Geometric Algebra: A Possible Foundation for Digital Twin Modeling and Analysis—A Case Study with PIR Scene

Digital twin (DT) refers to a virtual representation of an object or system that spans its entire life cycle, constantly updating with real-time data, and utilizes simulation, machine learning, and reasoning to aid decision-making. However, the complexity of the real world and the urgent need for seamless integration between the physical and virtual spaces have posed challenges in the development and implementation of DT. This is primarily due to the separation of expression and analysis in the traditional modeling approaches. Developing the fundamental mathematical space of DT is a important and critical topic. These problems can be addressed by leveraging Geometric Algebra (GA), which enables effective expression and computation in multidimensional space. The paper studies the concept of DT, employs the essential principles of GA as a tool, and proposes the DT’s modeling and analysis methods. To demonstrate the formulation and construction of DT, a typical scenario involving multi-factor coupling of passive infrared sensors (PIR) is presented as an example. The results showcase the effectiveness of the proposed approach in simulating human-sensor interactions, capturing real-space reaction records, and successfully deriving pedestrian trajectories from PIR data. The study presented in this paper offers valuable insights into how to build DT for complex scenarios and also sheds new light on analyzing human behavior using PIR technology.