用贝叶斯迭代优化模型参数，无需复杂梯度也能高效识别系统动态。
An Iterative Bayesian Approach for System Identification based on Linear Gaussian Models
- 基于线性高斯近似，逐轮更新参数并在线校准协方差
- 通过输入输出数据优化模型参数，提升拟合稳定性
- 适合无梯度信息的系统辨识，尤其适用于非线性系统
我们研究系统辨识问题，即通过选择输入、观测真实系统的输出，并优化模型参数以最佳拟合数据。提出一种实用且计算可处理的方法，适用于任意系统与参数化模型族。该方法仅需系统输入输出数据及模型对参数的一阶信息。其包含两个模块：首先从贝叶斯角度建模，采用线性高斯近似迭代优化参数；每轮利用输入输出数据调节线性高斯模型的协方差，实现在线协方差校准，稳定拟合并指示模型不准确性。其次，定义基于高斯的参数不确定性度量，可针对下一输入进行最小化优化。在线性和非线性动力学上测试了该方法。
原文摘要 · Abstract (English)
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally tractable methodology that is compatible with any system and parametric family of models. Our approach only requires input-output data from the system and first-order information of the model with respect to the parameters. Our approach consists of two modules. First, we formulate the problem of system identification from a Bayesian perspective and use a linear Gaussian model approximation to iteratively optimize the model's parameters. In each iteration, we propose to use the input-output data to tune the covariance of the linear Gaussian model. This online covariance calibration stabilizes fitting and signals model inaccuracy. Secondly, we define a Gaussian-based uncertainty measure for the model parameters, which we can then minimize with respect to the next selected input. We test our method with linear and nonlinear dynamics.
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