基于卡尔曼滤波的大学物理实验数据处理方法研究

A Study on Data Processing in University Physics Experiments Using Kalman Filter

摘要: 大学物理实验数据处理环节承载着丰富的科学方法论内涵，但当前教学中普遍采用的传统处理方法趋于固化，与后续专业课程体系衔接不足，制约了该环节育人效能的充分发挥。本文以教学改革为牵引，引入卡尔曼滤波算法，借助状态空间模型与递推估计机制，将现代滤波理论融入经典物理实验的数据处理过程。以液体表面张力电压测量、三线摆摆动周期测量及非平衡电桥温度传感器电压序列为对象，构建了一维与二维卡尔曼滤波模型。实验结果表明：一维滤波能够有效抑制重复测量中的随机波动与操作异常，二维滤波可自动拟合线性变化趋势，避免人工拟合引入的主观偏差。更关键的是，该方法的引入使学生在基础实验阶段即可接触状态估计与数据融合的基本方法，为后续自动控制、传感器技术、数字信号处理等专业课程奠定理论与方法基础。本文为大学物理实验教学改革提供了一条以数据处理方法创新为突破口、推动基础课程与专业教育有机融合的可行路径。

Abstract: The data processing component in university physics laboratory courses embodies substantial methodological significance. However, the conventional processing approaches currently employed in these courses have become increasingly ossified and inadequately aligned with subsequent specialized curricula, thereby constraining the pedagogical potential of this crucial instructional segment. Motivated by curriculum reform, this paper introduces the Kalman filtering algorithm into the data processing workflow of classical physics experiments, leveraging state-space models and recursive estimation mechanisms to integrate modern filtering theory with experimental practice. One-dimensional and two-dimensional Kalman filtering models are constructed for three representative cases: Voltage measurements in liquid surface tension experiments, oscillation period measurements in trifilar pendulum experiments, and voltage sequences from temperature sensors in unbalanced bridge circuits. Experimental results demonstrate that one-dimensional filtering effectively suppresses random fluctuations and operational anomalies in repeated measurements, while two-dimensional filtering automatically captures linear trends, thereby circumventing the subjective biases inherent in manual fitting. More significantly, the introduction of this method enables students to access fundamental concepts of state estimation and data fusion at the introductory laboratory stage, establishing a theoretical and methodological groundwork for subsequent courses in automatic control, sensor technology, and digital signal processing. This study offers a viable pathway for reforming university physics laboratory instruction by leveraging innovation in data processing methodologies as a catalyst for bridging fundamental coursework with professional education.