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Sensor nodes localization in wireless Internet of Things (IoT) sensor networks is crucial for the effective operation of diverse applications, such as smart cities and smart agriculture. Existing sensor nodes localization approaches heavily rely on anchor nodes within wireless sensor networks (WSNs). Anchor nodes are sensor nodes equipped with global positioning system (GPS) receivers and thus, have known locations. These anchor nodes operate as references to localize other sensor nodes. However, the presence of anchor nodes may not always be feasible in real-world IoT scenarios. Additionally, localization accuracy can be compromised by fluctuations in Received Signal Strength Indicator (RSSI), particularly under non-line-of-sight (NLOS) conditions. To address these challenges, we propose UBiGTLoc, a Unified Bidirectional Long Short-Term Memory (BiLSTM)-Graph Transformer Localization framework. The proposed UBiGTLoc framework effectively localizes sensor nodes in both anchor-free and anchor-presence WSNs. The framework leverages BiLSTM networks to capture temporal variations in RSSI data and employs Graph Transformer layers to model spatial relationships between sensor nodes. Extensive simulations demonstrate that UBiGTLoc consistently outperforms existing methods and provides robust localization across both dense and sparse WSNs while relying solely on cost-effective RSSI data.