基于自适应输入与状态估计的采样数据实时数值微分
Real-Time Numerical Differentiation of Sampled Data Using Adaptive Input and State Estimation
AI总结：
针对信号与噪声先验信息少的实时数值微分需求，提出基于回溯代价输入估计与在线更新协方差的自适应Kalman滤波的AIE/ASE方法，精度优于传统方法，可应用于车辆位置数据微分。
摘要：
实时数值微分在众多数字控制算法中至关重要，例如需要借助数值微分实现微分作用的PID控制。本文针对信号与噪声先验信息极少的实时应用场景，采用自适应输入与状态估计方法解决数值微分问题。自适应输入估计结合自适应状态估计（AIE/ASE）的输入估计部分基于回溯代价输入估计，状态估计部分则基于自适应Kalman滤波器，其输入估计误差协方差与测量噪声协方差可在线更新。研究通过数值计算将AIE/ASE的精度与多种传统数值微分方法进行了对比，最后将AIE/ASE应用于由CarSim生成的仿真车辆位置数据。
英文摘要：
Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper addresses the problem of numerical differentiation for real-time implementation with minimal prior information about the signal and noise using adaptive input and state estimation. Adaptive input estimation with adaptive state estimation (AIE/ASE) is based on retrospective cost input estimation, while adaptive state estimation is based on an adaptive Kalman filter in which the input-estimation error covariance and the measurement-noise covariance are updated online. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data generated from CarSim.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
