This paper proposes small and efficient machine learning models (TinyML) for resource-constrained edge devices, specifically for on-device indoor localisation. Typical approaches for indoor localisation rely on centralised remote processing of data transmitted from lower powered devices such as wearables. However, there are several benefits for moving this to the edge device itself, including increased battery life, enhanced privacy, reduced latency and lowered operational costs, all of which are key for common applications such as health monitoring. The work focuses on model compression techniques, including quantization and knowledge distillation, to significantly reduce the model size while maintaining high predictive performance. We base our work on a large state-of-the-art transformer-based model and seek to deploy it within low-power MCUs. We also propose a state-space-based architecture using Mamba as a more compact alternative to the transformer. Our results show that the quantized transformer model performs well within a 64 KB RAM constraint, achieving an effective balance between model size and localisation precision. Additionally, the compact Mamba model has strong performance under even tighter constraints, such as a 32 KB of RAM, without the need for model compression, making it a viable option for more resource-limited environments. We demonstrate that, through our framework, it is feasible to deploy advanced indoor localisation models onto low-power MCUs with restricted memory limitations. The application of these TinyML models in healthcare has the potential to revolutionize patient monitoring by providing accurate, real-time location data while minimizing power consumption, increasing data privacy, improving latency and reducing infrastructure costs.