IoT-based applications require effective anonymous authentication and key agreement (AKA) protocols to secure data and protect user privacy due to open communication channels and sensitive data. While AKA protocols for these applications have been extensively studied, achieving anonymity remains a challenge. AKA schemes using one-time pseudonyms face resynchronization issues after desynchronization attacks, and the high computational overhead of bilinear pairing and public key encryption limits its applicability. Existing schemes also lack essential security features, causing issues such as vulnerability to ephemeral secret leakage attacks and key compromise impersonation. To address these issues, we propose two novel AKA schemes, PUAKA and RCAKA, designed for different IoT traffic patterns. PUAKA improves end device anonymity in the periodic update pattern by updating one-time pseudonyms with authenticated session keys. RCAKA, for the remote control pattern, ensures anonymity while reducing communication and computation costs using shared signatures and temporary random numbers. A key contribution of RCAKA is its ability to resynchronize end devices with incomplete data in the periodic update pattern, supporting continued authentication. Both protocols' security is proven under the Real-or-Random model. The performance comparison results show that the proposed protocols exceed existing solutions in security features and communication costs while reducing computational overhead by 32% to 50%.