High-Precision and Long-Distance Detection Technology for Information Data Under Given Mass Based on Fractional-Order Calculus

High-quality information data refers to data meet the quality requirements of operational systems. Among these, the accuracy of information data measurement values serves as a key indicator for evaluating high-quality information data. Information data quality is reflected in two aspects: the measurement accuracy and signal transmission strength. The combined effect of these two issues results in significant measurement errors in the information detected by the information-detection system. Therefore, improving data quality essentially involves reducing the differences between information data to enhance measurement accuracy and increasing signal strength during information data transmission to compensate for energy loss and enhance anti-interference capability during long-distance transmission. In the field of signal detection and transmission, fractional calculus (FC) demonstrates dual advantages in data measurement: it can regulate signal strength across different frequencies and improve the algorithm’s generalization ability and data fusion accuracy, thereby significantly enhancing data quality. The spectral characteristics of the fractional differential operator indicate that data quality is closely related to frequency ω and fractional order v. In this study, the influence mechanism of parameters h and v on the information data quality of fractional-order differential operators constructs a mathematical model for information data fusion based on fractional-order operators, realizes high-precision detection technology for information data, and constructs a mathematical model for signal strength based on fractional-order differential operators to realize long-distance transmission of information data. By jointly solving these two models, high-precision, long-distance detection of information data under a given quality is achieved. Finally, application examples verify the feasibility of this method. In this case, we successfully met the quality requirement of a standard deviation Sg = 0.05 ± 0.05 for the information data transmitted over a distance of 3 km by the information detection system. The feasibility of the method was verified.