This paper presents a method for estimating uncertain spatial relationships in robotics. The approach involves representing spatial information as a stochastic map, which captures the best estimates of spatial relationships and their uncertainties. The map is built incrementally as new spatial information is obtained, and it allows for the propagation of uncertainty between different frames of reference. The stochastic map is based on probabilistic methods, which provide a more accurate and flexible approach to spatial reasoning compared to previous conservative methods like min-max bounds. The paper describes the representation of uncertain spatial relationships using mean and covariance matrices, and provides methods for combining and updating these estimates. The approach is applied to a mobile robot example, where the robot uses sensor information to update its map and improve its spatial estimates. The paper also discusses the use of Kalman filters for updating the map based on new sensor measurements, and highlights the importance of probabilistic reasoning in handling uncertainty in spatial relationships. The methods are developed within the context of state estimation and filtering theory, providing a solid foundation for further extensions and applications.