This paper enhances the obstacle avoidance of Autonomous Surface Vehicles (ASVs) for safe navigation in high-traffic waters with an active state estimation of obstacle's passing intention and reducing its uncertainty. We introduce a topological modeling of passing intention of obstacles, which can be applied to varying encounter situations based on the inherent embedding of topological concepts in COLREGs. With a Long Short-Term Memory (LSTM) neural network, we classify the passing intention of obstacles. Then, for determining the ASV maneuver, we propose a multi-objective optimization framework including information gain about the passing obstacle intention and safety. We validate the proposed approach under extensive Monte Carlo simulations (2,400 runs) with a varying number of obstacles, dynamic properties, encounter situations, and different behavioral patterns of obstacles (cooperative, non-cooperative). We also present the results from a real marine accident case study as well as real-world experiments of a real ASV with environmental disturbances, showing successful collision avoidance with our strategy in real-time.