信息最大化的轨迹合成
Trajectory Synthesis for Fisher Information Maximization
AI总结：
本文提出一种连续时间优化方法，通过改进Fisher信息矩阵的范数来生成局部最优轨迹，用于动态系统参数估计，实验验证显示轨迹优化显著提升了参数估计精度。
摘要：
动态系统模型参数估计可通过实验轨迹的选择得到显著提升。对于一般的非线性动态系统，找到全局最优轨迹通常不可行；然而，在给定初始模型参数估计和初始轨迹的情况下，本文提出了一种连续时间优化方法，生成在存在测量噪声下的局部最优轨迹。该优化算法旨在寻找能改进Fisher信息矩阵范数的系统轨迹。通过双臂小车装置进行数值和实验验证。在模拟中，优化轨迹使Fisher信息矩阵的最小特征值比初始轨迹提高了三个数量级。实验结果表明，优化轨迹在实践中使参数估计误差改善了一个数量级。
英文摘要：
Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general, nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix. A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the Fisher information matrix by three orders of magnitude compared to the initial trajectory. Experimental results show that this optimized trajectory translates to an order of magnitude improvement in the parameter estimate error in practice.
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