Mobile multi-machine environments consist of varying types of objects, either static or dynamic with the state known exactly or with some uncertainty. Sensors observe the environment from different positions and views, such as horizontally from the top of a mobile machine or vertically downward from an external observing machine. In this paper, we propose a simple grid-based framework for representing the information of varying types of objects in a 2-D environment and Bayesian methods for updating this information through observations and prediction models. This information about the current and near-future state of the environment is called situation awareness (SA). SA information can be utilized as the basis of the operator assistance system for enhancing the safety and efficiency of manual and semiautonomous multi-machine work environments. SA information can also be utilized in task planning of autonomous machines, via creating a dynamic costmap for path planning or entropy map for planning the optimal use of sensory systems. This paper aims at real-time mobile multi-machine environments; hence, the SA framework is kept simple for computational feasibility, but is also general enough to be applicable in other environments as well. Discussion on discretization errors and computational complexity are also covered.