Inertial localization is regarded as a promising positioning solution for consumer-grade IoT devices due to its cost-effectiveness and independence from external infrastructure. However, data-driven inertial localization methods often rely on increasingly complex network architectures to improve accuracy, which challenges the limited computational resources of IoT devices. Moreover, these methods frequently overlook the importance of modeling long-term dependencies in inertial measurements - a critical factor for accurate trajectory reconstruction - thereby limiting localization performance. To address these challenges, we propose a reparameterized inertial localization network that uses a multi-branch structure during training to enhance feature extraction. At inference time, this structure is transformed into an equivalent single-path architecture to improve parameter efficiency. To further capture long-term dependencies in motion trajectories, we introduce a temporal-scale sparse attention mechanism that selectively emphasizes key trajectory segments while suppressing noise. Additionally, a gated convolutional unit is incorporated to effectively integrate long-range dependencies with local fine-grained features. Extensive experiments on public benchmarks demonstrate that our method achieves a favorable trade-off between accuracy and model compactness. For example, on the RoNIN dataset, our approach reduces the Absolute Trajectory Error (ATE) by 2.59% compared to RoNIN-ResNet while reducing the number of parameters by 3.86%.

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