Integrating IoT Sensor Data with Geometric-Semantic and Quantum Probability Models for Dynamic Real Estate Valuation

Abstract

Real estate valuation has traditionally relied on periodic, point-in-time assessments that provide only static snapshots of a property's worth. This paper introduces a framework that integrates Internet of Things (IoT) sensor networks with geometric-semantic and quantum-inspired mathematical models, making valuation a continuous, dynamically updated process. Environmental, operational, and experiential data streams are embedded into complex Hilbert spaces, capturing both measurable building performance and intangible stakeholder perceptions. Projection operators map fused sensor and textual embeddings into valuation subspaces, allowing real-time assessment of attributes such as sustainability, governance quality and experiential comfort. Non-commutative operators model the observed effect that the order in which information is presented influences value judgments, while unitary transformations represent stakeholder-specific preference structures and negotiation dynamics. The framework is continuously recalibrated through empirical feedback and transformer-based semantic encoding, keeping the model aligned with changing market narratives and new sensor data. Practical challenges, including sensor heterogeneity, temporal synchronisation and semantic drift, are addressed through layered system designs. By bridging the gap between physical building performance data and the complex socio-cognitive processes that shape property values, this methodology offers an adaptive valuation approach suited to the sustainability and stakeholder-diversity goals increasingly required in modern real estate markets.