Cross-view object geo-localization (CVOGL) typically assumes a fixed query image, overlooking the ability of mobile agents to actively acquire more informative observations. To address this limitation, we introduce Active Cross-View Object Geo-Localization (ActiveGeo), where an agent sequentially selects new viewpoints and determines when to stop, aiming to improve localization with minimal observations. We further propose ActiveMoPT, an ActiveGeo framework with three-stage training. First, Multi-View Prompt-Preserving Adaptation enables the model to aggregate multiple query views while reusing the initial prompt. Second, Trajectory-Guided Policy Initialization uses supervised agent trajectories to learn viewpoint selection and initial stopping behavior. Third, Cost-Aware Policy Refinement employs GRPO with a gain-cost reward to jointly optimize localization accuracy and observation efficiency. We also construct ActiveGeo-858, a zero-shot test set containing 858 scenes and 1,716 target annotations. Experiments show that ActiveMoPT achieves state-of-the-art performance on MoP-UAV using only 1.45 query views on average, and substantially outperforms previous CVOGL approaches under zero-shot evaluation on ActiveGeo-858.

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