Reliable navigation in cooperative unmanned aerial vehicle (UAV) networks requires adaptively managing measurement degradations within Kalman-filter-based estimation frameworks. This paper introduces a learning-based Kalman approach for real-time detection of degraded measurements in mesh-network-based multi-UAV navigation. The method incorporates a data-driven pre-filtering module that assesses measurement reliability prior to the Kalman update, thereby improving the robustness of the estimation process under communication-induced degradations. Within this approach, four measurement fault detection strategies—Innovation Filter (IF), Deep Q-Network (DQN), Multi-Layer Perceptron (MLP), and Long Short-Term Memory (LSTM)—were implemented and comparatively evaluated through Monte Carlo simulations combining inertial sensors, time-of-arrival, and Doppler-based inter-agent observations. Additional statistical analyses, including ±1σ error bars and a Wilcoxon rank-sum test, were conducted to verify the significance of the performance differences among the methods. The results show that the proposed approach significantly enhances navigation reliability, particularly under degraded or intermittent GNSS and communication conditions. The MLP-based configuration achieved the best balance between fault-detection accuracy and overall filter consistency. These findings confirm the effectiveness of learning-augmented Kalman filtering architectures for robust and scalable cooperative UAV navigation.