## 1 Introduction
With the recent deep learning architectures, researchers are now including more advanced sensors such as passive RFID [24], ultrawideband (UWB) radars [25], and cameras [26]. While deep learning can readily extract features and transform complex data to learn meaningful patterns, in smart homes, for some specific tasks, it does not cover all scenarios and all needs. For instance, data may embed some spatial information that is not readily available, such as object movements and their spatial relationships. While it is likely that when granted enough data, deep learning could learn such relations, it is often simpler to use a non-learning algorithm. Moreover, it might provide details of the reasoning and be more interpretable than the classic black box of a deep learning approach [27]. Considering that qualitative spatial reasoning has, to the best of our knowledge, been infrequently explored by the research community focusing on Activities of Daily Living (ADLs) recognition, apart from the incorporation of limited location-related features [28], this paper introduces a straightforward yet highly efficient and effective algorithm for extracting spatial information. This algorithm capitalizes on the fuzzy tracking of everyday objects using passive Radio-Frequency Identification (RFID) technology. While our implementation builds upon our previous passive RFID tracking system [29; 30; 31], in principle, the algorithm is compatible with any imprecise tracking system. Termed the Atomic Gestures Identifier (AtomGID), this novel algorithm represents a departure from learning-based approaches. It can be configured using intuitive rules of thumb and does not necessitate a dataset for operation. While we acknowledge that it may not rival state-of-the-art deep learning methods in terms of performance when provided with extensive data, we posit that AtomGID serves as a complementary tool rather than a direct competitor. We propose that AtomGID addresses a crucial gap in the field by facilitating the incorporation of simple and explainable qualitative spatial reasoning (QSR) [32] into activity recognition frameworks for smart homes. By leveraging AtomGID, researchers and practitioners can harness the power of spatial information to enhance the interpretability and robustness of ADL recognition systems, thereby advancing the capabilities of smart home technologies. AtomGID is implemented and tested first with a home-made simulator that simply adds random Gaussian noise on the data. Then, we implemented it in a realistic smart home infrastructure using binary sensors (electromagnetic contacts, pressure mats, infrared sensors, light detection, and flowmeters) and using passive RFID. Passive tags are used to localize and track in real-time the objects which are used for ADLs in the smart home (e.g., a mug, a plate) [29]. A model of qualitative spatial reasoning is then exploited to extract movement features through AtomGID. We show that AtomGID can readily decompose positions into simple atomic spatial information. Then, a use case is proposed to show how AtomGID could be used in a complete pipeline. First, the extracted knowledge is processed by our clustering algorithm based on flocking [33]. Nevertheless, since flocking is based on the vectors' similarity, any other clustering could have been used for this purpose. Second, spatial knowledge is compared by creating a neighborhood graph of the atomic gestures. The resulting method is fully unsupervised. The various experiments conducted in our smart home demonstrate the feasibility of using the method for coarsely or finely grained ADLs. Finally, the method does not require any fine-tuning to work properly. This aspect represents a strong advantage of the method for generalization in new smart home infrastructures.