Accurate identification of gait phases is critical in effectively assessing the assistance provided by lower limb exoskeletons. In this study, we propose a novel gait phase recognition system called ObsNet to analyze the gait of individuals with spinal cord injuries (SCI). To ensure the reliable use of exoskeletons, it is essential to maintain practicality and avoid exposing the system to unnecessary risks of fatigue, inaccuracy, or incompatibility with human-centered devices. Therefore, we propose a new approach to characterize exoskeletal-assisted gait by estimating forces on exoskeletal joints during walking. Although these estimated forces are potentially useful for detecting gait phases, their nonlinearities make it challenging for existing algorithms to generalize accurately. To address this challenge, we introduce a data-driven model that simultaneously captures both feature extraction and order dependencies, and enhance its performance through a threshold-based compensational method to filter out momentary errors. We evaluated the effectiveness of ObsNet through robotic walking experiments with two practical users with complete paraplegia. Our results indicate that ObsNet outperformed state-of-the-art methods that use joint information and other recurrent networks in identifying the gait phases of individuals with SCI (p< 0.05). We also observed reliable imitation of ground truth after compensation. Overall, our research highlights the potential of wearable technology to improve the daily lives of individuals with disabilities through accurate and stable state assessment.