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Reliable motion classification is critical for autonomous driving, as false dynamic predictions of static objects can cascade into unnecessary planner interventions. Unstable bounding box predictions can lead to spurious velocity estimates in tracking and falsely predicted trajectories. We present a deployment-friendly mitigation strategy that augments a 3D object detector with aleatoric uncertainty estimates and applies a two-sample z-test over short observation windows to separate true motion from jitter. Integrated into Autoware with minimal changes, the approach reuses existing data association for minimal compute overhead. Empirical results show parity with velocity thresholding on nuScenes, but substantially fewer false dynamic predictions and unnecessary stops in real-world test drives, explained by the presence of an intermediate jitter band in the recorded data that speed-only rules misclassify. This demonstrates that uncertainty-aware detection and lightweight statistical testing can deliver practical performance gains for autonomous driving in noisier real-world settings.