This work introduces an adaptive Bayesian algorithm for real-time trajectory prediction via intention inference, where a target's intentions and motion characteristics are unknown and subject to change. The method concurrently estimates two critical variables: the target's current intention, modeled as a Markovian latent state, and an intention parameter that describes the target's adherence to a shortest-path policy. By integrating this joint update technique, the algorithm maintains robustness against abrupt intention shifts and unknown motion dynamics. A sampling-based trajectory prediction mechanism then exploits these adaptive estimates to generate probabilistic forecasts with quantified uncertainty. We validate the framework through numerical experiments: Ablation studies of two cases, and a 500-trial Monte Carlo analysis; Hardware demonstrations on quadrotor and quadrupedal platforms. Experimental results demonstrate that the proposed approach significantly outperforms non-adaptive and partially adaptive methods. The method operates in real time around 270 Hz without requiring training or detailed prior knowledge of target behavior, showcasing its applicability in various robotic systems.

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