Anxiety is a significant clinical concern in autism spectrum disorder (ASD) due to its negative impact on physical and psychological health. Treatment of anxiety in ASD remains a challenge due to difficulties with self-awareness and communication of anxiety symptoms. To reduce these barriers to treatment, physiological markers of autonomic arousal, collected through wearable sensors, have been proposed as real-time, objective, and language-free measures of anxiety. A critical limitation of the existing anxiety detection systems is that physiological arousal is not specific to anxiety and can occur with other user states such as physical activity. This can result in false positives, which can hinder the operation of these systems in real-world situations. The objective of this paper was to address this challenge by proposing an approach for real-time detection and mitigation of physical activity effects. A novel multiple model Kalman-like filter is proposed to integrate heart rate and accelerometry signals. The filter tracks user heart rate under different motion assumptions and chooses the appropriate model for anxiety detection based on user motion conditions. Evaluation of the algorithm using data from a sample of children with ASD shows a significant reduction in false positives compared to the state-of-the-art, and an overall arousal detection accuracy of 93%. The proposed method is able to reduce false detections due to user motion and effectively detect arousal states during movement periods. The results add to the growing evidence supporting the feasibility of wearable technologies for anxiety detection and management in naturalistic settings.