Indoor localization has become increasingly essential for applications ranging from asset tracking to delivering personalized services. Federated learning (FL) offers a privacy-preserving approach by training a centralized global model (GM) using distributed data from mobile devices without sharing raw data. However, real-world deployments require a continual federated learning (CFL) setting, where the GM receives continual updates under device heterogeneity and evolving indoor environments. In such dynamic conditions, erroneous or biased updates can cause the GM to deviate from its expected learning trajectory, gradually degrading internal GM representations and GM localization performance. This vulnerability is further exacerbated by adversarial model poisoning attacks. To address this challenge, we propose ARMOR, a novel CFL-based framework that monitors and safeguards the GM during continual updates. ARMOR introduces a novel state-space model (SSM) that learns the historical evolution of GM weight tensors and predicts the expected next state of weight tensors of the GM. By comparing incoming local updates with this SSM projection, ARMOR detects deviations and selectively mitigates corrupted updates before local updates are aggregated with the GM. This mechanism enables robust adaptation to temporal environmental dynamics and mitigate the effects of model poisoning attacks while preventing GM corruption. Experimental evaluations in real-world conditions indicate that ARMOR achieves notable improvements, with up to 8.0x reduction in mean error and 4.97x reduction in worst-case error compared to state-of-the-art indoor localization frameworks, demonstrating strong resilience against model corruption tested using real-world data and mobile devices.