A Precision-Adaptive Motion Deduction Model Based on Historical Velocity Slices: Type-Y Equation V2.0 and Its Multi-Scenario Verification

Traditional motion deduction models mostly rely on the assumption of instantaneous driving forces, leading to limited deduction accuracy in scenarios where driving forces are difficult to model or their mechanisms are unclear. Additionally, balancing deduction accuracy and computational efficiency remains a challenge. The Type-Y Velocity Evolution Equation (V2.0), initially proposed as a theoretical framework for motion deduction, is transformed into a data-driven motion deduction model in this study. For the first time, this paper realizes the sliced reconstruction of historical velocity data, supplements precision adaptation rules, and conducts multi-scenario empirical verification for the equation, constructing a novel precision-adaptive multi-dimensional motion deduction method. The mathematical expression and measurable parameter definitions of the equation are clarified, and multi-dimensional adaptation logic is embedded in the quantitative system of environmental coefficients. Multi-scale verification is completed using measured data of basic two-dimensional motion, public 3D trajectory data of unmanned aerial vehicles (UAVs), and simplified radial velocity data of celestial bodies, with systematic analysis of deduction accuracy and computational efficiency. Results show that the model can complete multi-dimensional motion state deduction solely through weighted superposition of historical velocity data slices without additional driving force assumptions. In low-precision scenarios, the number of effective slices is small, ensuring high computational efficiency; in high-precision scenarios, retaining low-weight slices significantly improves deduction accuracy, with overall fitting error superior to traditional basic deduction models. This study provides a configurable and verifiable data-driven tool for lightweight motion prediction in scenarios with unknown mechanisms or high-dimensional coupling. The proposed precision-adaptive rules offer key support for the engineering application of the model in scenarios with different precision requirements, and the reserved extended interfaces lay the foundation for subsequent tool development and cross-domain applications.